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 SurfaceReportar como inadecuado




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Kelvin-Helmholtz instability KHI appearsin stratified two-fluid flow at surface. When the relative velocity is higherthan the critical relative velocity, the growth of waves occurs. It is foundthat magnetic field has a stabilization effect whereas the buoyancy force has adestabilization effect on the KHI in the presence of sharp inter-face. The RTinstability increases with wave number and flow shear, and acts much like a KHIwhen destabilizing effect of sheared flow dominates. It is shown that both ofablation velocity and magnetic field have stabilization effect on RTinstability in the presence of continued interface. In this paper, we study theeffect of magnetic field on Kelvin-Helmholtz instability KHI in aCouple-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 derivethe dispersion relation for the growth rate of KHI. We replace the effect of boundarylayer with Beavers and Joseph slip condition at the rigid surface. Thedispersion relation is derived using suitable boundary and surface conditionsand results are discussed graphically. The stabilization effect of magneticfield takes place for whole waveband and becomes more significant for the shortwavelength. The growth rate decreases as the density scale length increases.The stabilization effect of magnetic field is more significant for the shortdensity scale length.

KEYWORDS

KHI, Magnetic Field, Couple-Stress Fluid Layer, BJ-Slip Condition, Porous Layer, Dispersion Relation

Cite this paper

Chavaraddi, K. , Awati, V. , Katagi, N. and Gouder, P. 2016 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. Applied Mathematics, 7, 2021-2032. doi: 10.4236-am.2016.716164.





Autor: Krishna B. Chavaraddi1*, Vishwanath B. Awati2, Nagaraj N. Katagi3, Priya M. Gouder2,4

Fuente: http://www.scirp.org/



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