Wave interaction with a rectangular bar in the presence of two trenches

Abstract

A coupled model of wave interaction with a rectangular bar in the presence of two trenches are proposed to study in the context of linear potential theory. The physical problem is converted to a set of integral equations using the eigenfunction expansion method by matching pressure and velocity at the interface boundaries of the structure. After solving the integral equations, the analytical solutions utilize the multi-term Galerkin method involving the Gegenbauer polynomials of order 1/6 with suitable weights as basis functions. The convergence and correctness of the method are confirmed by comparing the results with the one available in the literature. Energy balance relations for the present problem are derived and used to check the accuracy of the computed results. The effects of various parameters are analyzed through different graphs for a rectangular bar in the presence of submerged rectangular trenches. It is found that the reflection coefficient is increasing with increasing the rectangular bar length, thickness, and trench thickness. It can be concluded that the physical parameters of the structure have a significant effect on the present study. Moreover, it is observed that the value of the reflection coefficient reduces for the presence of a single trench compared to the presence of multiple trenches. The present study may be useful for understanding the performance of submerged rectangular trenches to protect the rectangular bar from wave action.