Parameters common to all four examples.
\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 191 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 261 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
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In this chapter we consider the full film regime, i.e. when the surfaces are fully separated by the lubricant. The pressure and the velocity field can be modelled using the Navier-Stokes equations and the continuity equation. However, in real applications the distance between the surfaces,
where
A fluid cannot sustain large tensile stress and it is known that when the pressure becomes too low the continuous film will rupture and air bubbles will be formed. This phenomenon is known as cavitation and has a huge impact on the hydrodynamic performance. In areas where cavitation takes place the pressure is usually treated as constant and is assumed to have the same value as the saturated vapour pressure, i.e., the pressure at which cavitation starts. This is commonly referred to as the cavitation pressure, here denoted by
The common practice in the field is to build mathematical models that consider hydrodynamic cavitation based on the Reynolds equation (1). These models rests on the assumption that the pressure can be regarded as constant in areas where cavitation takes place and this constant level of pressure is typically also assumed to be the saturated vapour pressure, i.e., the pressure at which cavitation starts. The most important pioneering works are the papers presenting the Jakobsson-Floberg-Olsson (JFO) cavitation boundary conditions [3–5], Elrod’s work [6] comprising these boundary conditions in one universal equation for the unknown pressure (or saturation) and its corresponding finite difference scheme and then Vijayaraghavan’s generalization [7] of Elrod’s results. These results have been frequently used to study the effects of cavitation in real applications and they have also been subject for many further generalizations.
\nIn Elrod’s approach the lubricant is treated as incompressible while Vijayaraghavan and Keith assumed that the relation between the density and the pressure is of the form
\nwhere
A significant progress in mathematical modeling of cavitation in hydrodynamic lubrication was recently presented by Giacopini et al. [12]. They reformulated the model presented in [9, 10] for incompressible fluids. The model in [9, 10] includes two unknowns, namely the pressure and the saturation (or density) while the unknowns in the reformulation are the pressure and a new unknown variable related to the saturation. The major advantage with the reformulation is that the two unknowns are complementary, i.e. their product is zero, in the whole domain. This implies that the discretized system of equations becomes a linear complementarity problem (LCP) which can be readily solved by standard numerical methods as e.g. the Lemke’s pivoting algorithm [13, 14]. The idea of using complementarity was further developed by Bertocci et al. [15]. They present a very comprehensive cavitation model, which discretized assumes the form of a nonlinear complementarity problem (NLCP).
\nIn the work by Almqvist et al. [14], a new approach for modeling cavitation was presented. The model was derived by first considering how the mass flow is influenced by cavitation and thereafter using the law of conservation of mass. This immediately leads to a linear complementarity problem formulation. This is in contrast to the approach in [12, 15] where the pressure–density relationship is inserted directly into the Reynolds equation, thereafter it is necessary to argue for that certain terms can be cancelled before they arrive at a complementarity formulation. Moreover, in addition to [12] the approach in Almqvist et al. [14] also covers compressible fluids. In the particular case when the pressure–density relationship is as in (2), a change of variables was introduced which transforms the problem such that the discrete formulation is an LCP.
\nThis chapter extends the mathematical modelling presented in [14] to also include more general pressure–density relationships and allow the viscosity and film thickness to depend on the pressure. In particular this means that the model can be used to efficiently study elastohydrodynamic lubrication where cavitation is present. To demonstrate the applicability and evaluate the proposed model and the associated numerical solution method, four model problems are analysed.
\nIn this section, a model considering cavitation in thin film flow between two surfaces in relative motion is developed. The flow is regarded as compressible, the viscosity can be shear rate and pressure dependent (non-Newtonian and piezo-viscous) and elastic deformation of the contacting surfaces can be considered.
\nLet us start by defining the (three dimensional) fluid domain Ω between the two lubricated surfaces
The fluid domain Ω is schematically illustrated in Figure 1 (left).
\nThe hydrodynamic pressures that develop may be large enough to deform the surfaces. This implies that the film thickness
Schematic illustration of the original (left) and the transformed (right) domain.
