Water wave interaction with dual asymmetric non-uniform permeable plates using integral equations

Abstract

In this study, we analyse the effect of two submerged unequal permeable plates in the propagation of water waves under the assumptions of linear water wave theory. The permeability of the plates varies along the depth of submergence of the plates. The plates are submerged in water of uniform depth. The velocity potential is expanded by using Havelock’s expansion of water wave potential. The associated boundary value problem is transformed into two coupled Fredholm type integral equations with the help of the Havelock’s inversion theorem and the porous plate condition. A multi-term Galerkin approximation in terms of Chebyshev polynomials is used to solve the vector integral equations and to obtain the numerical estimates for the reflection and the transmission coefficients. The computed numerical results for the reflection coefficient are depicted graphically for various values of several parameters. The present results are validated against the known results for the case of two identical impermeable plates and a single permeable plate submerged in water of finite depth.