\r\n\tSalmonella has changed its characteristics over time becoming the etiologic agent of many pathological processes such as cancer development, inflammatory process and immune-pathogenesis other than typhoid, paratyphoid and foodborne infections . \r\n\tListeria should be thoroughly studied as the most important cause of newborn meningitis and gynecological infection which can interfere with the pregnancy outcome. Listeria monocytogenes is the most important species in these pathologies. \r\n\tE. coli is a worldwide saprophyte microorganism which in specific situations can become pathogenic by secreting a large variety of exotoxins. Its antibiotic-resistance can be mediated by a strong ESBL especially found in retail meat products and in food-production cattle.
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1. Introduction
Violence in the hospital is not a new phenomenon, with health care and social service institutions being disproportionately affected by this serious problem [1, 2]. Also of major concern, every 16.6 min one American dies by suicide, amounting to over 30,000 suicides per year [3]. The prevalence of deliberate self-harm (DSH) in the hospitalized patient population is especially troubling, with one study reporting that DSH may be occurring in nearly 9% of hospital shifts on acute psychiatric wards [4]. Non-fatal DSH has also been called “parasuicide”—a term we will not be using in this chapter for the sake of uniformity and consistency [5]. Fortunately, the vast majority of self-harm events are classified as minor [4]. Figure 1 shows various factors that may, alone or in combination, result in violent behavior and DSH in the health care setting.
Figure 1.
Factors that may contribute to violence and self-harm in the health care setting.
DSH is defined as the intentional act of self-directed injury, irrespective of motivation. Important distinction is drawn between intentional self-directed injury without suicidal intent and an act of attempted suicide [6]. It is important to recognize that hospitalized patient population differs from individuals who engage in DSH across other settings, both in terms of impulsivity and the degree of violence involved during self-harm attempts [7–10]. It has also been noted that certain forms of DSH tend to result in patterns of escalation over time, up to and including suicidal acts [7–12]. The resultant long- and short-term burden is significant, with approximately 20–25% of individuals treated for DSH reporting previous self-inflicted injury [13], and a similar percentage of patients presenting with repeated DSH within 1 year [14]. Among adult patients who seek emergent treatment for self-inflicted injury, about half require admission for behavioral health evaluation and treatment [15, 16]. Despite the grave consequences, there are few standardized ways to reliably determine individual risk of DSH. Furthermore, the assessment of patients who present to the emergency department (ED) with obvious DSH tends to be fragmented and incomplete, with currently employed triage methods in need of significant improvement [17]. This status quo is not acceptable, as statistics have shown that a single episode of DSH is associated with 6-fold increase in future suicide risk [15, 18]. The type of DSH, as well as the patient’s response to treatment also influence the risk and patterns of subsequent DSH [9, 19]. Finally, the authors believe that the topics of DSH and violent patient behavior are interrelated, and that it is difficult to speak of one without mentioning or discussing the other.
Detailed behavioral health assessment following DSH episodes should commence as soon as the patient is deemed medically stable [20]. There should be an evaluation to determine the presence of any comorbid psychiatric disorders (e.g., depression, substance abuse, personality disorders) [21, 22]. This is critically important because certain psychiatric diagnoses are associated with significant lifetime risk of DSH [23–25]. Specific factors that strongly correlate with risk of future suicide include serious acts of DSH and the associated degree of potential lethality of the self-harming act [26, 27]. The list of proposed risk factors for DSH include young age, male sex, the presence of depression and psychosis, substance misuse, medical comorbidity, impulsivity, aggression, and/or loneliness [22, 28]. There is also evidence suggesting the involvement of specific neurotransmitter imbalances in the overall genesis of DSH [29]. While some factors contributory to DSH may be more readily modifiable (e.g., the availability of effective management of underlying psychiatric condition), some others may be difficult or impossible to influence (e.g., substance abuse, demographic factors). The following case describes a sequence of events secondary to a woman’s Emergency Department (ED) admission for an acute psychotic depressive episode. Despite specific precautions being implemented during her ED stay, the patient succeeded in inflicting significant DSH.
2. Clinical vignette
A 35-year-old Caucasian female presented to her primary care physician (PCP) on several occasions within the previous 6 months, complaining of increasing fatigue, loss of interest in daily activities, lack of energy, and “feelings of worthlessness”. Her husband prompted her to seek treatment after a recent violent episode in which she threatened to harm herself. Following an initial evaluation, the patient revealed that she had contemplated suicide on several occasions and was threatening to ingest a bottle of “sleeping pills” when she returned home later that day. The patient’s PCP called emergency medical services for urgent transport to the nearest ED for further evaluation and possible admission. Her husband was notified of the transfer.
Upon arrival, the patient was found to be irritable and aggressive towards hospital staff. She refused to provide a thorough history. Initial vital signs showed hypertension (160/90 mmHg). A toxicology screening was ordered to rule out substance abuse, and was later reported to be negative. The patient was placed in an isolation room due to her increasing agitation and violent behavior. A dedicated chaperone was placed in her room.
Once onsite, the husband was able to provide a thorough past medical history, revealing episodes of postpartum depression after the birth of their first and second child with symptoms mirroring her current presentation. These post-partum depressive episodes occurred 5 and 8 years prior to the current presentation, respectively. He also explained that the patient’s mother has been battling major depressive disorder for several years after the death of her husband. The patient’s PCP had previously prescribed Fluoxetine for each depressive episode resulting in complete symptom resolution within 6 months. She is currently not taking any medications, with the exception of a daily multivitamin. The husband reports no other illnesses. Past hospitalizations include the births of her three children during which there were no complications.
The patient’s current ED clinical course was complicated when she became increasingly agitated and began hitting her head against the padded wall of the isolation room. Her husband’s attempts at intervention were unsuccessful. Meanwhile, the chaperone alerted the nearest nursing station and the patient was sedated with 2.0 mg haloperidol intravenously. While under sedation, the patient was restrained using a four-point restraint system. Of note, the initial ECG showed no abnormalities, and telemetry monitoring was implemented during the initial 24 h following haloperidol administration. A physical examination of the patient following this episode of self-harm revealed a large cephalohematoma at the site of the self-inflicted traumatic injury. A cranial computed tomogram (CT) was obtained, revealing a small right subdural hematoma.
As the effects of the sedative abated, the patient became acutely agitated again and attempted to free herself from the previously placed restraints. During the struggle, the patient suddenly cried out in pain and cradled her right arm within the limits of the restraints. The chaperone immediately notified the nursing station of the patient\'s pain. Upon further examination by the ER resident, there appeared to be a deformity of the right shoulder. Radiographic work-up revealed an anterior dislocation of the patient’s right shoulder. During the struggle, the patient also managed to chip her left central maxillary incisor. Her injuries were immediately treated by the Trauma service, including shoulder relocation. Plans were also made for dental reconstruction after patient stabilization.
During the subsequent 24 h, the patient’s mental condition improved significantly. She was started on Fluoxetine and did not require any additional active therapy. Within 2 days of admission, the patient was transitioned to routine hospital care, with discharge to home 3 days later. Her post-injury clinic visit at 2 weeks showed uneventful recovery, and she continued to follow-up with her psychiatrist on monthly basis for the first 3 months, then quarterly for the remainder of the initial post-discharge year. After that, her care was transitioned to the PCP and she was continued on long-term maintenance Fluoxetine therapy.
3. Discussion
Self-harm is defined as the intentional act of an individual to cause self-directed injury or poisoning irrespective of motivation. The World Health Organization (WHO) further qualifies this definition as an “act with a nonfatal outcome, in which an individual deliberately initiates a non-habitual behavior that, without intervention from others, will cause self-harm… and which is aimed at realizing changes which the subject desired via the actual or expected physical consequences” [6]. The mode of injury can include cutting, stabbing, burning, skin carving, ingestion, and self-medicating, with more severe episodes of DSH resulting in serious secondary manifestations, such as traumatic brain injuries, infections, skeletal fractures, and even unintended death [30, 31]. In this chapter’s clinical vignette, the patient sustained significant injuries secondary to violent, self-destructive pattern of behavior. While establishing intent is an essential determinant for differentiating non-suicidal self-injury from a suicide attempt, understanding which populations are at greatest risk for DSH is crucial for properly allocating treatment resources and establishing appropriate patient management [31, 32]. The importance of objective and constructive approach by healthcare providers toward patients who present with DSH must be emphasized [33, 34].
The prevalence of DSH in the United States among adults (regardless of gender or pre-existing mental illness) is estimated to be between 1 and 4%, and this figure is projected to increase [35]. Previous episode of DSH continues to be the primary predictive factor for future DSH, although other parameters must be considered when determining the risk for each individual patient [6]. More specifically, it has been reported that up to 40% of psychiatric patients, independent of illness severity or disorder classification, have reported an episode of DSH [35]. Borderline personality disorder (BPD), marked by patterned instability of moods, behavior, and functioning, is one such condition, with as many as 75% of these patients engaging in self-injury [35]. In addition, it has been estimated that over 40% of patients engaging in DSH also meet the criteria for major depressive disorder (MDD) [35]. Our clinical vignette demonstrates this point well, with the patient having a documented history of depression. Furthermore, more than 75% of patients with substance abuse disorders are estimated to engage in DSH [36]. In the acute setting, a thorough understanding of a patient’s history of psychosis will be instrumental in preventing severe self-injury as well as DSH occurrences.
The need for prompt and effective management of DSH in the healthcare setting stems from the pattern of escalation and the high-risk of mortality among hospitalized patients [12, 37]. Of concern, suicide and DSH are among the leading causes of death in the United States, and their incidence is projected to increase over the next 2 decades [38]. The associated long- and short-term burden is also substantial, with approximately 1 in 4 individuals who are admitted for DSH reporting a previous self-inflicted injury [13]. Among adult patients who seek emergent treatment for self-inflicted injury, approximately half are admitted for further evaluation and treatment [15, 16]. Despite hospital admission, this patient population continues to be at high-risk for subsequent episodes of DSH and suicide attempts following discharge. Nearly 20% of patients who were admitted for DSH-related injury will be evaluated within a year for a repeated self-inflicted injury [14]. Although EDs are usually well equipped to manage acute presentations of patient self-harm, significant risk exists for discharge into the community without a mental health assessment [15, 16]. Furthermore, of those patients who were discharged directly, little more than half seek treatment in an outpatient facility within 30-days of their self-inflicted injury [15, 16]. Because previous DSH is among the strongest predictors of future DSH, inadequate clinical management and/or follow-up is likely to result in substantial financial and human burden for the community. The best way to improve the status quo and prevent repeated DSH events (including hospital readmissions) to proactively reform the medical delivery system. Greater availability of mental health specialists in our EDs, combined with protocols to better transition patients to outpatient treatment can help bridge the gap between acute and long-term management. However, without standardized protocols and procedures, even the best designed infrastructure will be unable to meet the enormous need that currently exists in this clinical arena.
4. Management of patients who engage in self-harm
The primary objective in the clinical management of a patient who engages in DSH in the acute setting is to prevent further injury to self and others. In addition to cognitive strategies and direct patient supervision, methods typically employed include both physical restraints and pharmacological agents. Caution must be exercised in the use of all of the above interventions in this population due to the complexity of the patient’s mental state and the degree of clinical unpredictability. General management pathway for patients who pose acute risk of self-harm is shown in Figure 2A–C.
Figure 2.
General management pathway for patients who pose acute risk of deliberate self-harm; [Part A] Patient risk stratification; [Part B] Management algorithms based on overall risk / acuity; [Part C] Interventional considerations based on suspected / established etiology.
5. Direct observation
The use of patient observation assistants (PtOA) or the so-called “sitters” has been utilized to facilitate safer patient environment [39]. Despite the widespread use of PtOAs, there are no clearly defined industry standards regarding key metrics of safety, quality, and effectiveness of this practice [39, 40]. Neither is there firmly established evidence that special observation using PtOAs is efficacious [41]. Nonetheless, the continued need for PtOAs is highlighted by the fact that the other mainstay approaches to preventing DSH—physical restraints and pharmacological interventions—both carry significant rate of complications and a non-trivial risk of mortality [42, 43]. Consequently, the use of PtOAs is considered an important component of the multi-pronged approach consisting of close monitoring and prevention of recurrent self-harm. Of importance, there is evidence to suggest that intermittent observation may be associated with reduced self-harm when compared to constant special observation [4].
6. Seclusion
Seclusion in management of severe agitation and/or violence first started in the mid-nineteenth century as an alternative option to mechanical restraint [44, 45]. In brief, seclusion represents involuntary confinement of the patient alone in a room (or another designated area) where the patient is physically prevented from leaving. In 2001 the UK Central Council for Nursing, Midwifery and Health Visiting determined there were no studies of value in using restraints and seclusion in mentally ill patients and could not recommend their effectiveness or use [46]. The fact is that since 2000 the use of what are termed “containment procedures,” i.e., seclusion and restraints, in US psychiatric hospitals has been trending downward [47]. Over the past 10 years best practices have been instituted to limit use of containment procedures in the US to assist mental health professionals in their clinical practices [48, 49]. Additionally, the National Association of State Mental Health Program Directors (NASMHPD) had released its six core strategies for reducing seclusion and restraint use to assist in the development of safe and effective mental health programs [50]. Nonetheless, there have been some reports that show a correlation between reduced use of seclusion and restraints and an increase in patient related violence [51, 52]. However, recent work demonstrated that the implementation of better sound leadership practices, the use of accurate clinical data, developing and training a good workforce, evidence based policies and procedures, along with the use of specialized response teams, behavioral therapy, and the discontinuation of nursing “as needed” orders for restraint and seclusion use resulted in better patient outcomes and more favorable behavioral patterns [44, 53]. When the above mentioned educational, clinical, and administrative best practices are combined with sensory modulation there can be marked reductions in disturbances and a dramatic drop in the use of seclusion [54]. It is critical to ensure both safety and dignity of the patient when using restraints or seclusion.