The classical thin film approximation, presented in e.g. [1, p. 147], can be obtained by employing the scaling\n
More precisely, using the fact that
where
In the following, the viscosity is assumed to be on the form
As pointed out above, Ω varies with time. In order to simplify the analysis, a transformation of the height coordinate
then the corresponding solution domain becomes
\nirrespectively of the shape of the surfaces
Integrating Eq. (8) twice with respect to
where\n
and
The flow is regarded as compressible according to the “arbitrary” pressure–density relation
\nThe function
With the aim set to derive an Reynolds type of equation for the pressure in the lubricant, the analysis continues by first formulating an expression for the mass flow and thereafter requiring continuity of the mass flow. By using Eq. (9) for the velocity field and Eq. (11) the mass flow,
where
With this expression for
In order to incorporate the effect of cavitation, we assume that the following holds. In the full film zones, the pressure is larger than the cavitation pressure and the density is expressed by Eq. (11). In the cavitation zones, the pressure equals the cavitation pressure and the density is interpreted as degree of saturation
Note that both
For computational purposes it is beneficial to introduce a change of variables
and\n
In this notation, Eq. (16) becomes\n
Now, because of complementarity, this piecewise definition of
which then leads to the following expression for the mass flow\n
Preservation of mass flow is ensured by inserting Eq. (21) and Eq. (20) into the continuity equation Eq. (15), which leads to the following mass preserving cavitation model:\n
The system in Eq. (22) can be solved numerically by the LCP-based solution procedure described in Section 3. When the solution
In this section, we present a numerical solution procedure for the cavitation model Eq. (22) such that the standard theory for linear complementary problems (LCP) can be applied.
\nLet us start by introducing the notation
\nwhile keeping in mind that
A spatial finite difference discretization of the problem Eq. (23) can be obtained by dividing the domain into a uniform rectangular grid with
Since the finite difference approximations of the partial derivatives w.r.t.
In order to present the finite differences we introduce the notation
\nand the approximation\n
In this notation, the first term in the right hand side of Eq. (23) becomes:\n
The upwind discretization of the second term reads
\nBy using Eq. (24), Eq. (25) and the corresponding finite difference approximations of the partial derivatives w.r.t.
together with the conditions
\nSince
where the vector
To fully discretize the problem at hand several approaches can be applied. For instance, first order forward (explicit) or backward (implicit) Euler, the second order implicit Crank-Nicolson method.
\nIn this section, the numerical solution procedure, for the cavitation model in Eq. (22), developed in Section 3, is examined by considering four different one-dimensional slider bearing examples. In all four examples, only the lower surface is moving, i.e.
where\n
where
The third example considers a double parabolic slider, which in addition to the single parabolic slider, exhibits reformation and highlight that mass is conserved.
\nThe fourth and last example considers a quadruple parabolic slider bearing. The reason for choosing this configuration is to test the hypothesis that an elastically deformable bearing, in general, does not generate more film than the corresponding rigid one.
\nIn all examples, the initial (undeformed) bearing geometry consists of 1, 2 or 4 parabolic parts. These bearing geometries,
where\n
In Table 1, parameters common to all four examples are listed. These are the bearing parameters
In this example, a model problem with rigid surfaces and two different Newtonian lubricants is considered in order to compare with previous results presented in [8]. Indeed, a single parabolic slider bearing of length
is considered here. Two different Newtonian lubricants are studied, one which obeys the constant bulk modulus pressure–density relationship;
\nwhile the other one obeys the Dowson-Higginson pressure–density relationship;
\nThe parameters for the two different lubricants are given in Table 2. As in [8], the case with constant bulk modulus,
76.2 mm | \n25.4 μm | \n4.57 m/s | \n117 kN/m | \n100 kPa | \n0.039 Pas | \n1.0001 | \n1 | \n
Parameters common to all four examples.
0.069 GPa | \n2.22 GPa | \n1.66 | \n
Parameters specific to Example 1.
Film thickness (left) and pressure distributions (right) for two lubricants obeying constant bulk modulus
This example extends the previous one, by including elastic deformation of the bearing surfaces. To illustrate the effect of surface deformation, the combined elastic modulus,
3.34 GPa | \n0.3 | \n210 GPa | \n
Parameters specific to Examples 2, 3 and 4.
In Figure 3, the film thickness
Film thickness (left) and pressure distributions (right) for the rigid and the elastic single parabolic slider bearings in Example 2.
