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Viscous potential flow analysis of magnetohydrodynamic interfacial stability through porous media

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  • M. H. Obied Allah

    (Assiut University)

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.

Suggested Citation

  • M. H. Obied Allah, 2013. "Viscous potential flow analysis of magnetohydrodynamic interfacial stability through porous media," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(4), pages 419-441, August.
    • Handle: RePEc:spr:indpam:v:44:y:2013:i:4:d:10.1007_s13226-013-0022-y
    DOI: 10.1007/s13226-013-0022-y
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    References listed on IDEAS

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    1. Asthana, Rishi & Agrawal, G.S., 2007. "Viscous potential flow analysis of Kelvin–Helmholtz instability with mass transfer and vaporization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 389-404.
    2. Pardeep Kumar & Hari Mohan & Roshan Lal, 2006. "Effect of magnetic field on thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-10, April.
    3. Sirwah, Magdy A., 2007. "Nonlinear Kelvin–Helmholtz instability of magnetized surface waves on a subsonic gas–viscous potential liquid interface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 381-400.
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