Hydrodynamic performance of a viscoelastic flexible membrane floating over a submerged rubble mound breakwater under oblique wave incidence

Abstract

This study investigates the scattering of oblique water waves by a viscoelastic membrane placed over a trapezoidal rubble-mound breakwater on a sloped seabed. This study considers both wave scattering and trapping when a partially reflecting seawall is positioned downstream. The boundary value problem related to the present physical setup is solved using the hybrid boundary element method-based approach by coupling the central difference scheme with the boundary element method (BEM) to handle the second-order dynamic boundary condition of the viscoelastic floating flexible membrane. The flow through the rubble mound porous breakwater is modeled using the Sollitt and Cross ["Wave transmission through permeable breakwaters," in Coastal Engineering (ASCE, 1972), pp. 1827-1846] model, while the flow through the flexible floating viscoelastic membrane is described based on the formulation presented by Agarwal et al. [J. Fluids Struct. 129, 104167 (2024)]. According to the given model, the transmitted energy is below 30% for moderate values of the viscoelastic damping parameter of the membrane. The moderate values of the breakwater's porosity and structural size are suitable for optimal performance of the present configuration of the viscoelastic membrane-breakwater setup. Also, the wave run-up coefficient, reflected energy, and wave force acting on the partially reflecting seawall show an oscillatory pattern for numerous values of seawall coefficient and inclination angle when plotted as a function of relative spacing between the breakwater and seawall. A rubble-mound breakwater combined with a viscoelastic flexible membrane effectively reduces wave energy, creating a calmer lee side zone.