Nonlinear oscillatory flow regimes with mixing in a two-layer fluid under a rigid lid

<title>Abstract</title> <p>We propose a nonlinear long-wave model describing the propagation of internal waves and turbulent mixing in a two-layer fluid under a rigid lid in the Boussinesq approximation. This model allows for the inclusion of non-hydrostatic effects in the lower layer, density non-uniformity and flow vorticity in the upper layer, as well as mixing at the interface. Periodic and damped oscillating stationary solutions are constructed, simulating finite-amplitude internal waves at the interface caused by the inflow of light fluid into the upper layer. For this class of solutions, the ratio of the wave amplitude to its wavelength is small, and therefore non-hydrostatic effects are rather weak. We propose an efficient numerical algorithm for simulating the non-stationary evolution of internal waves within the framework of the considered model. We also show that setting a constant fluid inflow in the upper layer at the inlet section leads to the formation of a stationary oscillatory interface during the unsteady evolution of the flow.</p>