Abstract
In this paper, we investigate the wave damping mechanism caused by the presence of submerged bars using the Shallow Water Equations (SWEs). We first solve these equations for the single bar case using separation of variables to obtain the analytical solution for the wave elevation over a rectangular bar wave reflector with specific heights and lengths. From the analytical solution, we derive the wave reflection and transmission coefficients and determine the optimal height and length of the bar that would give the smallest transmission coefficient. We also measure the effectiveness of the bar by comparing the amplitude of the incoming wave before and after the wave passes the submerged bar, and extend the result to the case of n-submerged bars. We then construct a numerical scheme for the SWEs based on the finite volume method on a staggered grid to simulate the propagation of a monochromatic wave as it passes over a single submerged rectangular bar. For validation, we compare the transmission coefficient values obtained from the analytical solution, numerical scheme, and experimental data. The result of this paper may be useful in wave reflector engineering and design, particularly that of rectangle-shaped wave reflectors, as it can serve as a basis for designing bar wave reflectors that reduce wave amplitudes optimally.
Highlights
Breakwaters are built near shorelines to weaken strong waves that could endanger beachfront structures
We will define the scheme to simulate wave propagation and see what happens to the wave that passes through the breakwater and how effective the breakwater is on reducing wave amplitude
We will implement the numerical scheme that has been formulated in the previous section to simulate wave propagation over rectangular submerged breakwater
Summary
Breakwaters are built near shorelines to weaken strong waves that could endanger beachfront structures. They control abrasion and erosion of the shoreline and subdue waves in the harbor so that ships can dock at the port with more ease. Breakwaters can do such protection on the shoreline due to the process of wave scattering, which allows the reduction of incoming waves’ amplitudes. In comparison to sub-aerial breakwaters, submerged structures permit the passage of some wave energy and in turn allow for circulation along the shoreline zone but at the cost of a reduced level of protection
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