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Resonance effect of the bottom topography on the surface of an inclined layer of a viscous liquid

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Thermophysics and Aeromechanics Aims and scope

Abstract

The reaction of the film interface to low-amplitude waviness of the wall was studied. A linearized version of the problem described by the Orr — Sommerfeld equation was considered; the solution was sought by asymptotic expansion in small parameter 1/Re, and usual spectral problem concerning stability to perturbations of exp[iα(x-ct)] type was solved.

According to calculations, for some specially chosen wave numbers α the drift and dispersion effects balance each other, providing zero resulting velocity c R = 0. If we assume that a rigid wall is corrugated with the same α, we can say that stationary waves caused by the wavy wall are in resonance with intrinsic perturbations of the second kind.

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Authors and Affiliations

  1. South Scientific Center RAS, Krasnodar, Russia

    E. A. Demekhin & E. M. Shapar

  2. Kuban State University, Krasnodar, Russia

    A. S. Selin

Authors
  1. E. A. Demekhin
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  2. E. M. Shapar
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  3. A. S. Selin
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Additional information

The work was financially supported by the Russian Foundation for Basic Research (Grants Nos. 05-08-33585a and 06-08-96637-r-yug-a.)

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Demekhin, E.A., Shapar, E.M. & Selin, A.S. Resonance effect of the bottom topography on the surface of an inclined layer of a viscous liquid. Thermophys. Aeromech. 15, 243–252 (2008). https://doi.org/10.1134/S086986430802008X

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  • DOI: https://doi.org/10.1134/S086986430802008X

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