7. Physical restraints
Approximately 50% of intensive care unit patients [55], 20% of patients on neurology-neurosurgery wards [56], and 25% of individuals admitted to mental health facilities experience at least one type of “control intervention” during acute hospitalization [57]. One method of such “control intervention” is the use of physical restraints (PhyR), defined as any device, material or equipment attached to or near a person’s body, which is intended to prevent a person’s free body movement to a position of choice and/or a person’s normal and unrestricted access to their body [58]. The use of PhyR is relatively common, with some authors suggesting that it is overused [43, 59]. As a consequence, there are numerous initiatives to reduce the reliance on PhyR, especially among the most vulnerable patient populations [60–62]. As mentioned in this chapter’s clinical vignette, restraints may not eliminate the risk of DSH. Therefore, the choice to use PhyR continues to be controversial and should only be entertained as a last resort option when there exists a real possibility of serious physical injury to self or others [63–65]. There is therefore a need for caution and balanced judgment on part of the treatment team, beginning with a well-informed understanding of potential complications and safety procedures designed to prevent adverse outcomes [63–65].
Published guidelines provide a framework for the use of PhyR in a variety of settings [66, 67]. The initial criteria for instituting PhyR should be based on a thorough evaluation of a patient’s mental status. An individual at risk for DSH, who is cognitively aware of this risk of harm to themselves, is less likely to become violent while in restraints and can therefore be placed in a soft restraint apparatus [56]. However, in the event that a patient becomes increasingly violent when actively restrained, there is an increased risk of limb injury due to a tendency for the device to tighten [68]. Moreover, patients who are restrained and sustain secondary trauma are prone to more serious injuries because part(s) of their body is/are physically tied, which may render normal protective, instinctive responses ineffective. Other complications of soft restraints include abrasions, contusions, immobility, and dislodgement of various devices (e.g., intravenous lines, feeding tubes) [68–71]. In some cases, leather restraints can be utilized if the patient becomes increasingly combative; however, appropriate precautions are critical when using leather PhyR because device removal can be challenging in emergent situations [70].
The specific placement of restraints and number of application points are important in ensuring the balance between satisfactory outcomes and minimizing complications [56, 58, 72]. If the patient poses a low risk of violence, a two-point restraint system can be utilized safely [70, 73]. Four-point restraints should be reserved for combative and violent patients in the acute setting to maximally prevent uncontrolled movements [70]. Again, applicable guidelines should be followed to reduce restraint-related complications (e.g., self-injury, overturning of the stretcher) while ensuring adequate immobilization of the patient [70, 74]. Belt and jacket restraints can serve as adjunct to extremity restraints, but mandate special precautions, such as the concurrent use of full side rails [75, 76].
Consideration must also be given to the immobilized patient’s positioning, including appropriate contingency plans if complications occur. If restrained while prone, patients may be in danger of suffocation. Consequently, if this position is utilized, the patient must be provided with adequate space for free chest expansion and his or her respiratory and airway status must be closely monitored [77, 78]. If restrained while supine, patients are at risk for aspiration [79]. Thus, the patient’s head should be positioned at 30° with the ability to rotate freely in order to avoid this complication [70, 79]. Moreover, optimal configuration of 4-point restraints calls for one arm being directed up toward the patient’s head and the other arm down toward the patient’s hip. Aside from these positional considerations, additional precautions must be instituted regarding prolonged immobilization due to the risk of pressure ulcers, focal neurovascular compression, and deep vein thrombosis [70, 80].
In addition to various potential physical complications inherent in the use of restraints, patients may experience significant emotional trauma from the ordeal, such as feelings of powerlessness, humiliation, and/or the sensation of terror seen with PhyR [81]. Common manifestations of restraint-related psychological trauma include “flashbacks” to the emotional ordeal (e.g., retraumatization), hopelessness and helplessness (e.g., “broken spirit”), negative general psychological impact, and perceptions of unethical healthcare practices [82, 83]. All of the above factors must be considered when implementing PhyR, although they should not prevent the use of restraints if clinically justified and necessary [84, 85].
Due to the potential for severe complications and even mortality associated with PhyR use, the Joint Commission established protocols pertaining to the usage of restraints in the healthcare setting [86]. Restraints need to be justified, well documented, and monitored at all times to help minimize the risk of iatrogenic injury [87]. Current guidelines recommend the restraint use for children ages < 9 years be limited to 1 h; 2 h for adolescents ages 9–17 years; and 4 h for adults before mandatory clinical re-evaluation [70, 88]. These precautions are necessary to minimize both the physical and psychological complications of PhyR use [89, 90]. Details regarding indications and maintenance of mechanical restraints are provided in Table 1.
General considerations
Detailed documentation of all restraint-related clinical decisions and procedures should be made in the medical record
Duration of restraint use should be firmly justified and continue for the least amount of time applicable
In all instances of mechanical restraint use, an individualized clinical management plan should be established and followed
Information regarding the restraint procedure should be given to the patient
Mechanical restraints should be utilized in “last resort” capacity when all other interventions have failed
Periodic re-evaluation, as frequent as every 30 min, should be performed to determine the need for continuation of restraints
Restraints should always be utilized under the supervision of a qualified physician/practitioner
Restraints should be placed and removed in team setting by sufficient number of staff members to prevent patient harm
The use of restraints for discipline or staff convenience is forbidden an illegal
Vital signs should be monitored at all times during mechanical restraint period
Specific indications for mechanical restraints
Facilitation of diagnosis through behavioral control under conditions requiring minimal or no medication use
Facilitation of the development of a therapeutic alliance with the patient
Mitigation of staff fears/anxiety
Physical containment
Protection of the patient, other patients, staff, and/or property
Provision of a respite for regaining control
Reduction of overall stimuli
Repression/control of aggression
Table 1.
Important considerations for placement and maintenance of mechanical restraints.
8. Pharmacological “restraints”
The high complication risk of PhyR has led to the increased use of pharmacological agents, as either monotherapy or polytherapy, in the management of high risk patients at risk for DSH. In fact, the prevalence of chemical restraints in certain settings exceeds 33% [91]. At times, pharmacological approaches are used in conjunction with PhyR [92]. Some of the most common pharmacological agents used in psychiatric emergencies include haloperidol, droperidol, lorazepam, olanzapine, and midazolam [93–95]. Due to the ethical considerations of PhyR, these pharmacological agents are often first line therapy in a patient who is at acute risk for self-harm. Multi-modality, high intensity, or combined therapy is often employed when a patient becomes acutely violent or combative, thus posing as an immediate danger to both themselves and others [95, 96].
Haloperidol is a butyrophenone antipsychotic agent with onset of action within 30–60 min of administration and clinical effect lasting up to 24 h [97]. Haloperidol is commonly used in the setting of psychosis and self-harming behaviors because of its minimal drug interactions with non-psychiatric medications, which is essential due to the challenge of obtaining a medical history from acutely agitated patients. In a study of ED patients with agitated, threatening, or violent behaviors, haloperidol resulted in significant clinical improvement within 30 min of administration in 83% of patients [98]. Furthermore, due to the lack of interactions and relatively favorable safety profile, this medication is used as first-line therapy for patients at risk for DSH [99, 100]. Caution is nonetheless necessary due to some rare, yet potentially serious adverse events associated with haloperidol use. The most prominent side effect includes extrapyramidal syndrome and dystonia, which can occur in up to 20% of patients [97]. Haloperidol can also increase the QTc interval, cause torsade de pointes, and even sudden death. Consequently, patients should optimally undergo an ECG prior to haloperidol administration [101].
Another agent, droperidol, may be considered when immediate sedation is required [102]. Droperidol has a rapid onset of 15–30 min, making it more suitable for acute situations [103]. It has been reported that droperidol can be given intramuscularly at a dosage up to 10 mg to have the same efficacy as other sedatives [103]. Of note, a prior history of cardiac disease is a contraindication due to a black box FDA warning for fatal cardiac arrhythmias when intravenous doses exceed 2.5 mg [104]. This warning carries a strong recommendation to precede the use of droperidol with an ECG to screen for any cardiac abnormalities. Other side effects include the risk of developing dystonia or akathisia [105]. These symptoms can be ameliorated through the co-administration of histamine (H1) antagonists such as Diphenhydramine or Promethazine [106]. Importantly, precautions should be taken when using droperidol (and other similar agents) as adjunctive therapy to mechanical restraints due to potentially elevated risk of suffocation or positional asphyxia [107].
There is a paucity of research on acute manifestations of DSH in patients under the influence of cocaine. The existing literature recommends the use of lorazepam as the primary agent of choice for physiological alterations secondary to cocaine use [108]. This medication can also be used as first-line therapy for patients experiencing withdrawal from alcohol or recreational stimulants, as it has been shown to be more effective than neuroleptic drugs, such as haloperidol [109]. However, due to its CNS depressive effects and long-duration, Lorazepam should not be used if a patient appears intoxicated or if he/she has ingested other sedatives [104]. Further precautions should be taken in patients of childbearing age as this medication is a class D agent in the setting of pregnancy [70].
Olanzapine, a second generation thienobenzodiazepine antipsychotic, may also be considered in cases of acute psychosis with associated DSH [110]. This medication, which antagonizes dopamine and serotonin, is equally as effective as lorazepam and haloperidol in the acute setting [70]. However, a thorough history is necessary before using this drug as it can lead to hypotension when combined with anti-muscarinic medications [70]. Currently, there is limited understanding of the use of this medication in patients presenting with acute psychosis, as well as substance abuse [111, 112].
Midazolam (a benzodiazepine) is indicated for situations where short duration of action is desired [113, 114]. Midazolam has similar efficacy to lorazepam or haloperidol and may therefore be beneficial in patients who do not require long term management and whose risk of DSH may be related to substance abuse and acute intoxication [109]. Furthermore, due to its short action, its systemic effects on the patient quickly wear off, allowing subsequent evaluations, discharge from the ED, and transition to outpatient setting in a more timely fashion [70].
Other agents have been described in the management of acute behavioral disturbances, including DSH, but the limited scope of this chapter does not permit a more in-depth discussion [103, 104, 114–119]. In all similar cases, the goal is to medically stabilize the patient and then prevent recurrent episodes of self-harm [115]. It is important to note that while our discussion describes largely a local pattern of practice, a number of effective professional guidelines have been published in this general area. Consequently, the reader is referred to those guidance documents for further information regarding the overall diagnostic framework and the associated implementation of both physical and pharmacological restraints [120–123].
9. Management and prevention of deliberate self-harm: key points
Emergency management of acutely violent patients, especially those involved in DSH, can be challenging [124]. Similar to many other medical conditions, prevention of DSH should be given the highest priority. This includes prevention of both initial and recurrent episodes of DSH [125, 126], especially since repeated self-harm is associated with long-term, cumulative risk of death [127]. Many patients who inflict self-harm can be treated quickly and effectively, without the need for clinical escalation. The initial approach to escalation usually involves close direct observation [39–41] and the provision of an injury-proof, secluded environment [128, 129]. However, individuals who continue to exhibit behaviors that constitute danger to self or others may require the implementation of physical or pharmacological restraints, i.e., containment procedures [70, 72, 117]. Because of the significant risk for potentially serious complications associated with the use of restraints, special care and attention is required in such situations [129–131]. Additionally, we highlighted progressive views regarding containment procedures and how they can be implemented effectively, while at the same time referencing their drawbacks. Once the patient has stabilized clinically, a combination of psychosocial and pharmacological approaches is utilized to prevent repetitive self-harming behaviors [125, 132]. Multidisciplinary teams including primary care practitioners, community and behavioral health experts provide the best framework for long-term recovery [133, 134].
10. Conclusions
DSH will continue to be a challenging problem that confronts health care providers in the ED (and other areas of the hospital). The approach to such patients must be multidisciplinary and occur in an evidence-based environment. Practitioners must be aware of their hospital protocols used to address patients who present with DSH. Detailed behavioral health assessment following DSH episodes should be completed as soon as the patient is medically stable. Specifically, an inventory of comorbid psychiatric disorders that put a patient at risk for DSH, especially suicide, must be catalogued as well as a determination of the presence of associated risk factors that may contribute to an escalation of illness severity. The practitioner must also become well versed in the use of direct observation, containment procedures (seclusion and physical restraints), and pharmacological restraints, as well as an appreciation as to the direction of new clinical evidence regarding care and the promulgation of new legislation. Clinical approaches and legal perspectives in this field will continue to evolve.
