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Long waves in two superposed layers of magnetic fluid

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Abstract

The equations and boundary conditions describing plane-parallel potential motions of two superposed layers of stably stratified magnetic fluid are formulated. The fluid is assumed to fill entirely a horizontal plane channel in the presence of a uniform longitudinal magnetic field induced by external sources. With reference to the case of long waves propagating over the interface between the upper and lower layers, it is shown that the action of the field may be interpreted as the result of an increase in the nondimensional surface tension by an amount proportional to the square of the undisturbed field. In the linear formulation the effect of the field on the evolution of a long-wave perturbation of the initially plane interface is investigated. Korteweg-de Vries equations with quadratic and cubic nonlinearities are derived and the action of the field on the internal solitary waves is analyzed.

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References

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

    Google Scholar 

  2. I. E. Tarapov, “Surface wave stability of a free surface of magnetizable fluid,”Zh. Prikl. Mekh. Tekh. Fiz.,4, 35 (1974).

    Google Scholar 

  3. R. Rozensweig,Ferrohydrodynamics, Cambridge (1986).

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

    Google Scholar 

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

    Google Scholar 

  6. V. I. Karpman,Nonlinear Waves in Dispersible Media [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  7. M. J. Ablowitz and H. Segur,Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Maths., Vol. 4), Philadelphia (1981).

  8. G. B. Whitham,Linear and Nonlinear Waves, Wiley-Interscience, New York (1974).

    Google Scholar 

  9. T. B. Benjamin, “The solitary wave with surface tension,”Q. Appl. Math.,40, 231 (1982).

    Google Scholar 

  10. B. B. Kadomtsev and V. I. Petviashvili, “On stability of solitary waves in weakly dispersible media,”Dokl. Akad. Nauk SSSR,192, 753 (1970).

    Google Scholar 

  11. A. Jeffrey and T. Kakutani, “Weak nonlinear dispersive waves: a discussion centered around the Korteweg-de Vries equation”,SIAM Rev.,14, 582 (1972).

    Google Scholar 

  12. C. F. Driscoll and T. M. O'Neil, “Modulational instability of cnoidal wave solutions of the modified Korteweg-de Vries equation,”J. Math. Phys.,17, 1196 (1976).

    Google Scholar 

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Authors and Affiliations

  1. Moscow

    V. M. Korovin

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  1. V. M. Korovin
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Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 126–133, May–June, 1993.

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Korovin, V.M. Long waves in two superposed layers of magnetic fluid. Fluid Dyn 28, 393–399 (1993). https://doi.org/10.1007/BF01051155

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  • DOI: https://doi.org/10.1007/BF01051155

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