EQUILIBRIUM MODEL OF THE MIXING LAYER IN SHEAR FLOW OF A STRATIFIED FLUID

A mathematical model is proposed that describes the formation of internal hydraulic jumps and the mixing of codirectional 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 inhomogeneous conservation laws. The rate of entrainment is given by the equilibrium condition within the framework of a more general model for the evolution of the mixing layer. The velocity of propagation of disturbances and the concepts of subcritical and supercritical flows are formulated. It is shown that the model is suitable for describing flow mixing and splitting in deep-sea currents. Solutions were constructed that correspond to the flow around an obstacle with the formation of an internal hydraulic jump and a region of intense mixing. The results of numerical simulation were shown to be in good agreement with experimental data.