| Abstract: | An investigation is made of the development of convective flows of a viscous incompressible liquid, subjected to high-frequency vibration. The nonlinear equations of convection are used in the Boussinesq approximation, averaged in time. The amplitude of the perturbations is assumed to be small, but finite. For a horizontal layer with solid walls the existence of both subcritical and supercritical stable secondary conditions is established. In a linear statement, the problem of stability in the presence of a modulation has been discussed in 1–3]. Articles 4–6] were devoted to investigation of the nonlinear problem. In 4], the method of grids was used to study secondary conditions in a cavity of square cross section. In the case of a horizontal layer with free boundaries 5, 6], the character of the branching is established by the method of a small parameter.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 90–96, March–April, 1976.The authors thank I. B. Simonenko for his useful evaluation of the work. |
