Two-Layer Equilibrium Model of Miscible Inhomogeneous Fluid Flow

Two-layer flow of a density-stratified fluid with mass transfer between the layers is considered. In the Boussinesq approximation, the equations of motion are reduced to a homogeneous quasilinear system of partial differential equations of mixed type. The flow parameters in the intermediate mixed layer are determined from the equilibrium conditions in a more general model of three-layer flow of a miscible fluid. In particular, the equilibrium conditions imply the constancy of the interlayer Richardson number in velocity-shift flows. A self-similar solution to the problem of breakdown of an arbitrary discontinuity (the lock-exchange problem) in the domain of hyperbolicity of the system under consideration is constructed. The transcritical flow regimes over a local obstacle are studied and the conditions under which the obstacle determines the upstream flow are determined. A comparison of steady-state and time-dependent solutions with the solutions obtained for the original three-layer models of miscible fluid flow is carried out.