Hu J, Yin X Y, Henry D, Hadid H Ben
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026312. doi: 10.1103/PhysRevE.80.026312. Epub 2009 Aug 20.
The spatiotemporal evolution of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect is investigated by carrying out fully nonlinear two-dimensional numerical simulations initiated by a pulselike disturbance. The traveling wave packets for positive as well as negative separation factors psi are obtained numerically for ethanol-water-like mixtures (Prandtl number Pr=10 , Lewis number Le=0.01) and selected combinations of Rayleigh and Reynolds numbers at psi=0.01, 0.1 and psi=-0.1. The characteristics of the wave fronts and the transitions observed between absolute and convective instabilities when changing the parameters are compared with the results previously obtained by linear spatiotemporal stability analysis. The simulations are in very good agreement with the stability results, which confirms the validity of both approaches. Finally, in order to characterize the possible interaction between the two wave packets of the so-called downstream and upstream modes for psi<0, the spatiotemporal stability analysis is used to detect a boundary curve in the (Re, Ra) parameter region beyond which the two wave packets will never completely separate. Numerical simulations illustrate the different evolutions of the wave packets on both sides of this boundary.
通过对由脉冲状扰动引发的完全非线性二维数值模拟，研究了具有索雷特效应的二元流体中泊肃叶 - 瑞利 - 贝纳德流动的时空演化。对于乙醇 - 水类混合物（普朗特数Pr = 10，路易斯数Le = 0.01）以及在分离因子ψ = 0.01、0.1和ψ = -0.1时瑞利数和雷诺数的选定组合，数值获得了正、负分离因子ψ的行波包。将改变参数时观察到的波前特征以及绝对不稳定性和对流不稳定性之间的转变与先前通过线性时空稳定性分析获得的结果进行了比较。模拟结果与稳定性结果非常吻合，这证实了两种方法的有效性。最后，为了表征ψ < 0时所谓下游和上游模式的两个波包之间可能的相互作用，使用时空稳定性分析在（Re，Ra）参数区域中检测出一条边界曲线，超过该曲线两个波包将永远不会完全分离。数值模拟说明了该边界两侧波包的不同演化。
