Abstract
Abstract. The problem on internal waves in a weakly stratified two-layer fluid is studied semi-analytically. We discuss the 2.5-layer fluid flows with exponential stratification of both layers. The long-wave model describing travelling waves is constructed by means of a scaling procedure with a small Boussinesq parameter. It is demonstrated that solitary-wave regimes can be affected by the Kelvin–Helmholtz instability arising due to interfacial velocity shear in upstream flow.
Highlights
We consider an analytical model of internal solitary waves in a two-layer fluid with the density continuously increasing with depth in both layers
Two-layer approximation is a standard model of a sharp pycnocline in a stratified fluid with constant densities in each layer, but which is discontinuous at the interface
In this paper we have considered the problem of internal stationary waves at the interface between exponentially stratified fluid layers
Summary
We consider an analytical model of internal solitary waves in a two-layer fluid with the density continuously increasing with depth in both layers. Several authors noted that solitary-wave solutions of such approximate models are in good agreement with the numerical solutions of fully non-linear Euler equations for a perfect two-layer fluid. The long-wave scaling procedure uses a small Boussinesq parameter which characterizes slightly increasing density in the layers and a small density jump at their interface This method combines the approaches applied formerly to a pure two-fluid system with the perturbation technique discussed for the first time by Long (1965) and developed by Benney and Ko (1978) for a continuous stratification. The Euler equations for continuously stratified, near two-layer fluids was studied numerically and analytically by Almgren et al (2012) They demonstrated that the wave-induced shear can locally reach unstable configurations and give rise to local convective instability. It seems that such a marginal stability of long internal waves could explain the formation mechanism of very long billow trains in abyssal flows observed by Van Haren et al (2014)
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