Flexural–gravity wave interaction with dual inverse Π-type breakwaters

Abstract

This study examines the interaction of flexural-gravity waves with dual inverse Pi-type breakwaters, which consist of two thin vertical plates extending upward from the seafloor. The goal is to analyse how the addition of these vertical plates impacts wave scattering on an ice-covered surface. The ice cover is modelled as a thin, flexible plate of uniform thickness, based on the Euler-Bernoulli beam equation. To solve the boundary value problem, a system of integral equations (Fredholm-type) is derived using mode-coupling relations, and the multi-term Galerkin method is applied. Chebyshev polynomials, weighted appropriately, are used to handle the sharp edges of the plates. This study evaluates key physical quantities, such as the reflection coefficient, transmission coefficient and horizontal wave force, under various structural configurations. To validate the findings, present results are compared with existing studies for various limiting cases. The analysis shows that adding thin plates on both sides of a conventional rectangular breakwater improves wave scattering performance. Bragg resonance is observed with variations in ice sheet thickness and submergence gap from the ice-covered surface of the breakwater. Additionally, the thickness of the ice cover plays a significant role in enhancing breakwater effectiveness.