Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The transmission of surface waves through a gap in a vertical barrier

D. Portera1

a1 Department of Mathematics, University of Beading


The two-dimensional configuration is considered of a fixed, semi-infinite, vertical barrier extending downwards from a fluid surface and having, at some depth, a gap of arbitrary width. A train of surface waves, incident on the barrier, is partly transmitted and partly reflected. The velocity potential of the resulting fluid motion is determined by a reduction procedure and also by an integral equation formulation. It is shown that the two methods lead to the same Riemann–Hilbert problem. Transmission and reflexion coefficients are calculated for several values of the ratio gap width/mean gap depth.

(Received June 21 1971)