On nonlinear baroclinic trapped waves over abrupt topography

Abstract

Nonlinear properties of baroclinic trapped topographic waves are examined analytically and numerically. Confined topography of finite amplitude that is intersected by an isopycnal surface is considered. A weakly nonlinear theory originally developed by Dewar and Leonov [2004. Variability on steep, confined topography. Deep-Sea Research II 51, 2973–2993] is extended here to include a term neglected in the original study. The analysis shows that the waves should break backward (pseudo-eastward) and that the steepening is stronger for off-shelf initial disturbances. A modified quasigeostrophic (QG) numerical model that allows finite-amplitude topography is developed. The model is first applied to initial disturbances of moderate steepness; the results are compared with the frontal theory predictions and reasonable agreement is demonstrated, which simultaneously justifies the extended theory and verifies the new numerical procedure. The numerical model is also applied to disturbances of stronger steepness, a case where the weakly nonlinear analysis is not applicable. Further, on-shelf/off-shelf asymmetry in steepening results in different structures produced by breaking of initial disturbances of different signs: an on-shelf initial disturbance results in a filamentation of the on-shelf fluid into the off-shelf regime, whereas an off-shelf disturbance produces anticyclones, which detach and transport off-shelf fluid onto the shelf.