Abstract
Kelvin-Helmholtz instability (KHI) appears in stratified two-fluid flow at surface. When the relative velocity is higher than the critical relative velocity, the growth of waves occurs. It is found that magnetic field has a stabilization effect whereas the buoyancy force has a destabilization effect on the KHI in the presence of sharp inter-face. The RT instability increases with wave number and flow shear, and acts much like a KHI when destabilizing effect of sheared flow dominates. It is shown that both of ablation velocity and magnetic field have stabilization effect on RT instability in the presence of continued interface. In this paper, we study the effect of magnetic field on Kelvin-Helmholtz instability (KHI) in a Couple-stress fluid layer above by a porous layer and below by a rigid surface. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of KHI. We replace the effect of boundary layer with Beavers and Joseph slip condition at the rigid surface. The dispersion relation is derived using suitable boundary and surface conditions and results are discussed graphically. The stabilization effect of magnetic field takes place for whole waveband and becomes more significant for the short wavelength. The growth rate decreases as the density scale length increases. The stabilization effect of magnetic field is more significant for the short density scale length.
Highlights
Kelvin-Helmholtz instability is one of the basic instabilities of two-fluid systems, which affects an interface
We study the effect of magnetic field on Kelvin-Helmholtz instability (KHI) in a Couple-stress fluid layer above by a porous layer and below by a rigid surface
In this study we have shown the effect of physical parameters involved in the problem on effect of magnetic field on surface instability of KH type in a couple- stress fluid layers bounded above by a porous layer and below by a rigid boundary
Summary
Kelvin-Helmholtz instability is one of the basic instabilities of two-fluid systems, which affects an interface. The prototypical case is that with one layer of lighter fluid overlying another of denser fluid, and the two moving horizontally in the same direction but with different velocities It is not uncommon for environmental fluids to be subject simultaneously to the destabilizing effect of a velocity shear and the stabilizing effect of density stratification, and, when such competition occurs, the outcome is often the so-called Kelvin-Helmholtz (KH) instability [1]. The study of the Kelvin-Helmholtz instability has a long history in hydrodynamics, The basic linear stability analysis of the magnetohydrodynamvic (MHD) K-H instability was carried out long ago (Chandrasekhar [8]). The considerable potential for much weaker fields to modify the nonlinear instability and, in particular, to reorganize the subsequent flow has only recently been emphasized
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