The combined refraction–diffraction effect on water wave scattering by a vertical flexible–porous structure

Abstract

This article investigates the combined effect of refraction–diffraction due to bottom topography on water wave scattering by a vertical flexible–porous structure. This model problem assumes two partial configurations of the structure, such as surface-piercing and bottom-standing positions. Wave scattering is studied under the assumptions of small amplitude water wave theory and Darcy law for flow through the porous medium. The solution method uses Eigenfunction expansion of velocity potentials in the uniform bottom region and the Galerkin-Eigenfunction expansion in the variable bottom region. The structure deflection is obtained by Green’s function technique. From the porous boundary condition, a Fredholm integral equation with Green’s function as the kernel is derived, and its solution is approximated by Galerkin expansion. The associated boundary value problem is converted to a system of algebraic equations. The variations of reflection and transmission coefficients of incident waves are illustrated with parameters related to waves and flexible structure. The flexible structure effect on Bragg resonance is explored in the case of a rippled bottom. Furthermore, the effect of depth ratio on wave scattering is studied in the case of a sloping plane step-type bottom. Some striking results are derived from this model. Bragg resonance reduces with increasing thickness of flexible structure and friction of porous medium at Bragg primary frequency, whereas it increases at other frequencies. On the other hand, the resonance enhances when plate flexibility decreases and porosity increases. Further, Bragg resonance magnifies with a wide frequency band while shifting towards the left at higher incident angles. In this situation, structure deflection increases with the increased incident wave angle and diminishes for angles greater than a particular incident angle. Structure deflection increases with decreasing water-depth ratio in the presence of sloping plane bottom.