Diffraction of water waves by slender barriers

Abstract

Linear water-wave theory is used to tackle the problem of diffraction of surface waves by a fixed slender barrier in deep water for two basic situations: (i) when the barrier is partially immersed, and (ii) when the barrier is completely submerged. Analytical expressions for the first-order corrections to the reflection and transmission coefficients are derived in terms of integrals involving the shape functions describing the two sides of the slender barrier. A relatively straightforward perturbation technique is used along with the application of Green's theorem in the fluid region. Corresponding analytical expressions representing the reflection and transmission coefficients are also deduced, (i) for a nearly vertical barrier and (ii) for a vertically symmetric slender barrier, as special cases for both the problems. For a nearly vertical barrier it is observed, analytically, that there is no first-order correction to the transmitted wave at any frequency. Computations for the reflection and transmission coefficients up to O(ɛ), where ɛ; is a small nondimensional number, are also performed and presented here.