Long wave reflection and transmission over a sloping step

Abstract

This investigation examines long wave reflection and transmission induced by a sloping step. Bellman and Kalaba's (1959) invariant imbedding is introduced to find wave reflection. An alternative method matching both the surface elevation and its surface slope of each region at the junction is applied to the determination of wave reflection and transmission. The proposed methods are compared with the accurate numerical results of Porter and Porter (2000) and those of Mei (1983) for a vertical step. The wave reflection obtained for a mildly sloping step differs significantly from the result of Mei. ne wave reflection is found to fluctuate owing to wave trapping for the mild sloping step. The height and the face slope of the step are important for determining wave reflection and transmission coefficients.