Large-amplitude internal waves and turbulent mixing in three-layer flows under a rigid lid

Abstract

We consider a nonlinear long-wave Boussinesq-type model describing the propagation of breaking internal solitary waves in a three-layer flow between two rigid boundaries. The Green–Naghdi-type equations govern the fluid flow in the top and bottom homogeneous layers. In the intermediate hydrostatic layer, the fluid is non-homogeneous, and its flow is described by the depth-averaged shallow water equations for shear flows. The velocity shear in the outer layers can lead to the development of the Kelvin–Helmholtz instability and turbulent mixing. To take this into account, we propose a simple law of vertical mixing, which governs the interaction of these layers. Stationary solutions and non-stationary calculations show the effect of mixing (or breaking) for waves of sufficiently large amplitude. We construct steady-state soliton-like solutions of the three-layer model adjacent to a given constant flow. The obtained theoretical profiles of breaking solitary waves are consistent with laboratory experiments.