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

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Abstract

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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References

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

Download references

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Author notes

  1. Abdel Raouf F. Elhefnawy

    Present address: Department of Mathematics, T.T. Junior College, P.O. Box 1083, 21912, Al-Qunfudah, Saudi Arabia

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Banha University, 13518, Banha, Egypt

    Abdel Raouf F. Elhefnawy

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  1. Abdel Raouf F. Elhefnawy
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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). https://doi.org/10.1007/BF00673981

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  • DOI: https://doi.org/10.1007/BF00673981

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