Abstract
The stability of boundary flows occurring near an inclined plane or a cylinder executing longitudinal periodic oscillations is studied within the framework of a system of embedded models (homogeneous fluid, stratified viscous fluid, and fluid in the presence of diffusion). It is shown that in a stratified fluid the resonance boundary-oscillation frequency, at which the boundary layer thickness increases without bound, exists not only in the problem with a plane boundary but also in the case of oscillations of an inclined cylinder. Taking diffusion into account leads to the boundary layer splitting into viscous and diffusion sublayers with considerably different thicknesses and properties. Nevertheless, the fact itself of the existence of the resonance oscillation frequency turns out to be stable and the resonance takes place also in the models of stratified flows with allowance for diffusion.
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Original Russian Text © V.G. Baidulov, 2010, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2010, Vol. 45, No. 6, pp. 3–11.
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Baidulov, V.G. Fine structure of one-dimensional periodic stratified flows. Fluid Dyn 45, 835–842 (2010). https://doi.org/10.1134/S0015462810060013
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DOI: https://doi.org/10.1134/S0015462810060013