The only difference between the problem studied in this example and the one studied in Example 2, is that the bearing geometry now corresponds to a double parabolic slider,
The film thickness
Film thickness (left) and pressure distributions (right) for the rigid and the elastic double parabolic slider bearings in Example 3.
Also, as in Example 1, the bearing with elastic surfaces generates a thicker lubricant film, a smaller zone of cavitation and a lower maximum pressure.
\nThe only difference between this example and Examples 2 and 3, is that the bearing geometry now corresponds to a quadruple parabolic slider,
Film thickness (left) and pressure distributions (right) for the rigid and the elastic quadruple parabolic slider bearings in Example 4.
A new mathematical model for thin film lubrication has been derived. The model is quite general, e.g., it accounts for lubricant compressibility, cavitation, pressure dependent viscosity, non-Newtonian rheology and elastic deformation of the surfaces. The main novelty of the model is that cavitation of a compressible fluid is considered via a formulation of the mass flow, which ultimately results in a complementarity problem. Hence, standard methods developed for linear complementarity problems can be used in the numerical solution procedure. The model’s applicability has been demonstrated in several numerical examples.
\nThe authors want to acknowledge The Swedish Research Council (VR) for the financial support through the grants no. 2013-4978 and 2014-4894.
\nIn the latest years, the Sun-Earth environment is studied to explain observed physical phenomena in the context of space weather/climate, such as climate changes. It is well known that the Sun continuously transfers its energy to the Earth’s environment through radiation and solar wind (SW). Although the Sun’s radiation represents the main source affecting the Earth’s atmosphere, the SW energy plays an important role during high geomagnetic activity time intervals [1]. On this regard, the magnetosphere-ionosphere represents a complex system able to partially convert SW impacting energy through nonlinearly related physical processes. Such effects are more evident at high latitudes where reconnection processes between interplanetary magnetic field (IMF), carried out by the solar wind, and magnetospheric field occur, making the polar cap an important laboratory to study the SW-atmosphere interactions. Solar wind-driven electrodynamic processes and ultralow frequency (ULF, 1 mHz–5 Hz) waves seem to lead to both diffusion and precipitation processes of energetic electrons in the outer radiation belts, leading also to chemical [2] and microphysical [3] processes in the atmosphere, characterized by different timescales.
The longer-term response, characterized by timescales of several weeks, is usually attributed to the odd nitrogen (NOx) production, due to precipitating energetic electrons, in the mesosphere and lower thermosphere. During the polar winter, NOx can live long enough to be transported downward into the stratosphere where it chemically perturbs the ozone distribution, altering the radiative balance in that region of the atmosphere.
This can in turn affect the overall circulation in the stratosphere, and such changes can propagate to the surface level, eventually leading to detectable changes in surface air temperatures, through dynamical coupling processes occurring on timescales of several weeks (e.g., [2, 4, 5, 6]).
Conversely, the shorter-time response (<1 day) of the atmosphere to the SW-magnetosphere coupling processes is probably related to changes in the atmospheric electrodynamics. It can be attributed to electric conductivity variations in the lower atmosphere by ionization mechanisms and/or to changes of the polar cap electric potential induced by SW perturbations [7]. The consequent modulation of the current density which flows from the upper boundary (being as low as 60 km, [8]) through the troposphere to the ground in the global electric circuit (GEC) [3, 9, 10, 11] could influence cloud formation through the release of latent heat, which in turn can affect atmospheric dynamics [12].
This work represents a review of our investigations on the experimental observation of the possible short (within ∼1 day) timescale response of the atmosphere to the SW dynamics, observed during 2003–2010, which correspond to the solar cycle 23 and the beginning of solar cycle 24. We analyzed the geomagnetic field variations monitored at the Mario Zucchelli station, at Terra Nova Bay (TNB, AACGM latitude
The ERA-Interim is a global atmospheric reanalysis dataset, continuously updated in real time (see [13] and references therein). Global atmospheric and surface parameters from 1 January 1979 are available from the surface up to 0.1 hPa as atmospheric fields on model levels and pressure levels, with a temporal resolution of 6 h, and as surface fields with a temporal resolution of 3 h. The data assimilation system used to produce ERA-Interim is based on a 2006 release of the ECMWF Integrated Forecast Model (IFS Cy31r2). The MACC dataset is a global reanalysis dataset of atmospheric composition data, produced by assimilating satellite data into a global model and data assimilation system (see [14] and references therein). The system includes a four-dimensional variational analysis (4D-Var) with a temporal resolution of 12 h analysis window. The ERA-Interim and MACC data, at 1 day resolution used for our studies, have been retrieved from the Meteorological Archival and Retrieval System at ECMWF.
