The Kelvin-Helmholtz instability of the plane interface separating two superposed viscous electrically conducting streaming Oldroydian fluids permeated with surface tension and magnetic field in a porous medium is considered. The stability motion is also assumed to have uniform two dimensional streaming velocity. The stability analysis has been carried out for two highly viscous fluids. By applying the normal mode technique to the linearized perturbation equations, the dispersion relation has been derived. As in the case of superposed Newtonian fluids, the system is stable in the potentially stable case and unstable in the potentially unstable case, that holds also for the present case. The behavior of growth rate with respect to kinematic viscosity, elasticity, permeability of porous medium, surface tension and streaming velocity are examined numerically and discussed in detail in section 5.
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The paper analyses the Rayleigh-Taylor instability of a viscous compressible rotating fluid through a porous medium in a vertical magnetic field. It is shown that the system is characterized by a variational principle and by making use of it, a solution is obtained for a layer having exponential density along the vertical. The dispersion relation has been obtained by employing the normal mode technique and solved numerically. It is found that the kinematic viscosity, rotation and permeability of the porous medium have a stabilizing and compressibility has a destabilizing influence on the growth rate of the unstable mode of disturbance.
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