Fluid Dynamics

, Volume 29, Issue 5, pp 661–673 | Cite as

Secondary flows in a layer with a free surface

  • D. S. Pavlovskii


The loss of stability of a plane-parallel incompressible viscous heat-conducting fluid flow in a horizontal layer subject to a longitudinal temperature gradient is considered. The lower surface of the layer is assumed to be rigid, while the upper one is free with a surface tension coefficient depending linearly on temperature. Both boundaries are assumed to be thermally-insulated. The critical value of the temperature gradient as a function of other relevant parameters is determined by analyzing the spectrum of the linearized problem. Secondary flows arising after the onset of instability are determined from an analysis of the full nonlinear problem using the expansion of the solution in a power series in terms of a supercritical state parameter in the vicinity of the bifurcation point. Three types of secondary flows are studied: plane two-dimensional waves propagating along the temperature gradient; plane waves travelling at a certain angle to the gradient; and three-dimensional waves propagating along the gradient. A numerical method of problem solution, based on the polynomial approximation, is described.


Surface Tension Temperature Gradient Fluid Flow Fluid Dynamics Power Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Plenum Publishing Corporation 1995

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  • D. S. Pavlovskii

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