Nonlinear study of Rayleigh-Taylor instability in thin films past a porous layer

Abstract

The linear and nonlinear Rayleigh-Taylor instability in a viscous fluid layer of finite thickness bounded above by a porous layer and below by a rigid surface, have been studied based on approximations in effect similar to lubrication and Stokes approximations. The linear problem is studied analytically while the nonlinear problem is investigated using both, harmonic evolution of the interface and numerical integration. It is shown that the nature of the linear stability curve is controlled by both the porous-slip parameter ß and the thickness h of the fluid layer while its shape is controlled only by the ratio of the surface tension y and the normal stress term J. Comparing the results of linear and nonlinear analysis we found that nonlinear effects are significant only for small values of h. In general, we observed that the change in the nature of the interface (i.e., the nominal surface) is related to changes of the value of the slip parameter alpha.