Solar wind parameters and interplanetary magnetic field are monitored by using OMNI data, time-shifted to the bow shock nose (i.e., the subsolar position of the supersonic-to-subsonic transition regions) and collected on CDAWeb (http://cdaweb.gsfc.nasa.gov). Geomagnetic activity was monitored by using a triaxial search-coil magnetometer data, recorded at TNB, at a sampling rate of 1 s.
The atmospheric parameters must be whitened to filter the longer period components (essentially 1 year and 6 months), which would obscure the weak effects produced by the ULF geomagnetic activity [15].
This review is structured as follows: in Section 2, we shortly introduce the interactions occurring between ULF waves and the energetic electrons in the outer radiation belt, leading particle precipitations, as well as polar cap potential difference related with SW parameters; in Section 3, we present the experimental evidence of SW effects on the atmospheric parameters in Antarctica at stratospheric and tropospheric heights; finally, in Section 4, we discuss the estimated timescale response of atmospheric parameters and the possible physical processes involved in SW-atmosphere coupling processes. For greater clarity, we described data analysis and methods in each section.
The estimation of the Earth’s surface temperature and lower atmosphere energy budget significantly changes due to small amount, distribution, or radiative properties of clouds [16]: therefore, they represent one of the largest sources of uncertainty in predictions of climate change [17]. Even small atmospheric electrical modulations can affect aerosol nucleation processes and cloud condensation nuclei production in troposphere and thus modify cloud properties. In this regard, the polar cap electrodynamics and the energetic particle precipitation seem to be important SW-atmosphere coupling mechanisms, responsible for atmospheric changes on timescales from several weeks to days. It is also known that a global electric current flows in the global electric circuit. It is generated mainly by charge separation in clouds at the tropics and maintains the global ionosphere at a potential of about 250 kV. Variations above and below this value occur in the high-latitude regions due to SW-magnetosphere-ionosphere coupling processes. In this section, we briefly discuss the solar wind-magnetosphere coupling processes, which could produce observable effects in the stratospheric and tropospheric dynamics due to energetic particle precipitation from the outer radiation belt, as well as to the polar cap electrodynamics at high latitudes.
ULF magnetohydrodynamic waves received particular attention in the past decades [18, 19, 20, 21, 22, 23], since they provide a convenient probe of the magnetosphere, by means of ground [24, 25, 26] and/or satellites magnetic field measurements [22, 27, 28, 29, 30] as well as inspect ground conductivity [31, 32, 33].
Generated by a variety of instabilities, ULF waves transport energy throughout the magnetosphere and are observed on the ground as continuous pulsations (Pc, Table 1). They can play important roles in the energization and loss of radiation belt particles (see [34] for a review). In particular, ULF waves can interact with the relativistic electrons (>300 keV) magnetically trapped in the radiation belts (
ULF waves | Magnetically trapped particles | ||||
---|---|---|---|---|---|
Pulsation type | Frequency range (mHz) | Period range (s) | Characteristic periodicity (s) | Motion type | |
Electrons | Protons | ||||
2–7 | 102 | ||||
Pc4 | 7–22 | 45–150 | — | — | — |
Pc3 | 22–100 | 10–45 | — | — | — |
Pc2 | 100–200 | 5–10 | — | — | — |
200–5000 | 100 | ||||
— | — | — | 10−3–10−4 | 10−1–10−2 | Gyro |
ULF wave classification and the characteristic timescales for the three types of trapped particle motion (see also [37]).
Periodicity correspondence between relativistic electrons and ULF waves is marked in bold.
