Abstract
The flow of a viscous liquid film down a vertical cylinder in the gravity field is considered. In the case of small Reynolds numbers for long-wave perturbations on a cylinder of radius much greater than the film thickness, the problem can be reduced to a single nonlinear equation for the evolution of the film thickness perturbation. For axially symmetric solutions, this equation coincides with the well-known Sivashinsky-Kuramoto equation. The results of a numerical analysis of this equation for three-dimensional stationary traveling solutions of the problem are reported. The effect of the problem parameters on the solution behavior is demonstrated. Soliton type solutions are presented.
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Bocharov, A.A., Tsvelodub, O.Y. Wave Regimes of Viscous Film Flow down a Vertical Cylinder. Fluid Dynamics 38, 321–327 (2003). https://doi.org/10.1023/A:1024237506130
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DOI: https://doi.org/10.1023/A:1024237506130