Study on Wave Scattering by Inverse T-Type Bottom-Standing Breakwater

In the present study, the scattering of normal incident wave by (i) single and (ii) dual inverse T-type bottom standing breakwaters are analyzed under the assumption of linearized water wave theory. The objective of the current study is to compare the effectiveness of the two breakwater configurations and to provide some useful results for engineering design and application. To address the physical problem, we employ Havelock’s expansion methodology and Galerkin’s approximation technique. We utilize multi-term Galerkin approximations that incorporate ultraspherical Gegenbauer polynomial to solve the integral equations that arises in the mathematical analysis. This study demonstrates how to encounter the singularity by using ultra-spherical Gegenbauer polynomial as basis function with suitable weight. To understand how the profile geometry can affect the performance of the bottom standing inverse T-type breakwater’s main dimensions, including its profile height and width, is conducted on several hydrodynamic quantities of interests such as reflection, transmission coefficient and horizontal drift force. The numerical estimates are first validated against the data of existing studies in the literature, computed and graphically discussed for a variety of structural conditions, including the height and width of breakwater submergence. The effectiveness of both single and dual breakwaters can be assessed by examining wave reflection and horizontal drift forces, as evident in the graphical representations. This theoretical framework not only offers a promising method for addressing wave interaction with bottom-standing in-verse T-type breakwater model but also serves as a dependable reference point for complex numerical solutions of integral equations.