The instability of streaming viscous-viscoelastic fluids in a porous medium

The Kelvin-Helmholtz instability of a Newtonian viscous fluid overlying a viscoelastic fluid in a porous medium is considered separately for Walters B' and Rivlin-Ericksen viscoelastic fluids. It is found that for the special case when perturbations in the directions of streaming are ignored, the system is unstable for a potentially unstable configuration and the system is stable for a potentially stable configuration for Rivlin-Ericksen viscoelastic fluids, which is in contrast to the case of the Walters B' viscoelastic fluid, where the system can be stable or unstable depending upon kinematic viscoelasticity, medium porosity, relative density of the viscoelastic fluid and medium permeability, for both potentially unstable and potentially stable configurations. In every other direction, a minimum value of wave-number has been found. The system is unstable for all wave-numbers greater than this minimum wave number.