KELVIN-HELMHOLTZ INSTABILITY OF TWO VISCOUS FLUIDS IN POROUS MEDIUM R. Asthana 1 , M. K. Awasthi 2 , and G. S. Agrawal 3 1 Department of Mathematics, Indian Institute of Technology Roorkee, India Email: rasthana4@gmail.com 2 Department of Mathematics, Indian Institute of Technology Roorkee, India Email: mukeshiitr.kumar@gmail.com 3 Department of Mathematics, Indian Institute of Technology Roorkee, India Email: gsa45fma@iitr.ernet.in Received 12 April 2011; accepted 19 August 2011 ABSTRACT The present paper deals with the study of Kevin-Helmholtz instability in a porous medium using viscous potential flow theory. Both fluids are taken as incompressible and viscous with different kinematic viscosities. A dispersion relation has been obtained and stability criterion is given by a critical value of relative velocity of two fluids. Medium porosity has stabilizing effect on critical value of the relative velocity. Reynolds number and viscosity ratio has destabilizing effect on growth rate while Bond number has stabilizing effect. Maximum growth rate increases with Darcy number. Keywords: Fluid-fluid interfaces; Kelvin-Helmholtz instability; porous media; viscous poten- tial flow; normal stresses. 1 INTRODUCTION Kelvin-Helmholtz instability occurs when there is a relative motion between different layers of fluids (Chandrashekhar 1981; Drazin and Reid 1981). The instability investigation of the in- terface between two layers of different velocities is important in several cosmic and laboratory situations, such as meteor entering the Earth’s atmosphere, when the air is blown over mercury, wind blowing over the ocean, in the theory of solar winds, studies of Earth’s magnetosphere instability, the helical wave motion observed in ionized comet tails etc. Viscous potential theory has played an important role in studying various stability problems. Joseph and Liao (Joseph and Liao 1994) have shown that irrotational flow of a viscous fluid satisfies Navier-Stokes equations. Tangential stresses are not considered in viscous potential theory and viscosity enters through normal stress balance. In this theory no-slip condition at the boundary is not enforced so that two dimensional solutions satisfy three dimensional solutions. Various vortocity and circulation theorems of inviscid potential flow also hold well in viscous potential flow. Joseph et al. (Joseph et al. 1999) studied viscous potential flow of Rayleigh- Taylor instability. Funada and Joseph (Funada and Joseph 2001) have done the viscous potential Int. J. of Appl. Math. and Mech. 8(14): 1-13, 2012.