INTERFACE WAVE DIFFRACTION BY A THIN VERTICAL BARRIER SUBMERGED IN THE LOWER FLUID

This paper is concerned with interface wave diffraction by a thin vert ical barrier which is completely submerged in the lower fluid of two s uperposed 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 hyp ersingular integral equation for the difference of potential across th e barrier. A numerical procedure is utilized to evaluate the reflectio n and transmission coefficients directly from this hypersingular integ ral equation. Also, an integro-differential equation formulation of th e 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 transm ission coefficients are also obtained up to O(s). Numerical results il lustrate that the reflection coefficient up to O(s) thus obtained is i n good agreement with the same evaluated directly from the hypersingul ar integral equation for 0 < s less than or equal to 0.5. The advantag e of the hypersingular integral equation formulation is that the refle ction and transmission coefficients can be evaluated for any value of s such that 0 less than or equal to s < 1. It is observed that the pre sence of the upper fluid reduces the reflection coefficients from thei r exact values for a single fluid significantly.