Double-diffusive Marangoni convection in a rectangular cavity: Onset of convection
Double-diffusive Marangoni convection in a rectangular cavity: Onset of convection
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DOI：
10.1063/1.3333436
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发表时间：
2010-03
影响因子：
4.6
通讯作者：
Zhiwu Chen;Y. Li;J. Zhan
中科院分区：
文献类型：
--
作者：
Zhiwu Chen;Y. Li;J. Zhan
研究了具有水平温度梯度和浓度梯度的矩形腔内的双扩散Marangoni对流。注意力仅限于相反的热和溶质Marangoni效应的情况下，是等量的溶质热Marangoni数比R = 1。在这种情况下，一个无流动的平衡解决方案存在，并可以保持稳定的临界热Marangoni数。线性稳定性分析和直接数值模拟表明，该临界值对应于一个超临界Hopf分岔点，该分岔点导致静止流体直接进入振荡流态。系统地研究了刘易斯数Le、普朗特数Pr和腔长/高比A对不稳定性的影响，得到了不同的振荡模式。第一模式首先失稳，然后稳定。有时候根本不会发作。提供了一个物理说明，以证明不稳定的机制，并解释为什么不稳定的发病后的振荡流对应于反向旋转涡在本配置中从右向左行驶，通过直接数值模拟获得。最后，同时存在的稳定和振荡的流动制度。虽然振荡流是由小扰动引起的，但文献中描述的定常流是由有限振幅扰动引起的。© 2010美国物理研究所。doi：10.1063/1.3333436
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 =�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. © 2010 American Institute of Physics. doi:10.1063/1.3333436