Abstract

We discuss the application of the Wiener-Hopf method to linear water-wave interactions with submerged plates. As the guiding problem, the Wiener-Hopf method is used to derive an explicit expression for the reflection coefficient when a plane wave is obliquely incident upon a submerged semi-infinite porous plate in water of finite depth. Having used the Cauchy Integral Method in the factorisation, the expression does not rely on knowledge of any of the complex-valued eigenvalues or corresponding vertical eigenfunctions in the region occupied by the plate. It is shown that the Residue Calculus technique yields the same result as the Wiener-Hopf method for this problem and this is also used to derive an analytical expression for the solution of the corresponding finite-plate problem. Applications to submerged rigid plates and elastic plates are discussed as well.