The authors have developed models for predicting beach changes applicable to various problems on real coasts. One of them is the contour-line-change model to predict long-term beach changes caused by the imbalance in longshore sand transport, which is a kind of N-line model. Because the calculation of the nearshore current is not needed in this model, and the computational load is small, it has an advantage in the prediction of long-term topographic changes on an extensive coast. However, the handling of boundary conditions becomes difficult when offshore coastal structures are constructed in a complicated manner, and in this regard the so-called 3D model has an advantage. Taking this point into account, the authors developed a morphodynamic model (BG model) by applying the concept of the equilibrium slope and the energetics approach, in which depth changes on 2D horizontal grids are calculated.Go to the book
Part of the book: Numerical Simulations
Part of the book: Numerical Simulation
Part of the book: Computational and Numerical Simulations
In a slender water body with a large aspect ratio, the angle of wind waves relative to the direction normal to the shoreline may exceed 45°, resulting in the emergence of cuspate forelands and the segmentation of the water body. The BG model was used to predict the segmentation of a rectangular water body by wind waves when the probability of occurrence of the wind direction is given by a circular or elliptic distribution, and the segmentation of a rectangular water body into a circular or elliptic lake was predicted in each case. The segmentation of a shallow water body with a triangular or crescent shape was also predicted together with the prediction of lakeshore changes when a rocky or sandy island exists in a circular lake.
Part of the book: Applications in Water Systems Management and Modeling
Beach changes on a coast subject to waves and seaward or shoreward strong currents were predicted using the Type 7 and 8 BG models. The formation of an ebb tidal delta subject to strong ebb tidal currents was studied first, taking the Imagire-guchi inlet connecting Lake Hamana with the Pacific Ocean as an example, and the long-term evolution of the tidal inlet was investigated using the bathymetric survey data. Then, the formation of a dynamically stable ebb tidal delta was predicted. Regarding the beach changes on a coast subject to waves and shoreward strong currents, the Type 8 was applied to the Kaike coast, where an artificial reef was constructed in place of a detached breakwater, resulting in the occurrence of strong shoreward currents over the artificial reef. A stable cuspate foreland behind a detached breakwater disappeared after the conversion of a detached breakwater into an artificial reef, suggesting that the artificial reef was less effective in sand deposition effect than the detached breakwater. Such beach changes were numerically predicted.
Beach changes related to human activities, such as the effect of construction of groynes and detached breakwaters on a coast with prevailing longshore sand transport, and offshore sand mining, which have engineering importance, were predicted using the Types 1 and 2 BG model. When a long port breakwater is extended, a large wave-shelter zone is formed and dominant longshore sand transport is induced from outside to inside the wave-shelter zone, resulting erosion outside the wave-shelter zone and accretion inside the wave-shelter zone. These beach changes were also predicted using the Type 2 BG model with the evaluation of the effect of a jetty extended at the port entrance to reduce sand deposition inside the port.
The formation of land-tied islands as a result of the extension of a cuspate foreland, when waves were incident to several islands composed of sand from two opposite directions, was first investigated, taking a land-tied island offshore of Shodoshima Island in the Seto Inland Sea, Japan, as an example, and their topographic changes were predicted using the Type 5 BG model. Then, the interaction among multiple circular sandy islands on flat shallow seabed owing to waves was investigated, taking the islands in Hingham Bay near Boston Harbor as an example. On the basis of this example, topographic changes were also predicted using the Type 5 BG model.
The segmentation and merging of elongated shallow water body with a large aspect ratio by wind waves were predicted using the Type 6 BG model. The deformation of a circular lake by wind waves was also studied when a straight seawall cutting a part of the water body was constructed in a lake for land reclamation, together with the investigation on the effect of the construction of detached breakwaters to the surrounding lakeshore. Finally, the formation of oriented lakes, groups of lake basins with a common long-axis orientation found in vast areas of the Arctic Coastal Plain, was predicted using the Type 6 BG model.
The formation of a sand spit and bay barrier was predicted using the BG model, covering three topics: (1) formation of a bay barrier in flat shallow sea and merging of bay mouth sand spits (Section 2), (2) elongation of a sand spit on a seabed with different water depths (Section 3), and (3) deformation of a sandbar formed at the tip of the Futtsu cuspate foreland owing to a tsunami which propagated into Tokyo Bay after the Great East Japan Earthquake on March 11, 2011 (Section 4). The Type 5 BG model was employed in Section 2, and Type 3 BG model in Sections 3 and 4.
Eight types of the BG models are introduced in this chapter. The Type 1 is a model using wave parameters at the breaking point. In the Type 2, the effect of longshore sand transport due to the effect of the longshore gradient of breaker height is included with an additional term given by Ozasa and Brampton. In the Type 3, the intensity of sand transport P is assumed to be proportional to the third power of the amplitude of the bottom oscillatory velocity um due to waves, and in the Type 4, P is given by the wave energy dissipation rate due to wave breaking at a local point. In the Type 5, wave power is calculated using the coordinate system different from that for the calculation of beach changes to predict the topographic changes of an island or a cuspate foreland in a shallow water body under the action of waves randomly incident from every direction. In the Type 6, the height of wind waves is predicted using Wilson’s formula using the wind fetch distance and wind velocity, and then sand transport fluxes are calculated. The Type 7 is a model for predicting the formation of the ebb-tidal delta under the combined effect of waves and ebb-tidal currents with an analogy of the velocity distribution of ebb-tidal currents to the wave diffraction coefficient, which can be calculated by the angular spreading method for irregular waves. In the Type 8, the effect of the nearshore currents induced by forced wave breaking is incorporated into the model by calculating the nearshore currents, taking both the wave field and the current velocity at a local point into account.