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Nonlinear Rayleigh-Taylor instability in magnetic fluids between two parallel plates


A nonlinear stage of the two-dimensional Rayleigh-Taylor instability for two magnetic fluids of finite thickness is studied by including the effect of surface tension between the two fluids. The system is subjected to a tangential magnetic field. The method of multiple scale perturbations is used in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable and unstable deformations. Two nonlinear Schrödinger equations are obtained, one of which leads to the determination of the cutoff wavenumber. The other Schrödinger equation is used to analyze the stability of the system. It is found that if a finite-amplitude disturbance is stable, then a small modulation to the wave is also stable. It is also found that the tangential magnetic field plays a dual role in the stability criterion. Finally, the magnetic permeability constants of the fluid affect the stability conditions.

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  1. Chandrasekhar, S. (1961).Hydrodynamic and Hydromagnetic Stability, Oxford University Press, London.

  2. Davey, A. (1972).Journal of Fluid Mechanics,53, 769–781.

  3. Elhefnawy, A. R. F. (1990).Journal of Applied Mathematics and Physics (ZAMP),41, 669–683.

  4. Hassam, A. B., and Huba, J. D. (1990).Physics of Fluids B,2(9), 2001–2006.

  5. Huba, J. D., Lyon, J. G., and Hassam, A. B. (1987).Physical Review Letters,59(26), 2971–2974.

  6. Iizuka, T., and Wadati, M. (1990).Journal of the Physical Society of Japan,59(9), 3182–3193.

  7. Malik, S. K., and Singh, M. (1989).Physical Review Letters,62(15), 1753–1756.

  8. Mohamed, A. A., and El Shehawey, E. F. (1983).Physics of Fluids,26(7), 1724–1730.

  9. Nayfeh, A. H. (1976).Journal of Applied Mechanics,98(4), 584–588.

  10. Oron, A., and Rosenau, P. (1989).Physics of Fluids A,1(7), 1155–1165.

  11. Rosensweig, R. E. (1985).Ferrohydrodynamics, Cambridge University Press, Cambridge.

  12. Saasen, A., and Tyvand, P. A. (1990).Journal of Applied Mathematics and Physics (ZAMP),41, 284–293.

  13. Zelazo, R. E., and Melcher, J. R. (1969).Journal of Fluid Mechanics,39, 1–24.

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Elhefnawy, A.R.F. Nonlinear Rayleigh-Taylor instability in magnetic fluids between two parallel plates. Int J Theor Phys 31, 1505–1520 (1992).

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  • Surface Tension
  • Stability Criterion
  • Parallel Plate
  • Multiple Scale
  • Magnetic Permeability