Wave scattering by [formula omitted]-shaped breakwaters in finite depth water

Abstract

This article illustrates surface gravity wave scattering by ⊓-shaped and inverse ⊓-shaped breakwaters in water of finite depth. The ⊓-shaped breakwater consists of a thick rectangular structure with two thin vertical plates protruding vertically downward when it is floating on the free surface. An inverse ⊓-shaped breakwater is a bottom-standing structure with two thin plates protruding upwards. The breakwater’s geometrical symmetry is used to simplify the wave scattering problems. Using Havelock expansion of water wave potentials, integral equations of Fredholm type are developed for the horizontal component of fluid velocity across the gap below or above the thin plates. The analysis presents the reflection and transmission coefficients in terms of integrals involving the unknown function of the integral equations. A Galerkin expansion with a collocation method is used to solve the integral equations approximately. The developed method produces the known numerical results for a rectangular breakwater without thin plates. The ⊓-shaped breakwater shows lower wave transmission than a traditional rectangular breakwater. Furthermore, increasing plate length makes the wave transmission even less. Fluid velocity is high in the vicinity of plate edge. By the present method, it is shown that the ⊓-shaped breakwaters offer higher reflection and lower transmission. Thus, attaching thin plates to a traditional rectangular breakwater enhances its performance in wave scattering.