Resonance effect of the bottom topography on the surface of an inclined layer of a viscous liquid
E.A. Demekhin1, E.M. Shapar2, A.S. Selin3
1 South Scientific Center RAS, Krasnodar, Russia 2 South Scientific Center RAS, Krasnodar, Russia 3 Kuban State University, Krasnodar, Russia
Pages: 243-252
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 cR = 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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