Topographic solitary waves and groups

Abstract

We examine nonlinear topographic waves in barotropic, rigid lid models with a focus on how depth shapes can or cannot support solitary waves. Comparisons between the full equations and the quasigeostrophic system show that the conditions for vanishing nonlinearity are different and that the transition from cyclonic to anticyclonic solitary waves does not happen for the same topographic shape. For these dynamics, however, such waves only exist for a channel geometry when the long waves can become non-dispersive. We therefore examine wave groups since short waves can have an isolated cross-topographic structure. Group solitary waves are found and analyzed with a hyperbolic tangent topography representing the transition from the shelf to deep water.