TITLE:
Effect of Magnetic Field on Kelvin-Helmholtz Instability in a Couple-Stress Fluid Layer Bounded Above by a Porous Layer and Below by a Rigid Surface
AUTHORS:
Krishna B. Chavaraddi, Vishwanath B. Awati, Nagaraj N. Katagi, Priya M. Gouder
KEYWORDS:
KHI, Magnetic Field, Couple-Stress Fluid Layer, BJ-Slip Condition, Porous Layer, Dispersion Relation
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.16,
October
28,
2016
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.