Shallow waves in density stratified shear currents

Abstract

In this paper we examine the role of nonlinearity on the evolution of surface and internal layers in density stratified fluids with steady but different shear currents in each stratified layer. As we show, when the difference between the vorticities in each layer is sufficiently large and of different signs, large amplitude nonlinear phenomena, particularly along the internal layer, emerges. Dispersive shock wave and solitary wave phenomena appear in the parameter regimes examined in this work. Our results show that jumps in density and vorticity generate strong nonlinear responses, and therefore fluid models should account for these variations in order to improve their predictive capabilities.