\n',keywords:"emergency department, evidence-based approach, patient safety, psychiatric emergency, self-harm",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/56069.pdf",chapterXML:"https://mts.intechopen.com/source/xml/56069.xml",downloadPdfUrl:"/chapter/pdf-download/56069",previewPdfUrl:"/chapter/pdf-preview/56069",totalDownloads:1395,totalViews:816,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:1,dateSubmitted:"November 28th 2016",dateReviewed:"May 8th 2017",datePrePublished:null,datePublished:"September 13th 2017",dateFinished:null,readingETA:"0",abstract:"Violence, deliberate self harm, and suicide in emergency departments and hospitals is likely to remain a significant problem for health care systems well into the future. Understanding how to confront, intervene, and manage episodes of patient deliberate self harm is extremely important, and can be life-saving. Here, through a clinical vignette, and a discussion of deliberate self harm we will highlight the importance of the direct observation of such patients, containment procedures (seclusion and physical restraints), and the use of pharmacological adjuncts. We hope that this concise, practically-oriented review will provide our readers with foundational understanding of the topic, including the most important theoretical and clinical considerations.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/56069",risUrl:"/chapter/ris/56069",book:{slug:"vignettes-in-patient-safety-volume-1"},signatures:"Ronya Silmi, Joshua Luster, Jacqueline Seoane, Stanislaw P.\nStawicki, Thomas J. Papadimos, Farhad Sholevar and Christine\nMarchionni",authors:[{id:"181694",title:"Dr.",name:"Stanislaw P.",middleName:null,surname:"Stawicki",fullName:"Stanislaw P. Stawicki",slug:"stanislaw-p.-stawicki",email:"stawicki.ace@gmail.com",position:null,institution:{name:"St. Luke's University Health Network",institutionURL:null,country:{name:"United States of America"}}},{id:"202737",title:"Dr.",name:"Ronya",middleName:null,surname:"Silmi",fullName:"Ronya Silmi",slug:"ronya-silmi",email:"ronya.silmi490@gmail.com",position:null,institution:null},{id:"202738",title:"Dr.",name:"Jacqueline",middleName:null,surname:"Seoane",fullName:"Jacqueline Seoane",slug:"jacqueline-seoane",email:"tug28330@temple.edu",position:null,institution:null},{id:"202739",title:"Dr.",name:"Joshua",middleName:null,surname:"Luster",fullName:"Joshua Luster",slug:"joshua-luster",email:"tug26845@temple.edu",position:null,institution:null},{id:"202740",title:"Dr.",name:"Christine",middleName:null,surname:"Marchionni",fullName:"Christine Marchionni",slug:"christine-marchionni",email:"Christine.Marchionni@sluhn.org",position:null,institution:null},{id:"202741",title:"Dr.",name:"Farhad",middleName:null,surname:"Sholevar",fullName:"Farhad Sholevar",slug:"farhad-sholevar",email:"Farhad.Sholevar@sluhn.org",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Clinical vignette",level:"1"},{id:"sec_3",title:"3. Discussion",level:"1"},{id:"sec_4",title:"4. Management of patients who engage in self-harm",level:"1"},{id:"sec_5",title:"5. Direct observation",level:"1"},{id:"sec_6",title:"6. Seclusion",level:"1"},{id:"sec_7",title:"7. Physical restraints",level:"1"},{id:"sec_8",title:"8. Pharmacological “restraints”",level:"1"},{id:"sec_9",title:"9. Management and prevention of deliberate self-harm: key points",level:"1"},{id:"sec_10",title:"10. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'Rothaus C. Violence Against Health Care Workers. 2017. Available from: http://blogs.nejm.org/now/index.php/violence-against-health-care-workers/2016/04/28/ [Accessed: 13 March 2016]'},{id:"B2",body:'Jacobson R. 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Randomized controlled trial of intramuscular droperidol versus midazolam for violence and acute behavioral disturbance: The DORM study. Annals of Emergency Medicine. 2010;56(4):392-401. e1'},{id:"B104",body:'Battaglia J. Pharmacological management of acute agitation. Drugs. 2005;65(9):1207-1222'},{id:"B105",body:'Wang SJ, Silberstein SD, Young WB. Droperidol treatment of status migrainosus and refractory migraine. Headache: The Journal of Head and Face Pain. 1997;37(6):377-382'},{id:"B106",body:'Perkins J, et al. American academy of emergency medicine position statement: Safety of droperidol use in the emergency department. The Journal of Emergency Medicine. 2015;49(1):91-97'},{id:"B107",body:'Duxbury J, Aiken F, Dale C. Deaths in custody: The role of restraint. Journal of Learning Disabilities and Offending Behaviour. 2011;2(4):178-189'},{id:"B108",body:'Richards JR, et al. Treatment of cocaine cardiovascular toxicity: A systematic review. Clinical Toxicology. 2016;54(5):345-364'},{id:"B109",body:'Rund DA, et al. The use of intramuscular benzodiazepines and antipsychotic agents in the treatment of acute agitation or violence in the emergency department. The Journal of Emergency Medicine. 2006;31(3):317-324'},{id:"B110",body:'Belgamwar RB, Fenton M. Olanzapine IM or velotab for acutely disturbed/agitated people with suspected serious mental illnesses. The Cochrane Library. 2005'},{id:"B111",body:'Wilson MP, et al. The psychopharmacology of agitation: Consensus statement of the American Association for Emergency Psychiatry Project BETA Psychopharmacology Workgroup. Western Journal of Emergency Medicine. 2012;13(1):26-34'},{id:"B112",body:'Wilson MP, et al. A comparison of the safety of olanzapine and haloperidol in combination with benzodiazepines in emergency department patients with acute agitation. The Journal of Emergency Medicine. 2012;43(5):790-797'},{id:"B113",body:'Knott JC, et al. Management of mental health patients attending Victorian emergency departments. Australian and New Zealand Journal of Psychiatry. 2007;41(9):759-767'},{id:"B114",body:'Zun LS. Pitfalls in the care of the psychiatric patient in the emergency department. The Journal of Emergency Medicine. 2012;43(5):829-835'},{id:"B115",body:'Allen MH, et al. The expert consensus guideline series. Treatment of behavioral emergencies. Postgraduate Medicine. 2001(Spec No):1-88; quiz 89-90'},{id:"B116",body:'Currier GW, Allen MH. Emergency psychiatry: Physical and chemical restraint in the psychiatric emergency service. Psychiatric Services. 2000;51(6):717-719'},{id:"B117",body:'Allen MH, Currier GW. Use of restraints and pharmacotherapy in academic psychiatric emergency services. General Hospital Psychiatry. 2004;26(1):42-49'},{id:"B118",body:'Sorrentino A. Chemical restraints for the agitated, violent, or psychotic pediatric patient in the emergency department: Controversies and recommendations. Current Opinion in Pediatrics. 2004;16(2):201-205'},{id:"B119",body:'Richards J, Derlet R, Duncan D. Chemical restraint for the agitated patient in the emergency department: Lorazepam versus droperidol. The Journal of Emergency Medicine. 1998;16(4):567-573'},{id:"B120",body:'Mortimer A, et al. Clozapine for treatment-resistant schizophrenia: National Institute of Clinical Excellence (NICE) guidance in the real world. Clinical Schizophrenia & Related Psychoses. 2010;4(1):49-55'},{id:"B121",body:'Borschmann R, et al. Measuring self-harm in adults: A systematic review. European Psychiatry. 2012;27(3):176-180'},{id:"B122",body:'Sansone RA, Wiederman MW, Sansone LA. The self-harm inventory (SHI): Development of a scale for identifying self-destructive behaviors and borderline personality disorder. Journal of Clinical Psychology. 1998;54(7):973-983'},{id:"B123",body:'NICE. New NICE guidelines set to improve treatment and management of people with borderline personality disorder. 2017; Available from: https://www.nice.org.uk/guidance/cg78/documents/new-nice-guidelines-set-to-improve-treatment-and-management-of-people-with-borderline-personality-disorder [Accessed: 6 May 2009]'},{id:"B124",body:'Binder RL, McNiel DE. Emergency psychiatry: Contemporary practices in managing acutely violent patients in 20 psychiatric emergency rooms. Psychiatric Services. 1999;50(12):1553-1554'},{id:"B125",body:'Hawton K, et al. Deliberate self harm: Systematic review of efficacy of psychosocial and pharmacological treatments in preventing repetition. BMJ. 1998;317(7156):441-447'},{id:"B126",body:'Morgan H, Jones E, Owen J. Secondary prevention of non-fatal deliberate self-harm. The green card study. The British Journal of Psychiatry. 1993;163(1):111-112'},{id:"B127",body:'Owens D, Horrocks JA. House, fatal and non-fatal repetition of self-harm. The British Journal of Psychiatry. 2002;181(3):193-199'},{id:"B128",body:'Sailas E, Wahlbeck K. Restraint and seclusion in psychiatric inpatient wards. Current Opinion in Psychiatry. 2005;18(5):555-559'},{id:"B129",body:'Fisher WA. Restraint and seclusion: A review of the literature. American Journal of Psychiatry. 1994;151(11):1584-1591'},{id:"B130",body:'Maccioli GA, et al. Clinical practice guidelines for the maintenance of patient physical safety in the intensive care unit: Use of restraining therapies—American College of Critical Care Medicine Task Force 2001-2002. Critical Care Medicine. 2003;31(11):2665-2676'},{id:"B131",body:'Burton LC, et al. Mental illness and the use of restraints in nursing homes. The Gerontologist. 1992;32(2):164-170'},{id:"B132",body:'Bennewith O, et al. General practice based intervention to prevent repeat episodes of deliberate self harm: Cluster randomised controlled trial. British Medical Journal. 2002;324(7348):1254'},{id:"B133",body:'Allen C. Helping with deliberate self-harm: Some practical guidelines. Journal of Mental Health. 1995;4(3):243-250'},{id:"B134",body:'Madge N, et al. Deliberate self‐harm within an international community sample of young people: Comparative findings from the Child & Adolescent Self‐harm in Europe (CASE) Study. Journal of Child Psychology and Psychiatry. 2008;49(6):667-677'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Ronya Silmi",address:null,affiliation:'
Temple University School of Medicine, St. Luke’s University Hospital Campus, Bethlehem, PA, USA
Department of Psychiatry, St. Luke’s University Health Network, Bethlehem, PA, USA
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1. Introduction
The development of waves under the action of wind is a process that is difficult to simulate since surface waves are very conservative and their energy changes over hundreds and thousands of periods. This is why the most popular method is spectral modeling based on the averaged over phase equations for spectral energy. In this approach, the waves as physical objects are actually absent since the evolution of spectral distribution of the wave energy is simulated. The description of input and dissipation in this approach is not directly connected with the formulation of the problem, but it is rather adopted from other branches of the wave theory where waves are the objects of investigation. However, the spectral approach was found to be the only method capable to describe the space and time evolution of wave field in the ocean. The phase resolving models (or ‘direct’ models) designed for reproducing waves themselves cannot compete with spectral models since such models typically can reproduce the evolution of just several thousands of large waves. Nevertheless, the direct wave modeling plays an ever-increasing role in the geophysical fluid dynamics because it gives the possibility to investigate the processes that cannot be reproduced by spectral models.
The spectral model assumes that wave field consists of a superposition of linear waves with random phases and arbitrary angle distribution. Being converted to a physical wave field, it looks unreal because real waves usually have prolonged smooth troughs and sharp peaks. Such shape suggests that the waves are similar to Stokes waves. For any given wave spectrum, the wave field can be represented as a superposition of linear Fourier modes with random phases [1]. It can be represented also as a superposition of Stokes modes. The calculations of statistical characteristics for both wave fields show that they are nearly identical. However, such conclusion could be made with no calculations because typical steepness of sea waves at reasonable spectral resolution is of the order of 0.01–0.05, so all the amplitudes of Stokes modes starting from the second one are small. It follows that the specific shape of sea waves is a dynamic property.
The breaking is usually initiated in the vicinity of wave peaks, so the breaking parameterization describes the processes, which are, in principle, impossible in a linear wave field. The breaking is concentrated in the separated narrow intervals; an instantaneous spectrum is discrete and is shifted to high frequencies. The spectral description of the isolated extreme waves is also impossible. The Fourier transform of a large-scale wave field including separated large waves does not provide any indications of their appearance.
The input energy to waves is based on the assumption that each mode induces a pressure mode with a certain amplitude and phase. In reality, the pressure field is quite complicated and not directly connected with the surface elevation because of the systematic separation of air flow behind wave crests (which was shown experimentally in Refs. [2, 3] with the coupled wind-wave model). There are many other complications in the coupled wind-wave dynamics [4] including the processes connected with sprays, bubbles, foam, and structure of the high-frequency wave spectrum.
Most (but not all) of the processes mentioned above can be investigated using the numerical modeling that is a perfect instrument for development of parameterization of physical processes for spectral wave models.
The phase-resolving models can completely replace the spectral models for direct simulation of wave regimes of small water basins, for example, port harbors (see Refs. [5, 6]). Other approaches of direct modeling are discussed in Refs. [7, 8].
Over the past decades, a big volume of papers devoted to the numerical methods developed for investigation of wave processes has been published. The most advanced among them are Finite Difference Method [5, 6], Finite Volume Method [9], Finite Element Method [10, 11], Boundary (Integral) Element Method [12], Spectral HOS Methods [13, 14, 15, 16, 17], the Smoothed Particle Hydrodynamics Method [18], Large Eddy Simulation Method (LES) [19, 20], Moving Particle Semi-Implicit Method [21], Constrained Interpolation Profile Method [22], and Method of Fundamental Solutions [23]. Most of the models were designed for engineering application handling such processes as overturning waves, broken waves, waves generated by landslides, freak waves, solitary waves, tsunamis, violent sloshing waves, interaction of extreme waves with beaches, as well as interaction of steep waves with fixed and different floating structures. The wave models designed for engineering applications seem to be more advanced than the models for pure geophysical research. However, as a rule, the engineering models pay little attention to description of physical processes that are responsible for a long-term evolution of wave spectrum. A more detailed review of direct numerical models is given in Ref. [8].
Until recently, the direct modeling was used for reproduction of a quasi-stationary wave regime when wave spectrum does not change significantly. An example of direct numerical modeling of surface wave evolution is given in Ref. [24] where the development of wave field was calculated by using of a two-dimensional model based on full potential equations written in the conformal coordinates. A model included the algorithms for parameterization of the input and dissipation of energy (a description of similar algorithms is given below). The model successfully reproduced the evolution of wave spectrum under the action of wind. That model was a prototype of 3-D model, because being very fast it was convenient for development of the physical process parameterization. However, the strictly one-dimensional (unidirected) waves are not quite realistic since the unidirected waves in the presence of the small-amplitude perturbations relatively quickly turn into the two-dimensional wave field [25]. Hence, the full problem of wave evolution should be formulated on the basis of three-dimensional equations. Such 3-D calculations were done by Chalikov [26]. The model included parameterization of the main physical processes: input energy, different types of dissipation, and transformation of spectrum due to the nonlinear interaction. The last process does not require any parameterization because the nonlinearity is described with equations. The model used a relatively poor resolution (1024×512 nodes in x and y directions). However, the calculations reproduced the evolution of wave spectrum and the spectra of the main physical processes such as input and dissipation of energy and nonlinear interactions. As long as we know, it was the first attempt to reproduce the development of waves based on full three-dimensional equations with a direct solution of 3-D equation for the velocity potential. The current paper is devoted to development of the method, including the tuning and modifications of the algorithm, the increase of resolution, and the integration for longer periods. The most important but pure technical modifications were introduced in the numerical scheme for Poisson equation for the velocity potential. The algorithms for calculation of the input and dissipation remain nearly the same, but the numerical parameters in those schemes were changed to achieve a better agreement with the rate of spectrum evolution given by JONSWAP approximation.
