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

Resonance effect of the bottom topography on the surface of an inclined layer of a viscous liquid 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Thermophysics and Aeromechanics Springer Journals

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

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Publisher
Springer Journals
Copyright
2008 Pleiades Publishing, Ltd.
ISSN
0869-8643
eISSN
1531-8699
DOI
10.1134/S086986430802008X
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Thermophysics and AeromechanicsSpringer Journals

Published: Jun 1, 2008

References