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Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids

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Abstract

The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schrödinger equations (l-NLS) with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoretically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

    Kadry Zakaria, Magdy A. Sirwah & Ahmed Assaf

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  1. Kadry Zakaria
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  2. Magdy A. Sirwah
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  3. Ahmed Assaf
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Correspondence to Ahmed Assaf.

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Zakaria, K., Sirwah, M.A. & Assaf, A. Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids. Acta Mech Sin 24, 497–514 (2008). https://doi.org/10.1007/s10409-008-0168-8

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  • DOI: https://doi.org/10.1007/s10409-008-0168-8

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