The study of water wave scattering by series of submerged elastic scatterers

Abstract

A submerged flexible breakwater can be used to control waves in shallow water as an advanced alternative to traditional rigid submerged structures. Submerged flexible breakwaters not only cost less to build than conventional submerged breakwaters but also allow ships and marine life to bypass them if they are deep enough. These marine structures decrease the intensity of the shock wave and prevent standing waves from forming. We present a solution for transmission/reflection using a series of submerged identical elastic scatterers. Scattering and transfer matrices will be used to compute the transmission and reflection coefficients for N-submerged elastic scatterers. The behavior of the transmission for different values of physical parameters such as submergence depth, length of the scatterer, the gap between two successive scatterers, stiffness of the scatterer, and the number of submerged elastic scatterers is given. In doing so, we can achieve the frequencies and the incident amplitudes at which these submerged elastic scatterers can be effectively used as breakwaters in water of finite depth. We have looked at the transmission and reflection behaviors for a range of physical parameter values, such as the submergence depth, the length of the scatterer, the spacing between successive scatterers, the stiffness of the elastic scatterer, and the number of scatterers over a wide frequency range. We have given a spectrum of frequencies for which, given certain values of physical parameters, we can achieve zero transmission. Furthermore, even at high frequencies, we have demonstrated an incidence amplitude range for which zero propagation of transmission is feasible.