Effect of variation in density on the stability of bilinear shear currents with a free surface

TL;DR

This paper analyzes how density variation affects the stability of bilinear shear currents with a free surface, revealing that stratification can significantly destabilize the flow, using a geometrical analytical approach.

Contribution

It introduces a simple analytical stability criterion for bilinear shear flows with free surfaces considering density stratification, extending classical stability analysis.

Findings

Density stratification strongly destabilizes shear flows.

The geometrical approach simplifies stability criteria derivation.

Comparison shows stratification effects are significant in real fluids.

Abstract

We perform the stability analysis for a free surface fluid current modeled as two finite layers of constant vorticity, under the action of gravity and absence of surface tension. In the same spirit as Taylor ["Effect of variation in density on the stability of superposed streams of fluid," Proc. R. Soc. A 132, 499 (1931)], a geometrical approach to the problem is proposed, which allows us to present simple analytical criteria under which the flow is stable. A strong destabilizing effect of stratification in density is revealed by comparison with the physical setting where the vorticity interface is also a density interface separating two immiscible fluids with constant densities.