2. Equations
The nonstationary surface-following nonorthogonal coordinate system is used as follows:
ξ=x,ϑ=y,ζ=z−ηξϑτ,τ=t,E1
where ηxyt=ηξϑτ is a moving periodic wave surface given by the Fourier series
ηξϑτ=∑−Mx<k<Mx∑−My<l<Myhk,lτΘk,l,E2
where k and l are the components of the wave number vector k; hk,lτ are Fourier amplitudes for elevations ηξϑτ; Mx and My are the numbers of modes in the directions ξ and ϑ, respectively, while Θk,l are the Fourier expansion basis functions represented as the matrix:
The 3-D equations of potential waves in the system of coordinates (1) at ζ≤0 take the following form:
ητ=−ηξφξ−ηϑφϑ+1+ηξ2+ηϑ2Φς,E4
φτ=−12φξ2+φϑ2−1+ηξ2+ηϑ2Φζ2−η−p,E5
Φξξ+Φϑϑ+Φζζ=ϒΦ,E6
where ϒ is the operator:
ϒ=2ηξξζ+2ηϑϑζ+ηξξ+ηϑϑζ−ηξ2+ηϑ2ζζ,E7
capital fonts Φ are used for the domain ζ<0, while the lower case φ refers to ζ=0. The term p in Eq. (5) describes the pressure on the surface ζ=0.
It is suggested by Chalikov et al. [7] that it is convenient to represent the velocity potential φ as a sum of the two components: a linear component Φ¯,φ¯=Φ¯ξϑ0 and an arbitrary nonlinear component Φ˜,φ˜=Φ˜ξϑ0:
φ=φ¯+φ˜,Φ=Φ¯+Φ˜.E8
The linear component Φ¯ satisfies Laplace equation:
Φ¯ξξ+Φ¯ϑϑ+Φ¯ζζ=0,E9
with a known solution:
Φ¯ξϑζτ=∑k,lφ¯k,lτexpkζΘk,l,E10
where k=k2+l21/2, φ¯k,l are the Fourier coefficients of the surface linear potential φ¯ at ζ=0). The solution satisfies the following boundary conditions:
The presentation (8) is not used for solution of the evolutionary Eqs. (4) and (5) because it does not provide any improvements of accuracy and speed.
Eqs. (4)–(6) are written in a nondimensional form by using the following scales: length L, where 2πL is a (dimensional) period in the horizontal direction; time L1/2g−1/2; and velocity potential L3/2g1/2 (g is the acceleration of gravity). The pressure is normalized by the water density, so that the pressure scale is Lg. Eqs. (4)–(6) are self-similar to the transformation with respect to L. The dimensional size of the domain is 2πL, so the scaled size is 2π. All of the results presented in this paper are nondimensional. Note that the number of the Fourier modes can be different in the x and y directions. In this case, it is assumed that the two-length scales Lx and Ly are used. The nondimensional length of the domain in the y-direction remains equal to 2π, and a factor r=Lx/Ly is introduced into the definition of a differential operator in the Fourier space.
The derivatives of a linear component Φ¯ in (7) are calculated analytically. The scheme combines a 2-D Fourier transform method in the ‘horizontal surfaces’ and a second-order finite-difference approximation on the stretched staggered grid defined by the relation Δζj+1=χΔζj (Δζ is a vertical step, while j=1 at the surface). The stretched grid provides an increase in accuracy of approximation for the exponentially decaying modes. The values of the stretching coefficient χ lie for different settings within the interval 1.01–1.20; in the current work, the value γ=1.2 was used at the number of levels Lw=10. Such poor resolution was possible to use because of the separation of the potential into a large linear and a small nonlinear part, so Eq. (12) was used only for calculation of a small correction for the potential. A high value of the stretching coefficient provided high resolution in the vicinity of surface for accurate calculations of the surface vertical derivative for the potential. The finite-difference second-order approximation of vertical operators in Eq. (12) on a nonuniform vertical grid is quite straightforward (see Ref. [8]). Eq. (12) is solved as Poisson equations with the iterations over the right-hand side by TDMA method [27]. At each time step, the iterations start with a right-hand side calculated at the previous time step. A relative accuracy of the solution in terms of the vertical derivative of the potential on the surface was equal to 10−6. The typical number of iterations was 2–5.
The accuracy of the adiabatic version of equations was validated by reproducing a moving Stokes wave with the steepness AK=0.40 (А is a half of trough-to-crest wave height; K=1 is the wave number of the first mode). An algorithm for calculation of Stokes wave with the prescribed accuracy was suggested by Chalikov and Sheinin [28]. The scheme based on the conformal coordinates is very effective: the calculations were carried out in 100 ms at notebook (2.10 GHz). The dependence of Stokes wave spectra on the wave number is shown in Figure 1. In fact, about 2000 curves obtained in the course of calculations, with the interval Δt=1, were plotted. Due to improvement of the numerical scheme, the accuracy of reproduction of Stokes wave is considerably higher than for the scheme used in Refs. [7, 8].
Figure 1.
The 2000 spectra of Stokes wave with steepness AK=0.40 as a function of wave number k superimposed on each other. The gray area in the right left corner is a computational noise.
As seen, up to S∼10−12k=22, the spectra of Stokes waves remain with high accuracy the same as it was assigned in initial conditions. At higher frequencies, the random disturbances appear. Note that this validation is not trivial: even small inaccuracies in the numerical scheme cause a fast distortion of the spectra, like in the bottom part of Figure 1. We consider these results as a serious evidence of high accuracy of the adiabatic version of the model. The previous version of 3-D model [26] allowed carrying out a long simulation of Stokes wave not steeper than AK=0.30. The right-hand sides of Eqs. (4) and (5) were calculated with a use of Fourier transform method: the nonlinear terms were calculated at the extended grid with size 4Mx×4My, and then by the inverse Fourier transform, they were returned to the Fourier grid. The fourth-order Runge-Kutta scheme was used for integration in time. The equation for the potential was solved at each of the four substeps of time step.
The simulations described by Chalikov [26] were a first attempt to reproduce the development of wave field assigned in the initial conditions as a group of small waves at high wave number under the action of strong wind. The initial elevation was generated as a superposition of linear waves corresponding to JONSWAP spectrum [29] with random phases. The initial Fourier amplitudes for the surface potential were calculated by the formulas of the linear wave theory. The details of the initial conditions are of no importance because the initial energy level is quite low. The wave peak was placed to the wave number equal to 100. The wind velocity was assigned equal to 4c100, where c100 is a phase velocity of the 100th mode. A detailed description of the scheme and its validation is given in Refs. [7, 8].
The simulation described in the current paper was performed with a doubled resolution in both directions, with the improved numerical scheme for Poisson equations and modified parameters in the scheme for calculations of energy transitions.
3. Energy input
The detailed description of the algorithm for calculation of energy input is given in Ref. [26]. The energy and momentum are transferred from air to water by the surface pressure field and tangent stress. According to the most reasonable theory [30], the Fourier components of surface pressure p are connected with those of the surface elevation through the following expression:
pk,l+ip−k,−l=ρaρwβk,l+iβ−k,−lhk,l+ih−k,−l,E14
where hk,l,h−k,−l,βk,l,β−k,−l are real and imaginary parts of elevation η, and the so-called β-function, ρa/ρw, is the ratio of air and water densities. Both β coefficients are the functions of the nondimensional frequency
Ω=ωU/g,E15
that characterizes the ratio of wind velocity to phase velocity of ck:
Ω=U/ckE16
Since the supplying of wave with the energy and momentum occurs in a layer whose height is proportional to the wave length, it is reasonable to suggest that the reference height for the wind velocity should be different for a different virtual wave length (distance λk/cosθi between the wave peaks in wind direction; the index i denotes a direction of mode). The wind velocity can be found by interpolation or extrapolation to the level:
zi,k=0.5λk/cosθiE17
The definition of Ωк should take into account the angle θi between the vector U and the direction of wave mode. Finally, the virtual nondimensional frequency takes the form:
Ωi,k=ωkcosθiUzk/g=cosθiUzk/ckE18
where ck=g/ωk is the phase velocity of kth mode.
For experimental derivation of the shape of β-function, it is necessary to simultaneously measure the wave surface elevation and nonstatic pressure on the surface [31, 32, 33, 34, 35]. The data obtained in this way allowed constructing an imaginary part of β-function used in some versions of the wave forecasting models [36]. The data on experimental β-function are compared in Ref. [4]. The values of β within the interval 0<Ω<10 differ by decimal orders. Hence, the question arises: in what way, using such a different input, the spectral models provide a reasonable agreement with the observations. The answer is very simple: the researchers have the possibility to modify the parameterization of dissipation. Despite the hundreds of papers, the knowledge on dissipation is even poorer than the knowledge on the energy input. Finally, only the sum of those source terms regulates the growth of total wave energy. Such situation is far from being perfect since the energy input and dissipation have totally different spectral properties.
The second way of the β-function evaluation is based on the results of numerical investigations of the statistical structure of the boundary layer above waves with the use of Reynolds equations and an appropriate closure scheme. In general, this method works so well that many problems in the technical fluid mechanics are often solved not experimentally but by using the numerical models [37, 38]. This method was being developed beginning from Refs. [39, 40] and followed by Refs. [41, 42, 43]. The results were implemented in the WAVEWATCH model, i.e., the third-generation wave forecast model [44], and thoroughly validated against the experimental data in the course of developing WAVEWATCH-III [45]. Most of the schemes for the calculations of β-function consider a relatively narrow interval of the nondimensional frequencies Ω. In the current work, the range of frequencies covers the interval 0<Ω<10, and occasionally, the values of Ω>10 can appear.
The most reliable data on β-function are concentrated in the interval −10<Ω<10 (the negative values of Ω correspond to the wave modes running against wind). In the current calculations, the modes running against wind are absent. The function β can be approximated by the formulas:
βi=β0+a0Ω−Ω0+a1Ω−Ω02Ω>Ω0β0−a0Ω−Ω0+a1Ω−Ω02Ω<Ω0,E19
βr=β1+a3Ω−Ω2Ω<Ω2a2Ω−Ω12Ω2<Ω<Ω3β1−a3Ω−Ω3Ω>Ω3,E20
where Ω0=0.355, Ω1=1.20, Ω2=−18.8, Ω3=21.2, a0=0.0228,a1=0.0948,a2=−0.372,a3=14.8,β0=−0.02,β1=−148.0.
The wind velocity remains constant throughout the integration. The values of Ω for other wave numbers are calculated by assuming that the wind profile is logarithmic.
Note that the formulation of wind and waves interaction can be significantly improved by coupling the wave model with the 1-D Wave Boundary Layer model [4]. The next step can be the coupling of wave model with the 3-D model of WBL based on the closure schemes or LES model (see Ref. [46]).
4. Energy dissipation
The current version of the model includes three types of dissipation (see details in Ref. [26]).
The energy can decrease due to the errors of approximations in space and time that depend on the number of Fourier modes, number of knots in the physical space, the vertical grid used for approximation of Poisson equation (6), and the criterion for accuracy of its solution. All of those errors that produce the ‘numerical dissipation’ can be referred to the adiabatic part of the models (4)–(6) at p=0. The rate of this dissipation can be reduced by the use of a better resolution and a higher accuracy of approximation, but this way leads to deceleration of the calculations with the model already running for a very long time.
Opposite to the numerical dissipation, there exists another type of energy loss that has rather a physical nature. The nonlinear interaction of different modes forms a flux of energy directed outside of the computational domain. We call it the ‘nonlinear dissipation.’ The numerical and nonlinear dissipation can hardly be considered separately. The estimation of rate of the numerical/nonlinear dissipation can be easily done by the comparison of full energy before and after the time step for the adiabatic part of the model (see Section 4 in Ref. [26]). In the current calculations, the loss of energy for one time step was about 10−4%, which is by 2–3 orders less that the rate of energy change due to input energy. Since we prefer to consider the process described by Eqs. (4)–(6) as adiabatic one, at each time step we restore the energy lost by both the numerical and nonlinear dissipation.
A long-term integration of full fluid mechanics equations always shows the spreading of spectrum to both high and low frequencies (wave numbers). The nonlinear flux of energy directed to the small wave numbers produces downshifting of spectrum, while an opposite flux forms a shape of the spectral tail. The second process that we call the ‘tail dissipation’ can produce accumulation of energy near the ‘cut’ wave number. The growth of amplitudes at high wave numbers is followed by growth of the local steepness and development of the numerical instability. To support the stability, additional terms are included into the right-hand sides of Eqs. (4) and (5):
∂ηk,l∂τ=Ek,l−μk,lηk,l,E21
∂φk,l∂τ=Fk,l−μk,lφk,lE22
(where Ek,l and Fk,l are the Fourier amplitudes of the right-hand sides of Eqs. (4) and (5); the value of μk,l is equal to zero inside the ellipse with semi-axes dmMx and dmМy; then, it grows quadratically with k up to the value cm and is equal to cm outside of the outer ellipse (see details in Ref. [26]). This method of filtration that we call the ‘tail dissipation’ was developed and validated with the conformal model [28]. The sensitivity of the results to the parameters in Refs. (21) and (23) is not large. The aim of the algorithm is to support smoothness and monotonicity of the wave spectrum within the high wave number range.
The main process of wave dissipation is the ‘breaking dissipation.’ This process is taken into account in all the spectral wave forecasting models similar to WAVEWATCH (see Refs. [44, 47]). Since there are no waves in the spectral models, no local criteria of wave breaking can be formulated. This is why the breaking dissipation is represented in the spectral models in a distorted form. The real breaking occurs in the relatively narrow areas of the physical space; however, the spectral image of such breaking is stretched over the entire wave spectrum, while in reality, the breaking decreases height and energy of separate waves. This contradiction occurs because the waves in the spectral models are assumed to be linear. In fact, a nonlinear sharp wave breaks in the physical space. Such wave is often composed of several local modes. It is clear that the state-of-art wave models should account for the threshold behavior of a breaking wave, that is, waves will not break unless their steepness exceeds the threshold [48, 49, 50].
The instability of the interface leading to breaking is an important though poorly developed problem of fluid mechanics. In general, this essentially nonlinear process should be investigated for the two-phase flow. Such approach was demonstrated, for example, by Iafrati [52].