In particular, wave-particle interactions are theoretically predicted [37, 38] because drift and bounce motion frequencies of trapped electrons are in the Pc5 (1–7 mHz) and Pc1-2 (100 mHz–5 Hz) frequency range, respectively. Experimental evidence confirms diffusion/acceleration of energetic electrons by Pc5 magnetospheric waves [39, 40, 41, 42] and their precipitations after pitch angle scattering, due to gyro-resonant interaction with electromagnetic ion cyclotron (EMIC) waves [38, 39, 40, 41]. Such waves are in the Pc1-2 frequency range and are generated at the magnetic equator by unstable distributions of ring current ions during geomagnetic storms [43]. Moreover, recent investigations show that Pc5 waves have their origin also in the leading edge of the corotating interaction regions (CIR) [42], while the origin of the Pc1-2 waves, observed at ∼80° latitude, appears to be due to substorm/storm-related instabilities and, in the dayside, to solar wind compressions of the magnetopause [44]. After conversion into Alfvén (shear) waves, ULF waves propagate along the geomagnetic field lines and can be observed on the ground at high latitudes [45, 46]. An example of energetic electron flux enhancements observed at geosynchronous orbit (
(Top) The relativistic electron flux (>600 keV) measured by GOES 12 satellite at geosynchronous orbit (red) and the geomagnetic power at TNB (black). (Bottom) The cross-correlation of the >600 keV (solid) and >2 MeV (dashed) electron flux with the Pc5 power at TNB, at low latitude station of L’Aquila AQU, and at GOES 12 during 2007–2008, together with the 95% confidence levels (dashed, gray lines). Figure adapted from [
As discussed by Tinsley and Yu [48], the galactic cosmic rays (GCR) flux is responsible for almost all the production of ionization below 15 km of altitude, which determines the conductivity in that region and at high latitudes. However, the MeV electrons and their associated X-rays produce ionization in the stratosphere and higher troposphere, which can affect the local conductivity (see also [7]). Moreover, due to electric potential difference between the ionospheric layer and the ground, a vertical current density is present:
It is directed along the stratosphere-troposphere-ground direction
In particular, the
An example of polar cap electric potential in the southern hemisphere is show in Figure 2, obtained using the Weimer [50, 51] ionospheric electrodynamic model. In this example, we assigned values of ±5 nT for
Computed polar cap electric potential, obtained using Weimer [
In their study, Francia et al. [15] examined surface air temperature measured at the automatic weather station ENEIDE, located at TNB, during 2007–2008, while signatures of ULF activity and polar cap potential difference were found by [54] in the stratosphere and troposphere, using the ERA-Interim reanalysis dataset.
Figure 3 shows the global wavelet (GW), i.e., the time-averaged wavelet [55, 56], separately for summer and winter months, of Pc5 and Pc1-2 powers at TNB and of the polar cap potential difference
The normalized global wavelet (GW) analysis during the summer (first column) and winter (second column) in 2007 (top panels); the GW, normalized to the corresponding variances, of the ULF activity indexes logPc5 and logPc1-2 at TNB, and of
Common power peaks emerge at ∼27 days, the Sun synodic rotation period, and its first subharmonics (13.5 and 9 days), in the SW-related parameter
Time averaged cross-wavelet amplitude (
In can be seen from Figure 4 that the correspondence at 27 days is high and statistically significant in both the troposphere and the stratosphere during winter months, while at 13.5 days it is restricted to
Analyzing the tropospheric temperature, specific humidity
The results, shown in Figure 5, revealed a clear correspondence between Pc1-2 and variations in temperature, specific humidity, and cloud cover. The most significant correspondence is found at latitudes higher than 85°S in both
(Top and middle panels) Composites of the zonal mean of temperature
Regarding the cloud cover (zonal mean) composite averages, computed at low (LCC,
As discussed in the Introduction, GEC affects atmospheric parameters, such as cloud cover through several proposed microphysical processes (e.g., [3, 10, 48]) able to produce changes in the atmospheric parameters, such as temperature. In particular, the accumulation of charge on droplets and aerosol particles, most importantly the interstitial cloud condensation nuclei (CCN) and ice-forming nuclei (IFN), directly affects scavenging rates.
