Resonance effect of the bottom topography on the surface of an inclined layer of a viscous liquidстатья
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Аннотация: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. The work was financially supported by the Russian Foundation for Basic Research (Grants Nos. 05-08-33585a and 06-08-96637-r-yug-a.)