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Rayleigh-Taylor Instability of A Thin Magnetic Fluid Layer in A Tangential Magnetic Field

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Abstract

A viscous magnetic fluid layer in a uniform horizontal magnetic field is considered. The upper boundary of the layer is a horizontal rigid wall and the lower boundary a the free surface. It is assumed that at the initial instant the free surface represents a randomly weakly deformed horizontal plane. A dispersion relation for the waves in a layer of arbitrary thickness is obtained within the framework of the linearized system of ferrohydrodynamic equations describing the evolution of spatial perturbations. The effect of a tangential magnetic field on the breakdown of a thin layer is investigated theoretically and experimentally.

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References

  1. M. D. Cowley and R. E. Rosensweig, “The interfacial stability of a ferromagnetic fluid,” J. Fluid Mech., 30, 671 (1967).

    Article  ADS  MATH  Google Scholar 

  2. R. E. Zelazo and J. R. Melcher, “Dynamics and stability of ferrofluids: surface interaction,” J. Fluid Mech., 39, 1 (1969).

    Article  ADS  MATH  Google Scholar 

  3. B. M. Berkovskii, V. F. Medvedev, and M. S. Krakov, Magnetic Fluids [in Russian], Khimiya, Moscow (1989).

    Google Scholar 

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

    Google Scholar 

  5. A. R. F. Elhefnawy, “Nonlinear Rayleigh-Taylor instability in magnetic fluids between two parallel plates,” Intern. J. Theor. Phys., 31, 1505 (1992).

    Article  MathSciNet  Google Scholar 

  6. R. Kant and S. K. Malik, “Nonlinear waves in superposed magnetic fluids,” Phys. Fluids, 28, 3534 (1985).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Y. O. El-Dib, “Nonlinear hydrodynamic Rayleigh-Taylor instability of viscous magnetic fluids: the effect of a tangential magnetic field,” J. Plasma Phys., 51, 1 (1994).

    Article  ADS  Google Scholar 

  8. L. A. Newhouse and C. Pozrikidis, “The Rayleigh-Taylor instability of a viscous liquid layer resting on a plane wall,” J. Fluid Mech., 217, 615 (1990).

    Article  ADS  MATH  Google Scholar 

  9. L. D. Landau and E. M. Lifshitz, Theoretical Physics. Vol. 6. Hydrodynamics [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  10. S. G. Yiantsios and B. G. Higgins, “The Rayleigh-Taylor instability in thin viscous films,” Phys. Fluids, A, 1, 1484 (1989).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. A. J. Babchin, A. L. Frenkel, B. G. Levich, and G. I. Sivashinsky, “Nonlinear saturation of Rayleigh-Taylor instability in thin films,” Phys. Fluids, 26, 3159 (1983).

    Article  ADS  MATH  Google Scholar 

  12. M. Fermigier, L. Limat, J. E. Wesfreid et al., “Two-dimensional patterns in Rayleigh-Taylor instability of a thin layer,” J. Fluid Mech., 236, 349 (1992).

    Article  ADS  MATH  Google Scholar 

  13. N. N. Moiseev and V. V. Rumyantsev, Dynamics of a Body with Fluid-Filled Cavities [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  14. R. Menikoff, R. C. Mjolsness, D. H. Sharp et al., “Initial value problem for Rayleigh-Taylor instability of viscous fluids,” Phys. Fluids, 21, 1674 (1978).

    Article  ADS  MATH  Google Scholar 

  15. P. H. LeBlond and F. Mainardi, “The viscous damping of capillary-gravity waves,” Acta Mech., 68, 203 (1987).

    Article  Google Scholar 

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Korovin, V.M., Kubasov, A.A. Rayleigh-Taylor Instability of A Thin Magnetic Fluid Layer in A Tangential Magnetic Field. Fluid Dyn 33, 645–654 (1998). https://doi.org/10.1007/BF02698612

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  • DOI: https://doi.org/10.1007/BF02698612

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