Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Novosibirsk participants

Wave flow regimes of a viscous film flowing on a vertical cylinder

Bocharov A.A., Tsvelodub O.Y.

Institute of Thermophysics,
SB RAS (Novosibirsk)

The flow of a thin film of viscous liquid flowing under gravity along the vertical cylinder of large radius is considered. In case of small Reynolds numbers the problem can be reduced to research of one non-linear equation for deviation of film thickness from a undisturbed level. For the axial - symmetrical solutions this equation passes in a well known equation Kuramoto–Sivashinsky. The periodic solutions in neighbourhoods of neutral wave numbers, are constructed analytically. Inside instability regions, the solutions were searched numerically. For this purpose they it was represented as the Fourier serieses. After breaking these series and substitution them in this equation, the system of non-linear algebraic equations was received, which one was decided by a modified method of Newton. As initial approximation the analytical results were used. After all, a few families of space steady-state traveling of periodic solutions are obtained. The sets of the solution passing into solitons are selected.

This work is supported by RFFI (grant N 00-01-00849 ) and INTAS (grant N 99-1107).

Note. Abstracts are published in author's edition

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