The problem of breaking parameterization includes two points: (1) establishment of a criterion of the breaking onset and (2) development of the algorithm of the breaking parameterization. The problem of breaking is discussed in details in Ref. [47]. It was found in Ref. [51] that the clear predictor of breaking formulated in dynamical and geometrical terms, probably, does not exist. The consideration of the exact criterion for the breaking onset for the models using transformation of the coordinate type of (1) is useless since the numerical instability in such models occurs not because of the approach of breaking but because of the appearance of the high local steepness. The description of breaking in the direct wave modeling should satisfy the following conditions: (1) it should prevent the onset of instability at each point of millions of grid points over many thousands of time steps; (2) it should describe in a more or less realistic way the loss of the kinetic and potential energies with preservation of balance between them; and (3) it should preserve the volume. It was suggested by Chalikov [53] that an acceptable scheme can be based on a local highly selective diffusion operator with a special diffusion coefficient. Several schemes of such type were validated, and finally, the following scheme was chosen:
ητ=Eη+J−1∂∂ξBξ∂η∂ξ+∂∂ϑBϑ∂η∂ϑ,E23
φτ=Fφ+J−1∂∂ξBξ∂φ∂ξ+∂∂ϑBϑ∂φ∂ϑ,E24
where Fη and Fφ are the right-hand sides of Eqs. (4) and (5) including the tail dissipation terms; Bξ and Bϑ are the diffusion coefficients. The probability of high negative values of the curvilinearity is by orders larger than the probability calculated over the ensemble of linear modes with the spectra generated by the nonlinear model.
The curvilinearity turned out to be very sensitive to the shape of surface. This is why it was chosen as a criterion of the approaching breaking. The coefficients Bξ and Bϑ depend nonlinearly on the curvilinearity
Bξ=CBηξξ2ηξξ<ηξξcr0ηξξ≥ηξξcrE25
Bϑ=CBηϑϑ2ηϑϑ<ηξξcr0ηϑϑ≥ηξξcrE26
where the coefficients at CB=0.05, ηξξcr=ηϑϑcr=−50. The algorithm (24)–(27) does not change the volume and decreases the local potential and kinetic energies. It is assumed that the lost momentum and energy are transferred to the current and turbulence (see Ref. [42]). Besides, the energy also goes to other wave modes. The choice of parameters in Refs. (24)–(27) is based on simple considerations: the local piece of surface can closely approach the critical curvilinearity but not exceed it. The values of the coefficients were chosen in the course of multiple experiments to provide agreement with the rate of spectrum development given by JONSWAP approximation.
5. Evolution of wave field
The integration was done for 1,200,000 steps with the time step Δt=0.005 up to the nondimensional time T=6000, which corresponded to 9550 initial wave peak periods. The total energy of wave motion Е=Ep+Ek (Ep is the potential energy, while Ek is the kinetic energy) is calculated with the following formulas:
Ep=0.25η2¯,Ek=0.5φx2+φy2+φz2¯¯,E=Ep+Ek,E27
where a single bar denotes the averaging over the ξ and ϑ coordinates, while a double bar denotes the averaging over the entire volume. The derivatives in Ref. (27) are calculated according to the transformation (1). An equation of the integral energy E evolution can be represented in the following form:
dЕdt=I¯+Db¯+Dt¯+N¯,E28
where I¯ is the integral input of energy from wind (Eqs. (14)–(20)); Db¯ is a rate of the energy dissipation due to wave breaking (Eqs. (23)–(26)); Dt¯ is a rate of the energy dissipation due to filtration of high-wave number modes (‘tail dissipation,’ Eqs. (21) and (22)); N¯ is the integral effect of the nonlinear interactions described by the right-hand side of the equations when the surface pressure p is equal to zero. The differential forms for calculation of the energy transformations can be, in principle, derived from Eqs. (4)–(6), but here a more convenient and simple method was applied. Different rates of the integral energy transformations can be calculated with the help of fictitious time steps (i.e., apart from the basic calculations). For example, the value of I¯ is calculated by the following relation:
I¯¯=1ΔtEt+Δt¯¯−Et¯¯,E29
where Et+Δt¯¯ is the integral energy of a wave field obtained after one time step with the right side of Eq. (6) containing only the surface pressure calculated with Eqs. (14)–(18).
The evolution of the characteristics calculated by formula (29) is shown in Figure 2.
Figure 2.
The evolution of integral characteristics. The rate of evolution of the integral energy multiplied by 108 due to: (1) nonlinear interaction I¯¯ (Eq. (29)); (2) tail dissipation D¯¯t(Eqs. (21) and (22)); (3) breaking dissipation Db (Eqs. (23)–(26)); (4) input of energy from wind I¯¯ (Eqs. (14)–(20)); and (5) balance of energy I¯¯+D¯¯t+D¯¯b. Curve 6 shows the evolution of wave energy 105E. Vertical gray bars show instantaneous values; thick curve shows the smoothed behavior.
The sharp variation of all the characteristics at t<500 is explained by adjustment of the linear initial fields to the nonlinearity. The integral effect of the nonlinear interaction I¯¯ (straight line 1) was very close to zero. The tail dissipation Dt¯¯ (curve 2) is smaller than the breaking dissipation Dt¯¯(curve 3). The value of Db¯¯ has significant fluctuations due to introduction of the criteria (25) and (26). The dissipation D¯¯b+D¯¯t absorbs nearly all of the incoming energy, and just a small part of it is going for growth of waves. The balance of energy B¯¯=I¯¯+D¯¯t+D¯¯b (curve 5) fluctuates and approaches zero when energy E¯¯ (curve 6 in Figure 2) approaches saturation.
The time evolution of the integral spectral characteristics is presented in Figure 3.
Figure 3.
Dependence of integral characteristics on fetch (Eq. (32)): (1) weighted mean frequency ωw (Eq. (31)); (2) peak frequency ωp; (3) energy E (Eq. (27)); and (4) approximation of the peak frequency evolution (Eq. (32)).
Curve 1 corresponds to the weighted frequency ωw
ωw=∫ωSdkdl∫Sdkdl1/2,E30
where integrals are taken over the entire Fourier domain. The value ωw is not sensitive to the details of spectrum; hence, it well characterizes the position of spectrum and spectral peak shifting. Curve 2 describes the evolution of the spectral maximum. The step shape of curve corresponds to the fundamental property of downshifting. Opposite to common views, the development of spectrum occurs not monotonically, but by appearance of a new maximum at a lower wave number as well as by attenuation of the previous maximum. It is interesting to note that the same phenomenon is also observed in the spectral model [36].
The value of fetch in the periodic problem can be calculated by integration of the peak phase velocity cp=k−1/2 over time.
F=∫t0tcpdt.E31
The numerical experiment reproduces the case when development of wave field occurs under the action of a permanent and uniform wind. This case corresponds to the JONSWAP experiment [29]. It is suggested that the frequency of spectral peak changes as F−1/3, while the full energy grows linearly with F. Neither of the dependences can be exact since they do not take into account approaching a stationary regime. Besides, the dependence of frequency on fetch is singular at F=0. A more accurate is the approximation:
ωp=75.65.63+F1/3.E32
Obviously, the dependence ωp∼F−1/3 is valid in a narrower interval of F. As seen, contrary to ωw, the peak frequency changes not monotonically, but by appearance of a new maximum at a lower wave number as well as by attenuation of the previous maximum. It is interesting to note that the same phenomenon is also observed in the spectral model (16). The dependence of the total energy E on fetch F does not look like a linear one, but it is worth to note that the JONSWAP dependence is evidently inapplicable to a very small and large fetch.
On the whole, the evolutions of integral characteristics of the solution shown in Figures 2 and 3 are smoother than those calculated by Chalikov [26]. It can be explained by multiple technical improvements of the numerical scheme and higher resolution.
The evolution of wave spectrum is shown in Figure 4.
Figure 4.
The wave spectra Shr integrated over angle ψ in the polar coordinates and averaged over the consequent intervals of length about 500 units of the nondimensional time t (thin curves). The spectra are growing and shifting from right to left. Thick dashed curve is the dependence S∼ω−4; dotted curve corresponds to S∼ω−5 .
The 2-D wave spectrum Skl0≤k≤Mx−My≤l≤My averaged over nine time intervals of length equal to Δt≈500 was transferred to the polar coordinates Spψr−π/2≤ψ≤π/20≤r≤Mx and then averaged over the angle ψ to obtain the 1-D spectrum Shr:
Shr=∑SpψrrΔψ.E33
The angle ψ=0 coincides with the direction of wind U, Δψ=π/180. Even the averaged over angle spectrum looks quite irregular and contains multiple holes and peaks. The spectra are smoothed.
The two-dimensional wave spectra are shown in Figure 5, where the log10Sψr averaged over the successive eight periods of length Δt=500 is given.
Figure 5.
Sequence of 2-D images of lоg10Srψ averaged over the consequent eight periods of length Δt=500. The numbers indicate the period of averaging (the first panel marked 0 refers to the initial conditions). The spectra are normalized by the maximum value of spectrum 8. The horizontal axis corresponds to the wave numbers r=k; the angles are shown by rays.
The first panel with a mark 0 refers to the initial conditions. The pictures well characterize the downshifting and angle spreading of spectrum due to the nonlinear interactions.
As seen, each spectrum consists of separated peaks and holes. This phenomenon was observed and discussed by Chalikov et al. [7]. The same results were obtained by Chalikov [26]. The repeated calculations with different resolutions showed that such structure of 2-D spectrum is typical. The locations of peaks cannot be explained by the fixed combination of interacting modes, since in different runs (with the same initial conditions but a different set of phases for the modes), the peaks are located in different locations in the Fourier space.
It is interesting to note that while increasing resolution, the patches with low energy extend. It can be supposed that the current and higher resolutions are excessive, and the process can be simulated with a lower resolution. This statement may be too optimistic, but it can be supported by the following arguments. The multi-mode wave mechanics is different from the multi-scale turbulent motion. The modeling of turbulence at increase of resolution just allows reproducing more details of motion. The increase of resolution in a wave model introduces other wave modes with different phase velocities. Due to dispersion, the solutions (i.e., the evolution of surface) in these two cases will be completely different. It means that the solution does not converge with increase of resolution, which makes no sense.
The situation can be saved if upon reaching the optimal resolution, the new added positions for the modes will not obtain the energy and not participate in solution. The existence of such effect should be carefully validated with the exact wave model. If this effect does not exist, it means that the results of simulations depend completely on the resolution, the reliable simulation of individual evolution of wave field being, in fact, impossible.
The method of calculation of the simulated one-dimensional input and dissipation spectra was described by Chalikov [26]; still, it will be explained here once again, though briefly.
The evolution of the integrated over angle ψ wave spectrum Shr can be described with the equation:
dShrdt=Ir+Dtr+Dbr+Nr,E34
where Ir,Dtr,DbrandNr are the spectra of the input energy, tail dissipation, breaking dissipation, and the rate of nonlinear interactions. All of the spectra shown below were obtained by transformation of the 2-D spectra into a polar coordinate ψr and then integrated over the angles ψ within the interval −π/2π/2. The spectra can be calculated using an algorithm similar to Eq. (29) for integral characteristics. For example, the spectrum of the energy input Ikl is calculated as follows:
Ikl=Sct+Δtkl−Sctkl/Δt,E35
where Sckxky is a spectrum of the columnar energy calculated by the relation:
where the grid values of velocity components u,v,w are calculated by the relations:
u=φξ+φζηξ,v=φϑ+φζηϑ,w=φζ,E37
and uk,l,vk,landwk,l are the real Fourier coefficients, while for the negative indices—the imaginary ones.
For calculation of Ikl, the fictitious time steps Δt are made only with a term responsible for the energy input, that is, the surface pressure p. The spectrum Ikl was averaged over the periods Δt≈500, then transformed into a polar coordinate system and integrated in the Fourier space over the angles ψ within the interval −π/2π/2. Such procedure was used for calculation of all the terms in the right side of Eq. (34). In the current version of the model, the calculations of integral (28) and spectral (34) transformations were combined with the calculations of the right sides of Eqs. (4) and (5).
The rates of transformation of spectrum are shown in Figure 6. The integral term describing the nonlinear interaction N¯ in Eq. (28) is small (as compared with the local values of Nk,l), but the magnitude of spectrum Nr is comparable with the input Ir and dissipation Dtr and Dbr terms (panel 1 in Figure 5). The shape of spectrum Nr confirms prediction of the quasi-linear theory [54, 55]. At the low wave number slope of the spectrum, the nonlinear influx of energy is positive, while at the opposite slope, it is negative. This process produces shifting of spectrum to the lower wave number (downshifting). The input of energy due to the nonlinear interactions is observed in a high frequency part of spectrum, which also agrees with Hasselmann’s theory. Note that the nonlinear interactions also produce widening of spectrum.
Figure 6.
The rates of transformation spectra multiplied by 109: (1) nonlinear interaction Nr(1); (2) input energy Ir; (3) breaking dissipation Dbr; (4) tail dissipations Dtr multiplied by 1011. All spectra are obtained by transformation of the 2-D spectra into the polar coordinate ψr and then integrated over the angles ψ within the interval −π/2π/2.
The spectral distribution of the energy input from wind Ir (panel 2 in Figure 6) is in general similar to wave spectrum since it depends linearly on the spectral density (Figure 3). The dissipation rate Dbr is negative (panel 3), and its minimum is shifted a little to higher frequencies from the wave spectrum peak. The tail dissipation (Panel 4) is smaller by two orders than the other terms, but it plays an important role of supporting numerical stability.
The residual rate of transformation of spectrum dShr/dt averaged over eight consequent periods is shown in Figure 7. The numbers in the top part of panel indicate the averaged wave number of the spectral peak. The second set of numbers refers to the corresponding spectrum of the residual input of energy. As seen, the maximum of the input energy is located to the left of the spectral peak, that is, on a low-wavenumber spectral slope. The obtained energy causes downshifting of spectrum and supports the shape of a high wavenumber slope and spectral tail. In the equilibrium regime, all the incoming energy are consumed for supporting the shape of the entire spectrum.
Figure 7.
The spectral distribution of the residual input of energy dShr/dt in the energy-containing part of spectrum for different stages of wave development. The numbered vertical lines indicate positions of the spectral peak. The second set of numbers shows the peaks of the corresponding residual input.
However, the dynamics of the tale is not adiabatic, that is, it is not completely controlled by the spectral energy cascade since the input of energy due to the nonlinear interaction competes with the energy input from wind (curve 2) and breaking dissipation (curves 3 and 4). The tail dissipation (curve 4) is small and concentrated in the vicinity of the cut wave number. The input and dissipation in the spectral tail are nearly in balance (curve 4) (Figure 8).
