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Rayleigh–Taylor Instability with General Rotation and Surface Tension in Porous Media

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Abstract

The Rayleigh–Taylor instability of a heavy fluid supported by a lighter one is investigated in the presence of general rotation and surface tension through a porous medium. The density in the lower region is assumed to be a decreasing exponential function, while the density in the upper region is an increasing exponential function. The dispersion relation that defines the growth rate N for the considered system has been derived and numerically analyzed for special cases. The results show that N decreases as the vertical and horizontal components of rotation, medium porosity (ε) and viscosity increase. In the general case, only one of the critical values \({(F_{s_c})}\) for the stability is determined.

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  1. G. A. Hoshoudy

    Present address: Faculty of Girls Education at Muhayel, King Khalid University, Muhayel, 504, Kingdom of Saudi Arabia

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  1. Department of Applied Mathematics, Faculty of Science, South Valley University, Kena, 83523, Egypt

    G. A. Hoshoudy

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  1. G. A. Hoshoudy
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Hoshoudy, G.A. Rayleigh–Taylor Instability with General Rotation and Surface Tension in Porous Media. Arab J Sci Eng 36, 621–633 (2011). https://doi.org/10.1007/s13369-011-0051-y

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  • DOI: https://doi.org/10.1007/s13369-011-0051-y

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