Internal wave shocks in continuously stratified flows with velocity shear

The eigenvalue problem for momentum-conserving internal jumps in a stratified shear flow is developed, and solutions for several classes of flows are considered. It is shown that the presence of velocity shear significantly enhances the parameter range within which energetically-permissible shock solutions exist, and that the maximum allowable amplitude is increased when the ambient state possesses a baroclinic shear. It is also shown that the presence of steep regions in the stratification allow a class of larger-amplitude solutions compared to the case with smooth density gradients.