Figure 8.
The rates of transformation spectra multiplied by 109 for the last period: (1) nonlinear interaction Nr(1); (2) input energy; (3) breaking dissipation Dbr; (4) tail dissipations 1010Dtr; and (5) balance of all the terms.
6. Statistical properties of wave field
The phase-resolving modeling requires a higher computer capacity for calculations of any statistical characteristics of sea waves. In the course of simulations, 1.200 two-dimensional fields of the elevation and surface potential with the size 2048 × 1024 points were recorded. Following the solution of the 3-D equation for the velocity potential, these data allow us to reproduce any kinematic and dynamic characteristics of the three-dimensional structure of waves.
The most important statistical characteristics of wave field are mean Hs, variance V, skewness Sk, and kurtosis Ku calculated by the averaging over each of 1200 fields:
V=η−η¯2¯,Sk=η−η¯3¯V−3/2,Ku==η−η¯4¯V−2−3.E38
The evolution of these characteristics in time is shown in Figure 9.
Figure 9.
Evolution of the statistical characteristics of elevation: (1) mean value η¯, (2) variance V, (3) skewness Sk, and (4) kurtosis Ku.
The volume of the domain characterized by η¯ is preserved with the accuracy of the order of 10−8. The variance V is the potential energy that is growing up to the saturation. When the wave field is a superposition of a large number of linear waves, both the skewness and kurtosis are equal to zero. The skewness S characterizes asymmetry of the probability distribution indicating that the positive values of η are larger than the negative ones, then S>0. The kurtosis Ku is positive if the crests are sharper and the troughs are smoother than in the case of linear waves.
The probabilities of the geometrical characteristics (elevation, first and second derivatives over x) are shown in Figure 10. The elevation Z (normalized by the significant wave height) is characterized by asymmetry: the heights of waves are significantly larger than the depths of troughs, that is, the wave field is closer to the superposition of Stokes waves than to that of the harmonic modes. The distribution of slopes exhibits horizontal asymmetry: the negative slopes are larger than the positive ones, that is, the waves, on the average, are inclined in the direction of movements. The second derivative (curvilinearity) has the most striking tendency for asymmetry: the negative values corresponding to the sharpness of crests are much larger by absolute value than the positive values corresponding to the curvilinearity of troughs. This property of curvilinearity was used for the parameterizing of breaking. The limit value Zxx=−50 was used as a criterion for the initiating of breaking (see Eq. (26)).
Figure 10.
Geometric characteristics of elevation: (1) probability of elevation PZ; (2) probability of slopes PZx; and (3) probability of curvilinearity PZxx.
The probability for three components of the surface velocity is given in Figure 11. The distributions of the vertical and transverse components of velocity are symmetrical. For a horizontal component, the values of positive fluctuations are considerably larger than the negative fluctuations. This effect cannot be explained by the influence of Stokes drift, which value for those specific conditions does not exceed 10−3. The asymmetry of the probability distribution for the u-components is definitely connected with the asymmetry of the probability distribution for inclinations of surface (Figure 10, panel 2).
Figure 11.
Probability of the longitudinal u, transverse v, and vertical w components of the surface velocity calculated for the last of nine periods corresponding approximately to the quasi-stationary regime.
The number of extreme waves with a high crest Zc/Hs>1.2 is shown in Figure 12. Because such wave is not presented in each of the wave fields, the picture looks as discrete bars of different heights. The total number of values Z/Hs>1.2 is 17.214. The formally calculated probability of the values equals 0.67⋅10−5. Note that the data on the probability of wave height contain uncertainty because it is not always clear which event should be considered as a single freak wave. The straightforward way suggests calculation of a portion of all the records including freak waves, out of the total volume of the data.
Figure 12.
The number of points where the nondimensional height Zc/Hs exceeds 1.2. The total number of values is 2.57⋅109.
However, some of the records can belong to the single moving freak waves. The cause of this uncertainty is the absence of a strict definition of freak wave being either a case or a process. The number of extreme waves grows with development of wave field.
The integral probability of the total wave height Ztc/Hs, the wave height above mean level Zc/Hs, and the depth of trough Zt/Hs are shown in Figure 13.
Figure 13.
The cumulative probability of crest-to-trough wave height Ztc/Hs (curve 3); crest height Zc/Hs (curve 2); and trough depth −Zt/Hs (curve 3). The number of points in each filed is equal to 2048×1024. The number of fields is 1200.
Thin lines show that Ztc/Hs=2 correspond approximately to Zc/Hs=1.2 and −Zt/Hs=−.86. It is worth to remind that here the nondimensional ‘extreme’ waves are considered. The true extreme waves are the product of the real wave field. The probability of real extreme waves can be estimated by multiplying the probability of the nondimensional wave by the probability of significant wave height.
The statistical connection between the total wave heights, crest heights, and trough depths is shown in Figure 14.
Figure 14.
Dependence of crest height Zc/Hs (top section) and depth trough Zt/Hs(bottom section) on the total wave height Ztc/Hs.
The dependences between these characteristics can be approximated by the formulas:
where the tilde denotes the normalizing by significant wave height Hs. Note that the first and third coefficients in (39) turned out to be a match. The correlation coefficient between Z˜tandZ˜c is −0.354, while between Z˜tandZ˜tc, it is −0.721, and between Z˜candZ˜tc, it is 0.903, that is, the correlation between the full wave height Z˜tc and the wave height above mean level Z˜c is so high that Z˜c can be used for identification of extreme waves.
The last characteristics that we consider here is the angle distribution of the spectral density. This characteristic can be described by the function ϒω/ωp (see Ref. [60]).
ϒ=∫Sωψθdωdψ∫SωψdωdψE40
where the integrals are taken over the domain 0<ω<ωc−π/2<ψ<π/2. The value ϒ is weighted by the absolute spectrum value of wave direction. The wave spectra as the functions of frequency ω normalized by peak frequency ωp for the first seven periods are shown in the upper panel of Figure 15.
Figure 15.
The shape of wave spectrum as a function of the nondimensional frequency ω/ωp (top panel) and a function ϒ (Eq. (40); ωp is the frequency in the spectral peak.
The function ϒω/ωp calculated for the same spectra is given in the bottom panel. As seen, the ϒ curves corresponding to different wave ages are close to each other. All of them have a sharp maximum at the frequencies below the spectral peak, a well-pronounced minimum in the spectral peak, and a relatively slow growth above the spectral peak. The decrease of ϒ at high frequencies is probably caused by the high-frequency dumping. The angle distribution was investigated in Refs. [56, 57, 58, 59, 60]. The approximations of ϒω/ωp from the different sources collected in Ref. [61] show considerable scatter, but the general features are quite similar to those calculated in the current work. Note that the spectrum has undergone a long development; hence, the characteristics presented in Figure 14 were produced by the numerical model itself.
7. Conclusions
The paper is devoted to the wind wave simulations based on the initial equations of potential motion of fluid with a free surface. The system of equations includes the evolutionary kinematic and dynamic surface conditions and Laplace equation for the velocity potential. In this paper, a case of the double-periodic domain of infinite depth is considered. The construction of the exact numerical scheme for a long-term integration of these equations in the Cartesian coordinate system is impossible, since the surface moves between the grid knots. Instead, the system of the curvilinear coordinates (1) fitted with the surface is introduced. The main advantage of this coordinate system is that the surface coincides with a coordinate line ζ=0. The penalty follows immediately after turning the simple Cartesian coordinates into the curvilinear, nonstationary, and nonorthogonal coordinate system. Fortunately, the evolutionary Eqs. (4) and (5) become just slightly complicated, while Laplace equation transforms into the full elliptic equation. At each time step, these equations can be represented as Poisson equation with the right-hand side depending on the solution itself as well as on the metric coefficient. Since the norm of the right sight of the equation is usually small, the solution of Poisson equation can be found with the three-diagonal matrix algorithm and with iterations over the right-hand side. This procedure being formulated in the Fourier space is greatly simplified by the assumption of periodicity since in this case the derivatives over the horizontal coordinates are represented by the absolute value of wave number k in the diagonal terms. When constructing a numerical scheme, we noticed that the significant simplification of the problem can be achieved by separation of the velocity potential into the linear and nonlinear components (see Ref. [7]). It is assumed that the linear component satisfies Laplace equations with the known solution. The equation for the nonlinear component can be obtained by extracting Laplace equation from the initial Poisson equation. Such procedure has a lot of advantages since the nonlinear component is on the average less by 1–2 decimal orders than the linear one. It means that for solution of the reduced Poisson equation the lesser number of levels in vertical, the lesser number of iterations and a smaller accuracy criterion can be used. The use of two components in the evolutionary equation does not seem to provide noticeable advantages; however, this way deserves further consideration.
The adiabatic version of the model was validated by simulation of a running Stokes wave with the steepness AK=0.40 in Ref. [7]. It was shown that the amplitudes of Stokes modes remain practically constant up to the accuracy of 10−7. The current version of the model after some technical improvements of the numerical scheme provides accuracy up to 10−12. Then, the adiabatic version of the model was used for reproduction of a quasi-stationary regime for investigation of the statistical properties of sea waves [1, 7, 8].
For calculations of development of wave field under the action of wind, it was necessary to include the algorithms for calculations of input and dissipation of energy. The scheme for calculation of the energy input was developed by Chalikov and Rainchik [3] on the basis of coupling the one-dimensional phase-resolving model and the two-dimensional boundary layer model with the second-order turbulence closure scheme. The parameterization suggested is still quasi-linear (similar to Miles’ scheme [30]), but in our opinion, it is the only scheme confirmed by the extended results of the numerical simulations. The theoretical and observational data on β− function are dramatically scattered (see Ref. [4], Figure 1).
For stabilization of the solution, the algorithm of high-frequency dumping in the Fourier space suggested by Chalikov and Sheinin [28] was used. The numerous attempts were made to improve that scheme (for example by reduction of the spectral interval of dumping) but without much success.
The most complicated problem is the parameterization of dissipation due to wave breaking. Such algorithm should not describe a process of breaking as it is, which within the frame of such model is impossible, but it should prevent the numerical instability that interrupts a run (see discussion in Ref. [26]). Currently, the algorithm used is very simple. It is based on the diffusion operator with a highly selective coefficient of ‘viscosity.’ It works satisfactorily, but we are far from thinking that it cannot be substantially improved or completely replaced by another one.
The results described in this paper show that the wave field development under the action of wind is reproduced quite realistically. The area of application of such models is very wide. Such modeling should be used for improvement of the algorithms of the energy input and dissipation. A model with the periodic boundary conditions can be used for the local interpretation of the spectral forecast in terms of real waves. The finite-difference version of the model can be used for simulation of wave regimes in the basins with real shapes and bathymetry (see, e.g., Ref. [5]).
Acknowledgments
Author would like to thank Mrs. O. Chalikova for her assistance in preparation of the manuscript. This research was performed in the framework of the state assignment of Russian Academy of Science (Theme No. 0149-2019-0015) supported in part 15 (Section 2) by RFBR (project No. 18-05-01122).
