MIXING LAYER IN TWO-LAYER STRATIFIED FLOWS

Two nonlinear models are proposed that describe the formation and evolution of the mixing layer between two codirectional stratified fluid flows in the long-wave approximation using a three-layer representation of the flow. The models are similar in structure, and in the Boussinesq approximation, the equations of motion are written uniformly as a system of inhomogeneous conservation laws. The velocities of perturbation propagation are determined, and the concept of subcritical (supercritical) flow is formulated. Continuous and discontinuous solutions of the models are constructed. It is shown that for a sufficiently large difference between the velocities of codirectional flows, the steady-state mixing layer expands monotonically and maximum entrainment is achieved. With a decrease in the initial difference between the velocities of the flows, an oscillating steady-state solution occurs and the structure of the mixing layer becomes wavy. For one of the flow regimes, the obtained solutions are compared with experimental data.