Long nonlinear internal waves and mixing in a three-layer stratified flow in the Boussinesq approximation

TL;DR

This paper introduces a one-dimensional model for long nonlinear internal waves in a three-layer stratified flow, accounting for turbulent mixing, and analyzes various flow regimes including transcritical flow over obstacles.

Contribution

A novel one-dimensional model for three-layer stratified flows with turbulent mixing, including analysis of stationary solutions and flow over obstacles.

Findings

Model accurately describes different flow regimes

Solutions match experimental and field data

Identifies subcritical and supercritical flow conditions

Abstract

A one-dimensional long-wave model of an unsteady three-layer flow of a stratified fluid under a lid is proposed, taking into account turbulent mixing in the intermediate layer. In the Boussinesq approximation, the equations of motion are reduced to an evolutionary system of balance laws, which is hyperbolic for a small difference in velocities in the layers. Classes of stationary solutions are studied and the concept of subcritical (supercritical) three-layer stratified flow is introduced. Oscillating solutions are constructed that describe the spatial evolution of the mixing layer. The problem of transcritical flow over an obstacle is considered. Solutions are obtained that describe qualitatively different flow regimes on the leeward side of the obstacle. The proposed model is validated using experimental data and field observations on the entrainment of ambient fluid.