A note on the use of two-layer models of coastally trapped waves

Several aspects of coastally trapped wave behavior in two-layer models and in continuously stratified models are considered. A two-layer model and a uniformly stratified model are compared over a step shelf showing that, although they predict qualitatively different free-wave dispersion properties, some features of their long wave behavior are qualitatively similar. A sharp pycnocline model (a continuously stratified approximation to the two-layer model) is used to show that the presence of a vertical coastal wall (required in most two-layer models) produces substantial changes in the free-wave behavior. With a vertical coastal wall, baroclinic motions may be trapped close to the coast when the bottom there appears locally flat. Without a vertical coastal wall, such near-cost trapping apparently does not occur and the lowest mode of the sharp pycnocline model behaves more like the lowest mode of a uniformly stratified model.