\n',keywords:"numerical simulation, wind waves, waves’ development, wave spectrum, Fourier-transform method, wind input, waves’ dissipation, wave statistics",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/72024.pdf",chapterXML:"https://mts.intechopen.com/source/xml/72024.xml",downloadPdfUrl:"/chapter/pdf-download/72024",previewPdfUrl:"/chapter/pdf-preview/72024",totalDownloads:108,totalViews:0,totalCrossrefCites:0,dateSubmitted:"December 13th 2019",dateReviewed:"March 25th 2020",datePrePublished:"June 3rd 2020",datePublished:null,dateFinished:null,readingETA:"0",abstract:"The paper describes the numerical experiments with a three-dimensional phase-resolving model based on the initial potential equation of motion with free surface at deep water in the periodic domain written in the surface-following nonstationary curvilinear nonorthogonal coordinate system. The numerical scheme is based on Fourier-transform method. The vertical velocity on surface is calculated by solving the three-dimensional Poisson equation for the velocity potential. The velocity potential is represented as a sum of linear and nonlinear components. The linear component is described by Laplace equation. The nonlinear component is calculated by solution of the three-dimensional Poisson equation with the iterated right-hand side. The model includes some algorithms for calculation of the energy input from wind as well as for calculation of breaking and high-frequency dissipation. Initially, the conditions are assigned as a set of small waves corresponding to JONSWAP spectrum at high wave number. In response to waves’ growth, the spectrum shifts to lower wave numbers. The evolution of spectrum is generally in an agreement with the observed data. The wave spectrum and the spectra of different rates of energy transformation as well as the statistical characteristics of wave field for different stages of development are described.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/72024",risUrl:"/chapter/ris/72024",signatures:"Dmitry Chalikov",book:{id:"9984",title:"Geophysics and Ocean Waves Studies",subtitle:null,fullTitle:"Geophysics and Ocean Waves Studies",slug:null,publishedDate:null,bookSignature:"Prof. Khalid S. S. Essa, Prof. Marcello Di Risio, Dr. Daniele Celli and Dr. Davide Pasquali",coverURL:"https://cdn.intechopen.com/books/images_new/9984.jpg",licenceType:"CC BY 3.0",editedByType:null,editors:[{id:"102766",title:"Prof.",name:"Khalid S.",middleName:null,surname:"Essa",slug:"khalid-s.-essa",fullName:"Khalid S. Essa"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Equations",level:"1"},{id:"sec_3",title:"3. Energy input",level:"1"},{id:"sec_4",title:"4. Energy dissipation",level:"1"},{id:"sec_5",title:"5. Evolution of wave field",level:"1"},{id:"sec_6",title:"6. Statistical properties of wave field",level:"1"},{id:"sec_7",title:"7. Conclusions",level:"1"},{id:"sec_8",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Chalikov D, Babanin AV. Comparison of linear and nonlinear extreme wave statistics. Acta Oceanologica Cinica. 2016;5(5):99-105. DOI: 10.1007/313131-016-0862-5'},{id:"B2",body:'Troitskaya YI, Sergeev DA, Kandaurov AA, Baidakov GA, Vdovin MA, Kazakov VI. Laboratory and theoretical modeling of air-sea momentum transfer under severe wind conditions. Journal of Geophysical Research. 2012;117:C00J21. DOI: 10.1029/2011JC007778'},{id:"B3",body:'Chalikov D, Rainchik S. Coupled numerical modelling of wind and waves and the theory of the wave boundary layer. Boundary-Layer Meteorol. 2011;138:1-41. 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Shirshov Institute of Oceanology RAS, Russia
University of Melbourne, Australia
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The effects of external pressure, initial packing structure, and SiC content on the packing densification were systematically presented. Various macro and micro properties such as relative density and distribution, stress and distribution, particle rearrangement (e.g. sliding and rolling), deformation and mass transfer, and interfacial behavior within composite particles were characterized and analyzed. The results show that by properly controlling the initial packing structure, pressure, and SiC content, various anisotropic and isotropic Al/SiC particulate composites with high relative densities and uniform density/stress distributions can be obtained. At early stage of the compaction, the densification mechanism mainly lies in the particle rearrangement driven by the low interparticle forces. In addition to sliding, accompanied particle rolling also plays an important role. With the increase of the compaction pressure, the force network based on SiC cores leads to extrusion on Al shells between two cores, contributing to mass transfer and pore filling. During compaction, the debonding between the core and shell of each composite particle appears and then disappears gradually in the final compact.",signatures:"Xizhong An, Yu Liu, Fen Huang and Qian Jia",authors:[{id:"114055",title:"Prof.",name:"Xizhong",surname:"An",fullName:"Xizhong An",slug:"xizhong-an",email:"anxz@mail.neu.edu.cn"},{id:"237739",title:"Mr.",name:"Yu",surname:"Liu",fullName:"Yu Liu",slug:"yu-liu",email:"823891779@qq.com"},{id:"237740",title:"Ms.",name:"Fen",surname:"Huang",fullName:"Fen Huang",slug:"fen-huang",email:"389767834@qq.com"},{id:"242885",title:"Ms.",name:"Qian",surname:"Jia",fullName:"Qian Jia",slug:"qian-jia",email:"958710210@qq.com"}],book:{title:"Powder Technology",slug:"powder-technology",productType:{id:"1",title:"Edited Volume"}}}],collaborators:[{id:"162799",title:"Ph.D.",name:"Nelly Cecilia",surname:"Alba De Sánchez",slug:"nelly-cecilia-alba-de-sanchez",fullName:"Nelly Cecilia Alba De Sánchez",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Universidad Autónoma de Occidente",institutionURL:null,country:{name:"Colombia"}}},{id:"195555",title:"Ph.D. Student",name:"Prashantha",surname:"Kumar H G",slug:"prashantha-kumar-h-g",fullName:"Prashantha Kumar H G",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/195555/images/4783_n.jpg",biography:null,institutionString:null,institution:{name:"Vellore Institute of Technology University",institutionURL:null,country:{name:"India"}}},{id:"237739",title:"Mr.",name:"Yu",surname:"Liu",slug:"yu-liu",fullName:"Yu Liu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"237740",title:"Ms.",name:"Fen",surname:"Huang",slug:"fen-huang",fullName:"Fen Huang",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"238055",title:"Dr.",name:"Ilmars",surname:"Zalite",slug:"ilmars-zalite",fullName:"Ilmars Zalite",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"242885",title:"Ms.",name:"Qian",surname:"Jia",slug:"qian-jia",fullName:"Qian Jia",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"244241",title:"MSc.",name:"Gundega",surname:"Heidemane",slug:"gundega-heidemane",fullName:"Gundega Heidemane",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"244242",title:"Dr.",name:"Janis",surname:"Grabis",slug:"janis-grabis",fullName:"Janis Grabis",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"244243",title:"MSc.",name:"Mikhail",surname:"Maiorov",slug:"mikhail-maiorov",fullName:"Mikhail Maiorov",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"255849",title:"Ph.D.",name:"Hector",surname:"Jaramillo S.",slug:"hector-jaramillo-s.",fullName:"Hector Jaramillo S.",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/255849/images/system/255849.jpeg",biography:"Héctor E. Jaramillo S. is a full-time professor-researcher of the\nAutónoma de Occidente University (Cali, Colombia). He has a\nPhD from the Universidad del Valle with an emphasis in the mechanics of solids. The PhD dissertation was about the design and\ndevelopment of a finite element model of the L4-L5-S1 segment\nof the human spine and the experimental characterization was\nmade in the Orthopaedic Bioengineering Research Laboratory\nof the Colorado State University. He has vast experience in finite element analysis\nusing no linear, orthotropic, and hyperelastic materials. He has a masters degree in\ncivil engineering (2004), and a BSc in Mechanical Engineering (1992). His topics\nof interest are the mechanics of solids, fatigue fracture mechanics, mechanical engineering design, and finite element analysis",institutionString:"Universidad Autónoma de Occidente",institution:{name:"Universidad Autónoma de Occidente",institutionURL:null,country:{name:"Colombia"}}}]},generic:{page:{slug:"scientific-advisors",title:"Scientific Advisory Boards",intro:"
IntechOpen’s team of Scientific Advisors supports the publishing team by providing editorial and academic input and ensuring the highest quality output of free peer-reviewed articles. The Boards consist of independent external collaborators who assist us on a voluntary basis. Their input includes advising on new topics within their field, proposing potential expert collaborators and reviewing book publishing proposals if required. Board members are experts who cover major STEM and HSS fields. All are trusted IntechOpen collaborators and Academic Editors, ensuring that the needs of the scientific community are met.
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Physical Sciences, Technology and Engineering Board
\\n\\n
Chemistry
\\n\\n
\\n\\t
Ayben Kilislioglu - Department of Chemical Engineering Istanbul University, İstanbul, Turkey
\\n\\t
Goran Nikolic - Faculty of Technology, University of Nis, Leskovac, Serbia
\\n\\t
Mark T. Stauffer - Associate Professor of Chemistry, The University of Pittsburgh, USA
\\n\\t
Margarita Stoytcheva - Autonomous University of Baja California Engineering Institute Mexicali, Baja California, Mexico
Joao Luis Garcia Rosa - Associate Professor Bio-inspired Computing Laboratory (BioCom) Department of Computer Science University of Sao Paulo (USP) at Sao Carlos, Brazil
\\n\\t
Jan Valdman - Institute of Mathematics and Biomathematics, University of South Bohemia, České Budějovice, Czech Republic Institute of Information Theory and Automation of the ASCR, Prague, Czech Republic
\\n
\\n\\n
Earth and Planetary Science
\\n\\n
\\n\\t
Jill S. M. Coleman - Department of Geography, Ball State University, Muncie, IN, USA
\\n\\t
İbrahim Küçük Erciyes - Üniversitesi Department of Astronomy and Space Sciences Melikgazi, Kayseri, Turkey
\\n\\t
Pasquale Imperatore - Electromagnetic Environmental Sensing (IREA), Italian National Council of Research (CNR), Naples, Italy
\\n\\t
Mohammad Mokhtari - Director of National Center for Earthquake Prediction International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran
\\n
\\n\\n
Engineering
\\n\\n
\\n\\t
Narottam Das - University of Southern Queensland, Australia
\\n\\t
Jose Ignacio Huertas - Energy and Climate Change Research Group; Instituto Tecnológico y Estudios Superiores de Monterrey, Mexico
Likun Pan - Engineering Research Center for Nanophotonics and Advanced Instrument, Ministry of Education, Department of Physics, East China Normal University, China
\\n\\t
Mukul Chandra Paul - Central Glass & Ceramic Research Institute Jadavpur, Kolkata, India
\\n\\t
Stephen E. Saddow - Electrical Engineering Department, University of South Florida, USA
\\n\\t
Ali Demir Sezer - Marmara University, Faculty of Pharmacy, Department of Pharmaceutical Biotechnology, İstanbul, Turkey
\\n\\t
Krzysztof Zboinski - Warsaw University of Technology, Faculty of Transport, Warsaw, Poland
\\n
\\n\\n
Materials Science
\\n\\n
\\n\\t
Vadim Glebovsky - Senior Researcher, Institute of Solid State Physics, Chernogolovka, Russia Expert of the Russian Fund for Basic Research, Moscow, Russia
\\n\\t
Jianjun Liu - State Key Laboratory of High Performance Ceramics and Superfine Microstructure of Shanghai Institute of Ceramics, Chinese Academy of Sciences, China
\\n\\t
Pietro Mandracci - Department of Applied Science and Technology, Politecnico di Torino, Italy
\\n\\t
Waldemar Alfredo Monteiro - Instituto de Pesquisas Energéticas e Nucleares Materials Science and Technology Center (MSTC) São Paulo, SP, Brazil
Toshio Ogawa - Department of Electrical and Electronic Engineering, Shizuoka Institute of Science and Technology, Toyosawa, Fukuroi, Shizuoka, Japan
\\n
\\n\\n
Mathematics
\\n\\n
\\n\\t
Paul Bracken - Department of Mathematics University of Texas, Edinburg, TX, USA
\\n
\\n\\n
Nanotechnology and Nanomaterials
\\n\\n
\\n\\t
Muhammad Akhyar - Farrukh Nano-Chemistry Lab. Registrar, GC University Lahore, Pakistan
\\n\\t
Khan Maaz - Chinese Academy of Sciences, China & The Pakistan Institute of Nuclear Science and Technology, Pakistan
\\n
\\n\\n
Physics
\\n\\n
\\n\\t
Izabela Naydenova - Lecturer, School of Physics Principal Investigator, IEO Centre College of Sciences and Health Dublin Institute of Technology Dublin, Ireland
\\n\\t
Mitsuru Nenoi - National Institute of Radiological Sciences, Japan
\\n\\t
Christos Volos - Physics Department, Aristotle University of Thessaloniki, Greece
\\n
\\n\\n
Robotics
\\n\\n
\\n\\t
Alejandra Barrera - Instituto Tecnológico Autónomo de México, México
\\n\\t
Dusan M. Stipanovic - Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign
\\n\\t
Andrzej Zak - Polish Naval Academy Faculty of Navigation and Naval Weapons Institute of Naval Weapons and Computer Science, Gdynia, Poland
Petr Konvalina - Faculty of Agriculture, University of South Bohemia in České Budějovice, Czech Republic
\\n
\\n\\n
Biochemistry, Genetics and Molecular Biology
\\n\\n
\\n\\t
Chunfa Huang - Saint Louis University, Saint Louis, USA
\\n\\t
Michael Kormann - University Children's Clinic Department of Pediatrics I, Pediatric Infectiology & Immunology, Translational Genomics and Gene Therapy in Pediatrics, University of Tübingen, Tübingen, Germany
\\n\\t
Bin WU - Ph.D. HCLD Scientific Laboratory Director, Assisted Reproductive Technology Arizona Center for Reproductive Endocrinology and Infertility Tucson, Arizona , USA
\\n
\\n\\n
Environmental Sciences
\\n\\n
\\n\\t
Juan A. Blanco - Senior Researcher & Marie Curie Research Fellow Dep. Ciencias del Medio Natural, Universidad Publica de Navarra Campus de Arrosadia, Pamplona, Navarra, Spain
\\n\\t
Mikkola Heimo - University of Eastern Finland, Kuopio, Finland
\\n\\t
Bernardo Llamas Moya - Politechnical University of Madrid, Spain
\\n\\t
Toonika Rinken - Department of Environmental Chemistry, University of Tartu, Estonia
\\n
\\n\\n
Immunology and Microbiology
\\n\\n
\\n\\t
Dharumadurai Dhanasekaran - Department of Microbiology, School of Life Sciences, Bharathidasan University, India
Isabel Gigli - Facultad de Agronomia-UNLPam, Argentina
\\n\\t
