Water Wave Scattering by Two Circular-Arc-Shaped Thin Plates With Non-Uniform Permeability

Abstract

Abstract The interaction of small amplitude water waves with a pair of circular-arc-shaped thin porous plates is studied under the assumption of linear theory. The plates are submerged at different depths in deep water and the permeability of the plates varies along the circumference of the plates. Applying Green’s integral theorem to the fundamental potential function and the scattered potential function and using the condition on the porous plates, the problem is reduced to that of solving a set of coupled integral equations for the potential difference functions across the plates. Two kernels of these integral equations are hypersingular and the other two kernels are regular. An expansion-cum-collocation method involving Chebyshev polynomials is employed to obtain the approximate solution of the integral equations. The numerical estimates for the reflection and the transmission coefficients are computed utilizing the approximate solution of the aforesaid integral equations. The numerical results for the reflection and the transmission coefficients are depicted graphically for several values of various parameters. Known results for dual symmetric circular-arc-shaped porous plates are recovered as special case.