Interface wave diffraction by a thin vertical barrier submerged in the lower fluid

Abstract

This paper is concerned with interface wave diffraction by a thin vertical barrier which is completely submerged in the lower fluid of two superposed infinite fluids and which extends infinitely downwards into the lower fluid. By a suitable application of Green's integral theorem in the two fluid regions, the problem is formulated in terms of a hypersingular integral equation for the difference of potential across the barrier. A numerical procedure is utilized to evaluate the reflection and transmission coefficients directly from this hypersingular integral equation. Also, an integro-differential equation formulation of the problem is considered, wherein the equation is solved approximately up to O( s), s being the ratio of the densities of the upper and lower fluids. Utilizing this approximate solution, the reflection and transmission coefficients are also obtained up to O( s). Numerical results illustrate that the reflection coefficient up to O( s) thus obtained is in good agreement with the same evaluated directly from the hypersingular integral equation for 0 < s ≤ 0.5. The advantage of the hypersingular integral equation formulation is that the reflection and transmission coefficients can be evaluated for any value of s such that 0 ≤ s < 1. It is observed that the presence of the upper fluid reduces the reflection coefficients from their exact values for a single fluid significantly.