A new model for surface wave propagation over undulating topography

Abstract

A new model is presented for the propagation of monochromatic surface waves over a region of arbitrary, one-dimensional bottom topography. The smoothly varying bed profile is divided into a series of shelves separated by abrupt steps. The wave fields on either side of each step are related by a “transfer matrix”, and the propagation of waves along the shelf between adjacent steps is described by a “rotation matrix”. Starting from a point where the surface wavefield is known, the step by step application of the appropriate combination of these matrices allows computation of the wavefield over the region of interest. If the individual steps are small then the transfer matrix reduces to a simpler plane-wave form, with considerable savings in computational effort. Comparisons are made with an exact potential solution for single and double steps in order to investigate the accuracy and validity of the matrix method. Finally, the model is applied to the case of wave reflection by fixed sinusoidal bottom undulations, and good agreement is found between its predictions and existing laboratory data.