环形液池热毛细对流的线性稳定性研究

对外壁加热的环形液池热毛细对流进行了线性稳定性分析.采用Chebyshev配点法对Pr=6.8、内外径之比为0.5、深宽比A范围为0.25～1.4的数值结果进行分析，发现流动的临界状态均为振荡形式，并且随着A的增大，临界雷诺数减小，相应的临界波数与振荡频率也呈减小趋势.能量分析结果表明，小扰动与基本流相互作用项较小，表面张力在径向做功与周向做功对小扰动的动能变化起主导作用.观察三者与液池深宽比的关系，发现A=0.8时表面张力在径向做功项达到极小值，周向做功项以及小扰动与基本流相互作用项达到极大值. 

Linear Stability Analysis of Thermocapillary Convection in Annular Pools

The linear stability of thermocapillary convection in annular pools is studied through the Chebyshev-collocation method. As Pr=6.8, the ratio of outer radius and inner radius is 0.5, and the range of aspect ratio A is from 0.25 to 1.4, numerical results show that the critical mode of the flow are oscillating. The critical Marangoni number, critical wave number and oscillating frequency decreases as A increases. Energy analysis shows that surface tension in the radial and azimuthal directions plays a leading role in the variation of perturbation energy. And the interaction between perturbation flow and the basic flow is small compared to the two former terms. We find out that the work done by the surface tension in the radial direction reaches minimum were analyzed, while the work done by the surface tension in the azimuthal direction and the interaction between the perturbation flow and the basic flow reach maximum, as A=0.8.