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Title: Double-diffusive Marangoni convection in a rectangular cavity : onset of convection
Authors: Chen, ZW
Li, YS 
Zhan, JM
Keywords: Bifurcation
Computational fluid dynamics
Flow instability
Fluid oscillations
Issue Date: Mar-2010
Publisher: American Institute of Physics
Source: Physics of fluids, Mar. 2010, v. 22, no. 3, 034106, p. 1-13 How to cite?
Journal: Physics of fluids 
Abstract: Double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the case where the opposing thermal and solutal Marangoni effects are of equal magnitude (solutal to thermal Marangoni number ratio R[sub σ]=−1). In this case a no-flow equilibrium solution exists and can remain stable up to a critical thermal Marangoni number. Linear stability analysis and direct numerical simulation show that this critical value corresponds to a supercritical Hopf bifurcation point, which leads the quiescent fluid directly into the oscillatory flow regime. Influences of the Lewis number Le, Prandtl number Pr, and the cavity aspect ratio A (height/length) on the onset of instability are systematically investigated and different modes of oscillation are obtained. The first mode is first destabilized and then stabilized. Sometimes it never gets onset. A physical illustration is provided to demonstrate the instability mechanism and to explain why the oscillatory flow after the onset of instability corresponds to countersense rotating vortices traveling from right to left in the present configuration, as obtained by direct numerical simulation. Finally the simultaneous existence of both steady and oscillatory flow regimes is shown. While the oscillatory flow arises from small disturbances, the steady flow, which has been described in the literature, is induced by finite amplitude disturbances.
ISSN: 1070-6631 (print)
1089-7666 (online)
DOI: 10.1063/1.3333436
Rights: © 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Z.W. Chen, Y.S. Li & J.M. Zhan, Phys. Fluids 22, 034106 (2010) and may be found at
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