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Some self-similar solutions of the Leibenzon equation

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Abstract

Self-similar one-dimensional solutions of the Leibenzon equation c2θt=θ kzz (z ≥ 0, k ≥ 2) are considered. Approximate solutions are constructed for the two cases in which the initial value θ = θ1 = const > 0 and on the boundary either a constant value θ = θ2 < θ1 is maintained or the flow (directed “outwards”) is given. In the first problem the dependence of the boundary flow on the governing parameters is determined. A characteristic property of the types of motion in question is the existence near the boundary of a region, expanding with time, in which the flow is almost independent of the coordinate.

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Authors and Affiliations

  1. Rostov-on-Don

    M. V. Kachan, S. F. Pimenov, S. M. Sushchii & M. B. Entel'

Authors
  1. M. V. Kachan
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  2. S. F. Pimenov
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  3. S. M. Sushchii
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  4. M. B. Entel'
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Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–150, September–October, 1991.

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Kachan, M.V., Pimenov, S.F., Sushchii, S.M. et al. Some self-similar solutions of the Leibenzon equation. Fluid Dyn 26, 758–763 (1991). https://doi.org/10.1007/BF01050998

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  • DOI: https://doi.org/10.1007/BF01050998

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