Destabilizing effect of density gradient on the Kelvin–Helmholtz instability

Abstract

In this paper, we derive explicit analytic formulas for the linear growth rate and frequency of the Kelvin–Helmholtz instability in fluids with the density gradient. The analytic formulas are in excellent agreement with the results of two-dimensional numerical simulation. We found that the density gradient effect enforces (destabilizes) the Kelvin–Helmholtz instability by increasing its linear growth rate in the direction normal to the perturbed interface. The frequency is reduced (stabilized) by the density gradient effect, i.e., the density gradient decreases the transmission of the perturbation in the direction along to the perturbed interface. In most cases, the combined effect of density and velocity gradients stabilizes the Kelvin–Helmholtz instability.