Milad Manafi - Department of Animal Science, Faculty of Agricultural Sciences, Malayer University, Malayer, Iran
\\n\\t
Rita Payan-Carreira - Universidade de Trás-os-Montes e Alto Douro, Departamento de Zootecnia, Portugal
\\n
\\n\\n
Medicine
\\n\\n
\\n\\t
Mazen Almasri - King Abdulaziz University, Faculty of Dentistry Jeddah, Saudi Arabia Dentistry
\\n\\t
Craig Atwood - University of Wisconsin-Madison, USA Stem Cell Research, Tissue Engineering and Regenerative Medicine
\\n\\t
Oreste Capelli - Clinical Governance, Local Health Authority, Modena, Italy Public Health
\\n\\t
Michael Firstenberg - Assistant Professor of Surgery and Integrative Medicine NorthEast Ohio Medical University, USA & Akron City Hospital - Summa Health System, USA Surgery
\\n\\t
Parul Ichhpujani - MD Government Medical College & Hospital, Department of Ophthalmology, India
Amidou Samie - University of Venda, SA Infectious Diseases
\\n\\t
Shailendra K. Saxena - CSIR-Centre for Cellular and Molecular Biology, Hyderabad, India Infectious Diseases
\\n\\t
Dan T. Simionescu - Department of Bioengineering, Clemson University, Clemson SC, USA Stem Cell Research, Tissue Engineering and Regenerative Medicine
\\n\\t
Ke Xu - Tianjin Lung Cancer Institute Tianjin Medical University General Hospital Tianjin, China Oncology
\\n
\\n\\n
Ophthalmology
\\n\\n
\\n\\t
Hojjat Ahmadzadehfar - University Hospital Bonn Department of Nuclear Medicine Bonn, Germany Medical Diagnostics, Engineering Technology and Telemedicine
\\n\\t
Miroslav Blumenberg - Department of Ronald O. Perelman Department of Dermatology; Department of Biochemistry and Molecular Pharmacology, Dermatology, NYU School of Medicine, NY, USA Dermatology
\\n\\t
Wilfred Bonney - University of Dundee, Scotland, UK Medical Diagnostics, Engineering Technology and Telemedicine
\\n\\t
Christakis Constantinides - Department of Cardiovascular Medicine University of Oxford, Oxford, UK Medical Diagnostics, Engineering Technology and Telemedicine
\\n\\t
Atef Mohamed Mostafa Darwish - Department of Obstetrics and Gynecology , Faculty of Medicine, Assiut University, Egypt Gynecology
\\n\\t
Ana Polona Mivšek - University of Ljubljana, Ljubljana, Slovenia Midwifery
\\n\\t
Gyula Mozsik - First Department of Medicine, Medical and Health Centre, University of Pécs, Hungary
\\n\\t
Shimon Rumelt - Western Galilee-Nahariya Medical Center, Nahariya, Israel Ophthalmology
\\n\\t
Marcelo Saad - S. Paulo Medical College of Acupuncture, SP, Brazil Complementary and Alternative Medicine
\\n\\t
Minoru Tomizawa - National Hospital Organization Shimoshizu Hospital, Japan Gastroenterology
\\n\\t
Pierre Vereecken - Centre Hospitalier Valida and Cliniques Universitaires Saint-Luc, Belgium Dermatology
\\n
\\n\\n
Gastroenterology
\\n\\n
\\n\\t
Hany Aly - Director, Division of Newborn Services The George Washington University Hospital Washington, USA Pediatrics
\\n\\t
Yannis Dionyssiotis - National and Kapodistrian University of Athens, Greece Orthopedics, Rehabilitation and Physical Medicine
\\n\\t
Alina Gonzales- Quevedo Instituto de Neurología y Neurocirugía Havana, Cuba Mental and Behavioural Disorders and Diseases of the Nervous System
\\n\\t
Margarita Guenova - National Specialized Hospital for Active Treatment of Haematological Diseases, Bulgaria
\\n\\t
Eliska Potlukova - Clinic of Medicine, University Hospital Basel, Switzerland Edocrinology
\\n\\t
Raymond L. Rosales -The Royal and Pontifical University of Santo Tomas, Manila, Philippines & Metropolitan Medical Center, Manila, Philippines & St. Luke's Medical Center International Institute in Neuroscience, Quezon City, Philippines Mental and Behavioural Disorders and Diseases of the Nervous System
\\n\\t
Alessandro Rozim - Zorzi University of Campinas, Departamento de Ortopedia e Traumatologia, Campinas, SP, Brazil Orthopedics, Rehabilitation and Physical Medicine
\\n\\t
Dieter Schoepf - University of Bonn, Germany Mental and Behavioural Disorders and Diseases of the Nervous System
\\n
\\n\\n
Hematology
\\n\\n
\\n\\t
Hesham Abd El-Dayem - National Liver Institute, Menoufeyia University, Egypt Hepatology
\\n\\t
Fayez Bahmad - Health Science Faculty of the University of Brasilia Instructor of Otology at Brasilia University Hospital Brasilia, Brazil Otorhinolaryngology
\\n\\t
Peter A. Clark - Saint Joseph's University Philadelphia, Pennsylvania, USA Bioethics
\\n\\t
Celso Pereira - Coimbra University, Coimbra, Portugal Immunology, Allergology and Rheumatology
\\n\\t
Luis Rodrigo - Asturias Central University Hospital (HUCA) School of Medicine, University of Oviedo, Oviedo, Spain Hepatology & Gastroenterology
\\n\\t
Dennis Wat - Liverpool Heart and Chest Hospital NHS Foundation Trust, UK Pulmonology
\\n
\\n\\n
Social Sciences and Humanities Board
\\n\\n
Business, Management and Economics
\\n\\n
\\n\\t
Vito Bobek - University of Applied Sciences, FH Joanneum, Graz, Austria
Joao Luis Garcia Rosa - Associate Professor Bio-inspired Computing Laboratory (BioCom) Department of Computer Science University of Sao Paulo (USP) at Sao Carlos, Brazil
\n\t
Jan Valdman - Institute of Mathematics and Biomathematics, University of South Bohemia, České Budějovice, Czech Republic Institute of Information Theory and Automation of the ASCR, Prague, Czech Republic
\n
\n\n
Earth and Planetary Science
\n\n
\n\t
Jill S. M. Coleman - Department of Geography, Ball State University, Muncie, IN, USA
\n\t
İbrahim Küçük Erciyes - Üniversitesi Department of Astronomy and Space Sciences Melikgazi, Kayseri, Turkey
\n\t
Pasquale Imperatore - Electromagnetic Environmental Sensing (IREA), Italian National Council of Research (CNR), Naples, Italy
\n\t
Mohammad Mokhtari - Director of National Center for Earthquake Prediction International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran
\n
\n\n
Engineering
\n\n
\n\t
Narottam Das - University of Southern Queensland, Australia
\n\t
Jose Ignacio Huertas - Energy and Climate Change Research Group; Instituto Tecnológico y Estudios Superiores de Monterrey, Mexico
Likun Pan - Engineering Research Center for Nanophotonics and Advanced Instrument, Ministry of Education, Department of Physics, East China Normal University, China
\n\t
Mukul Chandra Paul - Central Glass & Ceramic Research Institute Jadavpur, Kolkata, India
\n\t
Stephen E. Saddow - Electrical Engineering Department, University of South Florida, USA
\n\t
Ali Demir Sezer - Marmara University, Faculty of Pharmacy, Department of Pharmaceutical Biotechnology, İstanbul, Turkey
\n\t
Krzysztof Zboinski - Warsaw University of Technology, Faculty of Transport, Warsaw, Poland
\n
\n\n
Materials Science
\n\n
\n\t
Vadim Glebovsky - Senior Researcher, Institute of Solid State Physics, Chernogolovka, Russia Expert of the Russian Fund for Basic Research, Moscow, Russia
\n\t
Jianjun Liu - State Key Laboratory of High Performance Ceramics and Superfine Microstructure of Shanghai Institute of Ceramics, Chinese Academy of Sciences, China
\n\t
Pietro Mandracci - Department of Applied Science and Technology, Politecnico di Torino, Italy
\n\t
Waldemar Alfredo Monteiro - Instituto de Pesquisas Energéticas e Nucleares Materials Science and Technology Center (MSTC) São Paulo, SP, Brazil
Toshio Ogawa - Department of Electrical and Electronic Engineering, Shizuoka Institute of Science and Technology, Toyosawa, Fukuroi, Shizuoka, Japan
\n
\n\n
Mathematics
\n\n
\n\t
Paul Bracken - Department of Mathematics University of Texas, Edinburg, TX, USA
\n
\n\n
Nanotechnology and Nanomaterials
\n\n
\n\t
Muhammad Akhyar - Farrukh Nano-Chemistry Lab. Registrar, GC University Lahore, Pakistan
\n\t
Khan Maaz - Chinese Academy of Sciences, China & The Pakistan Institute of Nuclear Science and Technology, Pakistan
\n
\n\n
Physics
\n\n
\n\t
Izabela Naydenova - Lecturer, School of Physics Principal Investigator, IEO Centre College of Sciences and Health Dublin Institute of Technology Dublin, Ireland
\n\t
Mitsuru Nenoi - National Institute of Radiological Sciences, Japan
\n\t
Christos Volos - Physics Department, Aristotle University of Thessaloniki, Greece
\n
\n\n
Robotics
\n\n
\n\t
Alejandra Barrera - Instituto Tecnológico Autónomo de México, México
\n\t
Dusan M. Stipanovic - Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign
\n\t
Andrzej Zak - Polish Naval Academy Faculty of Navigation and Naval Weapons Institute of Naval Weapons and Computer Science, Gdynia, Poland
Petr Konvalina - Faculty of Agriculture, University of South Bohemia in České Budějovice, Czech Republic
\n
\n\n
Biochemistry, Genetics and Molecular Biology
\n\n
\n\t
Chunfa Huang - Saint Louis University, Saint Louis, USA
\n\t
Michael Kormann - University Children's Clinic Department of Pediatrics I, Pediatric Infectiology & Immunology, Translational Genomics and Gene Therapy in Pediatrics, University of Tübingen, Tübingen, Germany
\n\t
Bin WU - Ph.D. HCLD Scientific Laboratory Director, Assisted Reproductive Technology Arizona Center for Reproductive Endocrinology and Infertility Tucson, Arizona , USA
\n
\n\n
Environmental Sciences
\n\n
\n\t
Juan A. Blanco - Senior Researcher & Marie Curie Research Fellow Dep. Ciencias del Medio Natural, Universidad Publica de Navarra Campus de Arrosadia, Pamplona, Navarra, Spain
\n\t
Mikkola Heimo - University of Eastern Finland, Kuopio, Finland
\n\t
Bernardo Llamas Moya - Politechnical University of Madrid, Spain
\n\t
Toonika Rinken - Department of Environmental Chemistry, University of Tartu, Estonia
\n
\n\n
Immunology and Microbiology
\n\n
\n\t
Dharumadurai Dhanasekaran - Department of Microbiology, School of Life Sciences, Bharathidasan University, India
Isabel Gigli - Facultad de Agronomia-UNLPam, Argentina
\n\t
Milad Manafi - Department of Animal Science, Faculty of Agricultural Sciences, Malayer University, Malayer, Iran
\n\t
Rita Payan-Carreira - Universidade de Trás-os-Montes e Alto Douro, Departamento de Zootecnia, Portugal
\n
\n\n
Medicine
\n\n
\n\t
Mazen Almasri - King Abdulaziz University, Faculty of Dentistry Jeddah, Saudi Arabia Dentistry
\n\t
Craig Atwood - University of Wisconsin-Madison, USA Stem Cell Research, Tissue Engineering and Regenerative Medicine
\n\t
Oreste Capelli - Clinical Governance, Local Health Authority, Modena, Italy Public Health
\n\t
Michael Firstenberg - Assistant Professor of Surgery and Integrative Medicine NorthEast Ohio Medical University, USA & Akron City Hospital - Summa Health System, USA Surgery
\n\t
Parul Ichhpujani - MD Government Medical College & Hospital, Department of Ophthalmology, India
Amidou Samie - University of Venda, SA Infectious Diseases
\n\t
Shailendra K. Saxena - CSIR-Centre for Cellular and Molecular Biology, Hyderabad, India Infectious Diseases
\n\t
Dan T. Simionescu - Department of Bioengineering, Clemson University, Clemson SC, USA Stem Cell Research, Tissue Engineering and Regenerative Medicine
\n\t
Ke Xu - Tianjin Lung Cancer Institute Tianjin Medical University General Hospital Tianjin, China Oncology
\n
\n\n
Ophthalmology
\n\n
\n\t
Hojjat Ahmadzadehfar - University Hospital Bonn Department of Nuclear Medicine Bonn, Germany Medical Diagnostics, Engineering Technology and Telemedicine
\n\t
Miroslav Blumenberg - Department of Ronald O. Perelman Department of Dermatology; Department of Biochemistry and Molecular Pharmacology, Dermatology, NYU School of Medicine, NY, USA Dermatology
\n\t
Wilfred Bonney - University of Dundee, Scotland, UK Medical Diagnostics, Engineering Technology and Telemedicine
\n\t
Christakis Constantinides - Department of Cardiovascular Medicine University of Oxford, Oxford, UK Medical Diagnostics, Engineering Technology and Telemedicine
\n\t
Atef Mohamed Mostafa Darwish - Department of Obstetrics and Gynecology , Faculty of Medicine, Assiut University, Egypt Gynecology
\n\t
Ana Polona Mivšek - University of Ljubljana, Ljubljana, Slovenia Midwifery
\n\t
Gyula Mozsik - First Department of Medicine, Medical and Health Centre, University of Pécs, Hungary
\n\t
Shimon Rumelt - Western Galilee-Nahariya Medical Center, Nahariya, Israel Ophthalmology
\n\t
Marcelo Saad - S. Paulo Medical College of Acupuncture, SP, Brazil Complementary and Alternative Medicine
\n\t
Minoru Tomizawa - National Hospital Organization Shimoshizu Hospital, Japan Gastroenterology
\n\t
Pierre Vereecken - Centre Hospitalier Valida and Cliniques Universitaires Saint-Luc, Belgium Dermatology
\n
\n\n
Gastroenterology
\n\n
\n\t
Hany Aly - Director, Division of Newborn Services The George Washington University Hospital Washington, USA Pediatrics
\n\t
Yannis Dionyssiotis - National and Kapodistrian University of Athens, Greece Orthopedics, Rehabilitation and Physical Medicine
\n\t
Alina Gonzales- Quevedo Instituto de Neurología y Neurocirugía Havana, Cuba Mental and Behavioural Disorders and Diseases of the Nervous System
\n\t
Margarita Guenova - National Specialized Hospital for Active Treatment of Haematological Diseases, Bulgaria
\n\t
Eliska Potlukova - Clinic of Medicine, University Hospital Basel, Switzerland Edocrinology
\n\t
Raymond L. Rosales -The Royal and Pontifical University of Santo Tomas, Manila, Philippines & Metropolitan Medical Center, Manila, Philippines & St. Luke's Medical Center International Institute in Neuroscience, Quezon City, Philippines Mental and Behavioural Disorders and Diseases of the Nervous System
\n\t
Alessandro Rozim - Zorzi University of Campinas, Departamento de Ortopedia e Traumatologia, Campinas, SP, Brazil Orthopedics, Rehabilitation and Physical Medicine
\n\t
Dieter Schoepf - University of Bonn, Germany Mental and Behavioural Disorders and Diseases of the Nervous System
\n
\n\n
Hematology
\n\n
\n\t
Hesham Abd El-Dayem - National Liver Institute, Menoufeyia University, Egypt Hepatology
\n\t
Fayez Bahmad - Health Science Faculty of the University of Brasilia Instructor of Otology at Brasilia University Hospital Brasilia, Brazil Otorhinolaryngology
\n\t
Peter A. Clark - Saint Joseph's University Philadelphia, Pennsylvania, USA Bioethics
\n\t
Celso Pereira - Coimbra University, Coimbra, Portugal Immunology, Allergology and Rheumatology
\n\t
Luis Rodrigo - Asturias Central University Hospital (HUCA) School of Medicine, University of Oviedo, Oviedo, Spain Hepatology & Gastroenterology
\n\t
Dennis Wat - Liverpool Heart and Chest Hospital NHS Foundation Trust, UK Pulmonology
\n
\n\n
Social Sciences and Humanities Board
\n\n
Business, Management and Economics
\n\n
\n\t
Vito Bobek - University of Applied Sciences, FH Joanneum, Graz, Austria
Denis Erasga - De La Salle University, Phillippines
\n\t
Rosario Laratta - Associate Professor of Social Policy and Development Graduate School of Governance Studies, Meiji University, Japan
\n
\n\n
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