The Rayleigh - Taylor instability of a viscous fluid layer with viscosity stratification

Abstract

The effects of viscosity stratification and surface tension on Rayleigh-Taylor (RT) instability in a finite thickness layer of an incompressible viscous fluid bounded above by a denser fluid and below by a rigid impermeable surface have been studied using linear stability analysis. A relation for the R T instability growth rate is found by calculating the eigenvalues of the stability equation. It is shown that the shape of the dispersion curve is controlled by the ratio of surface tension to the stress gradient, with the layer thickness and the viscosity stratification affecting the rate of growth of the instability. The growth rate, infact, is shown to increase with increase in viscosity stratification and the thickness of the fluid layer. The results are shown to revert to those of the case of a viscous fluid layer in the absence of viscosity stratification.