Wave Transmission by Rectangular Submerged Breakwaters

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.