Numerical model studies of long-period edge waves

A numerical modelling study of aspects of the generation and propagation of long-period edge waves along a continental shelf is described. The numerical model is based upon the traditional shallow-water dynamics. A scale analysis indicates that rotation, nonlinearity, and bottom friction can be ignored for the long-period edge waves in the study. Edge-wave growth rates leading to amplifications of the order of 10-15 times the amplitude of the air pressure signal are obtained for simulations of 3-5 hr of generation. The forced edge-wave phase velocity is always the same as that of the forcing, but the two wavenumbers are not necessarily matched. If there is no matching between the wavenumbers of the zero-mode forced edge wave and the forcing, higher mode edge waves are generated. The propagation characteristics of free and forced edge waves, traveling along an exponential-shaped shelf with linear variations in the width and smooth variations in the depth are described. For free waves, the frequency is conserved, whereas for forced waves, there is an adjustment in the frequency and wavenumber so that the phase speed of the edge wave is conserved. In the more general case of both free and forced waves present over a continental shelf that does have longshore variations in depth, there will be complicated changes in frequency and wavenumber because of the different modifications of the free and forced waves by the topography. This feature was found in the observations of edge waves along the southern coast of Africa reported by Shillington, which stimulated this study.