Kelvin-Helmholtz Instability in a Fluid Layer Bounded Above by a Porous Layer and Below by a Rigid Surface in Presence of Magnetic Field

Krishna B. Chavaraddi, Nagaraj N. Katagi, Vishwanath B. Awati

Department of Mathematics, Government First Grade College, Yellapur, India.
Department of Mathematics, Maharani’s Science College for Women, Bangalore, India.
Department of Mathematics, Manipal Institute of Technology, Manipal, India.

DOI: 10.4236/am.2012.36086                

Abstract

We study the stability of an interface between two fluids of different densities flowing parallel to each other in the presence of a transverse magnetic field. A simple theory based on fully developed flow approximations is used to de-rive the dispersion relation for the growth rate of KHI. We replace the effect of boundary layer with Beavers and Joseph slip condition. The dispersion relation is derived using suitable boundary and surface conditions and results are discussed graphically. The magnetic field is found to be stabilizing and the influence of the various parameters of the problem on the interface stability is thoroughly analyzed. These are favorable to control the surface instabilities in many practical applications discussed in this paper.

Keywords

KHI; Magnetic Field; BJ-Slip Condition; Porous Layer; Dispersion Relation

Conflicts of Interest

The authors declare no conflicts of interest.

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