Viscous potential flow analysis of magnetohydrodynamic interfacial stability through porous media

M. H. Obied Allah ()
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M. H. Obied Allah: Assiut University

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 4, 419-441

Abstract: Abstract In the view of viscous potential flow theory, the hydromagnetic stability of the interface between two infinitely conducting, incompressible plasmas, streaming parallel to the interface and subjected to a constant magnetic field parallel to the streaming direction will be considered. The plasmas are flowing through porous media between two rigid planes and surface tension is taken into account. A general dispersion relation is obtained analytically and solved numerically. For Kelvin-Helmholtz instability problem, the stability criterion is given by a critical value of the relative velocity. On the other hand, a comparison between inviscid and viscous potential flow solutions has been made and it has noticed that viscosity plays a dual role, destabilizing for Rayleigh-Taylor problem and stabilizing for Kelvin-Helmholtz. For Rayleigh-Taylor instability, a new dispersion relation has been obtained in terms of a critical wave number. It has been found that magnetic field, surface tension, and rigid planes have stabilizing effects, whereas critical wave number and porous media have destabilizing effects.

Keywords: Interfacial flows; viscous potential flow; Kelvin Helmholtz instability; Rayleigh-Taylor instability; Magnetic field; Porous media (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0022-y

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