Mixing layer in two-layer cocurrent flows of stratified fluid

Two nonlinear models are proposed that describe the formation and evolution of the mixing layer between two codirectional stratified fluid flows based on a three-layer flow representation in the long-wavelength approximation. The models are similar in structure, and in Boussinesq approximation, the equations of motion are written in a uniform way in the form of a system of inhomogeneous conservation laws. The speeds of propagation of perturbations 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 stationary mixing layer expands monotonically and the maximum entrainment mode occurs. With a decrease in the initial difference in the velocities of the cocurrent flows, an oscillating stationary solution is obtained and the structure of the mixing layer becomes wavy. For one of the flow modes, the obtained solutions are compared with experimental data.