Scavenging is due to collisions between the nuclei and droplets, entailing size-dependent collection of nuclei and changes in their size distribution and overall concentration. It affects a number of microphysical processes, which cause changes in macroscopic cloud properties and in turn partitioning of energy flow in the system. In particular, the charge can increase or decrease the scavenging rates, depending on size, changing the concentrations and size distributions. Size distribution changes in CCN produce size distribution changes in droplets, affecting coagulation, precipitation, latent heat transfer, and cloud cover. Scavenging of ice-forming nuclei by supercooled droplets promotes contact ice nucleation, releasing latent heat. The latent heat changes cause storm invigoration [59] and in winter storms can cause changes in the amplitude of Rossby waves and blocking. Since the typical lifetime of CCN in an air mass can be up to 10 days, the change in their properties can affect also later cycle of evaporation/condensation, flux of latent heat, and the amount of water vapor released into the troposphere.
Figure 6 shows the results of superposed epoch analysis (SEA) conducted by [57] on
Composites of the zonal mean of temperature
Timescales are important in order to discriminate the involved physical processes in the SW-atmosphere coupling. In their pioneering work, Francia et al. [15] found that, during 2007 and 2008, the ULF activity, in both Pc1-2 and Pc5 frequency ranges, is correlated with the surface air temperature with different delays. Their results, shown in Figure 7a, indicate that the temperature is significantly correlated with the Pc1-2 power at a time lag of 1 day. Although lower, the correlation with the Pc5 power is also significant, reaching the maximum value when the temperature is delayed by 3 days with respect to the Pc5 power.
(a) The cross-correlation between the Pc5 and the Pc1-2 power and the surface air temperature, at TNB, at different time lags
In the meanwhile, Regi et al. [57] computed the cross-correlation between high cloud cover (HCC,
In this work we presented a short review of our experimental results regarding the possible relationship between SW and atmospheric parameters at high latitude, in Antarctica, at Terra Nova Bay. Examining possible relationship between geomagnetic activity in the Pc1-2 and Pc5 frequency range and the polar cap potential difference with stratospheric and tropospheric parameters, the results provided in [54] can be summarized as follows:
Common power peaks emerge at ∼27 days, the synodic Sun rotation period, and its first subharmonics (13.5 and 9 days), in the polar cap potential difference
The correspondence is more evident during winter, when solar radiation-driven processes are absent.
Around the tropopause, approximately at 8 km, the correspondence is low, and in the stratosphere it appears mostly at the 27 day periodicity.
Further investigations [57] at tropospheric heights at high latitudes indicate that SW-driven electrodynamic processes and energetic particle precipitation related with enhancement of Pc1-2 activity can affect tropospheric temperature, specific humidity, and cloud cover. The response is quick (within ∼1 day) at ground and in the troposphere. These results suggest that the electrodynamics modulate the physical properties of clouds, probably through electron scavenging microphysical mechanism. It is a matter of fact that electron scavenging is strongly dependent on vertical tropospheric-stratospheric conductivity variations, due to energetic particle precipitation driven by ULF waves, and on the vertical electric current, modulated by polar cap potential, associated to SW-magnetosphere reconnection processes. More recently, evidence of an SW signature in the mesosphere [62] has been published, indicating that the SW can affect the atmosphere through the whole atmospheric column. As discussed by [63], the processes involved in each atmospheric layer are almost certainly different, and transport phenomena could be important.
Our conclusions are supported by the observed short (<1–2 days) delay response in the atmospheric parameters at troposphere altitudes and at ground with respect to the much longer delay expected for chemical mechanism [15, 57]. However, this matter should be further investigated as underlined by [63] in particular through the examination of the time delays at stratospheric and mesospheric altitudes and at lower latitudes; the study of the dependence on different interplanetary conditions might be also useful for a more deep understanding of the atmosphere response to the SW.
The authors acknowledge J. H. King and N. Papatashvilli at NASA and CDAWeb for solar wind data (http://cdaweb.gsfc.nasa.gov) and Daniel Weimer at Space Science Center for Space Science and Engineering Research (Virginia Tech) who provided the ionospheric electrodynamic model. The authors would also like to thank the MACC and ERA-Interim project data provider. The reanalysis data were provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) and can be downloaded from the ECMWF Data Server (http://apps.ecmwf.int/datasets). Measurements of the geomagnetic field fluctuations at Terra Nova Bay are supported by the Italian PNRA (Programma Nazionale di Ricerche in Antartide, PdR2013/B2.09).
The authors declare that they are not competing interests.
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