The ANZIAM Journal

Research Article

On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions

A. Chakrabartia1

a1 Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India; e-mail: alok@math.iisc.ernet.in

Abstract

Closed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.

(Received August 07 1998)

(Revised January 13 1999)