Viscous Corrections for the Viscous Potential Flow Analysis of Rayleigh–Taylor Instability With Heat and Mass Transfer

Abstract

Viscous corrections for the viscous potential flow analysis of Rayleigh–Taylor instability of two viscous fluids when there is heat and mass transfer across the interface have been considered. Both fluids are taken as incompressible and viscous with different kinematic viscosities. In viscous potential flow theory, viscosity enters through a normal stress balance and the effects of shearing stresses are completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface of the two fluids. It has been observed that heat and mass transfer has a stabilizing effect on the stability of the system. It has been shown that the irrotational viscous flow with viscous corrections gives rise to exactly the same dispersion relation as the dissipation method in which no pressure term is required and the viscous effect is accounted for by evaluating viscous dissipation using irrotational flow. It has been observed that the inclusion of irrotational shearing stresses has a stabilizing effect on the stability of the system.