Propagation of water waves over an infinite step

Abstract

Theoretical and experimental results are presented for the reflexion and transmission of water waves, passing over a step bottom between regions of finite and infinite depth. Two-dimensional motion is assumed, with the wave crests parallel to the step, and in the theory linearized irrotational flow is assumed. By matching ‘wavemaker’ solutions for the two regions at the cut above the step, an integral equation is derived for the horizontal velocity component on the cut. This integral equation is solved numerically and the reflexion and transmission coefficients and associated phase shifts are obtained. These results are compared with the long-wave theory and significant frequency effects are found, even for quite long waves. Experimental results are presented, which are in fair agreement with the theory.