The onset of transient Marangoni convection in a liquid layer subjected to rotation about a vertical axis
In view of the interesting possibilities of controlling surface tension-driven convection, anticipated in space experiments involving fluid interfaces, the problem of the stability of a thin horizontal fluid layer subjected to rotation about a vertical axis, when the thermal (or concentration) gradient is not uniform is examined by linear stability analysis. Attention is focussed on the situation where the critical Marangoni number is greater than that for the case of uniform thermal gradient and the convection is not, in general, maintained. The case of adiabatic boundary condition is examined because it brings out the effect of surface tension at the free surfaces and allows a simple application of the Galerkin technique, which gives useful results. Numerical results are obtained for special cases and some general conclusions about the destabilizing effects of various basic temperature profiles and the stabilizing effect of coriolis force are presented. The results indicate that the most destabilizing temperature gradient is one for which the temperature gradient is a step function of the depth. Increase in Taylor number and the inverted parabolic basic temperature profile suppress the onset of convection.
Volume 43, 2020
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