Rayleigh-Benard对流中小扰动的发展及对流斑图

Growth of perturbation and convective patterns in Rayleigh-Benard convection

通过二维流体力学的扰动方程组的数值模拟,探讨了分离比ψ=-0.2时,长高比Γ=30的矩形腔体中混合流体Rayleigh-Benard对流发生点附近扰动的成长和斑图的形成。结果表明:温度场线性成长阶段扰动的成长率γ_m是相对瑞利数r的函数,成长率γ_m随着相对瑞利数r的变化关系式为γ_m=0.9351r^(5.2039);在对流发生点附近的瞬态斑图取决于相对瑞利数r。给出了不同的相对瑞利数r(r分别为1.5、1.7、1.8)的情况下从小振幅到大振幅稳定状态的过渡过程中的两种不同的对流斑图,并讨论了其动力学特性。研究发现,当r较大时,存在行波与定常波共存的现象。

Using the numerical simulations of the two-dimensional full perturbation equations of hydrodynamics, the growth of perturbation and pattern formation near the onset of Rayleigh-Benard convection in the binary fluid mixture with a separation ratio equals to-0.20 and in a rectangular cell with a large-aspect-ratio equals to 30 are studied. It is found that the growth rate of perturbation in linear stage of temperature field is a function of the reduced Rayleigh number, and the transient patterns near the onset of convection depend on relative Rayleigh number. A formula on variation of the growth rate with relative Rayleigh number is proposed. Furthermore, two types of different patterns in transition process from small amplitude to large amplitude for different relative Rayleigh numbers are given, where an interesting coexistence phenomenon of traveling wave and stationary overturning convection is shown.