Abstract
The waves excited topographically in the water surface, stratified fluids or roating fluids are reviewed with an emphasis on their nonlinear aspects. Those waves appear in different contexts but, as is well known, have many mathematical similarities. For example, the long water waves, as well as long internal waves, long inertial waves and the long Rossby waves are in general governed by the 'KdV-type' equations. An important exception occurs when the flow has uniform stratification, uniform rotation or no zonal shear. In these cases the long waves are governed by the strongly nonlinear equation derived by 'Grimshaw & Yi.' In this review, the comparisons are made between the numerical solutions of the Navier-Stokes or the quasi-geostrophic equations and the theoretical predictions, illustrating the applicabilities and the shortcomings of the existing theories.
