Rayleigh-Taylor instability in non-uniform magnetized rotating strongly coupled viscoelastic fluid

Abstract

The Rayleigh-Taylor instability (RTI) in an incompressible strongly coupled viscoelastic fluid is investigated considering the effects of inhomogeneous magnetic field, density gradient, and uniform rotation. The generalized hydrodynamic equations have been formulated, and linear dispersion relation is derived taking appropriate density and magnetic field profiles for the considered system. The gravity induced stable and unstable configurations of RTI are analyzed in hydrodynamic and kinetic limits. In the kinetic limit, shear wave modified dispersion relation and the condition of RTI are derived in terms of magnetic-viscoelastic Mach number and viscoelastic Froude number. The criteria of RTI and critical wavenumber for the growth of RTI to be unstable are estimated numerically for white dwarf and inertial confinement fusion target. It is observed that magnetic field, rotation, and viscoelastic effects play a significant role in the suppression of RTI in these systems. The stabilizing influence of magnetic field, rotation, and magnetic-viscoelastic Mach number while the destabilizing influence of viscoelastic Froude on the growth rate of RTI number is observed graphically. The growth rate of RTI decreases faster in kinetic limit as compared to the hydrodynamic limit.