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Stability of unsteady rotational motion of a plane layer of ideal fluid with free boundaries

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Abstract

The exact solution of the equations of an ideal incompressible fluid describing the unsteady rotational motion of a plane layer with free boundaries is obtained. For constant vorticity the stability problem is studied in the linear approximation. The asymptotic behavior of the free boundaries of the layer as t → ∞ is calculated. It is shown that the vorticity of the basic motion stabilizes the boundaries of the layer.

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Authors and Affiliations

  1. Krasnoyarsk

    V. K. Andreev

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  1. V. K. Andreev
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 15–21, March–April, 1986.

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Andreev, V.K. Stability of unsteady rotational motion of a plane layer of ideal fluid with free boundaries. Fluid Dyn 21, 179–184 (1986). https://doi.org/10.1007/BF01050166

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  • DOI: https://doi.org/10.1007/BF01050166

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