Equilibrium model of the mixing layer in shear flow of stratified fluid

A mathematical model is proposed that describes the formation of internal hydraulic jumps and the mixing of co-directed flows of an ideal stratified fluid in the Boussinesq approximation. The model is based on a three-layer representation of the flow taking into account the entrainment of fluid from the outer layers into the intermediate vortex layer and is represented as a system of heterogeneous conservation laws. The speed of entrainment is given by the equilibrium condition within the framework of a more general model of evolution of the mixing layer. The speed of propagation of disturbances and the concepts of subcritical and supercritical flows are formulated. It is shown that the model is suitable for describing the mixing and splitting of flow in deep-sea currents. Solutions corresponding to the flow around an obstacle with the formation of an internal hydraulic jump and a region of intense mixing were constructed. The results of numerical modeling were shown to be in good agreement with experimental data.