The Influence of Variable Rotation and Variable Depth on Barotropic Kelvin and Poinearé Waves

Abstract

Asymptotic solutions, to first order, are found for linearized, shallow water, inertia-gravity (Kelvin and Poincaré) waves in a zonal channel for two different cases in which the environment varies linearly with latitude: a beta plane (variable rotation, constant depth) and an equivalent beta plane (variable depth, constant rotation). Unlike the results for quasi-geostrophic motions, the solutions show that the environments of varying rotation and varying depth produce markedly different behaviors in the inertia-gravity waves The equivalent beta-plane environment is found to perturb the inertia-gravity waves considerably more than the beta-plane environment, but in both case long zonal waves are generally more resilient than short waves to changes in their environment. The results indicate also that the channel inertia-gravity waves respond somewhat differently than do coastal Kelvin, edge and shelf waves to the two different environments; nevertheless, similarities are also found.