Spatio-temporal instability of the natural-convection boundary layer in thermally stratified medium
Spatio-temporal instability of the natural-convection boundary layer in thermally stratified medium
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DOI：
10.1017/s0022112004001119
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发表时间：
2004-10
影响因子：
3.7
通讯作者：
J. Tao;P. Quéré;S. Xin
中科院分区：
文献类型：
--
作者：
J. Tao;P. Quéré;S. Xin
本文研究了浸入热分层环境介质中垂直受热平板附近的自然对流边界层流动的时空不稳定性。板表面的温度呈线性分布。通过在壁面和介质之间引入温度梯度射电，我们得到了一个相似解，它可以光滑地描述等温和等热流边界条件下状态之间的演化。结果表明，当$a$大于某一临界值时，基本流中的回流现象消失。在Orr-Sommerfeld方程和能量方程耦合的情况下，确定了这种流动的一种新的绝对对流不稳定转捩。增大$a$会减小绝对不稳定的范围，当$a$足够大时，绝对不稳定消失。特别是当$a\,{=}\,0$（等温面）时，较大普朗特数的流体的绝对不稳定区间变窄，大于70的普朗特数不发生绝对不稳定；当$a\,{=}\,1$（均匀热流面）时，不稳定性在很大的普朗特数范围内保持对流。对该问题的瑞利方程的分析表明，支持这种新的不稳定过渡的基本流具有对流不稳定的非粘源。基于陡峻全局模态理论，讨论了a和普朗特数对全局频率的影响。
This paper investigates the spatio-temporal instability of the natural-convection boundary-layer flow adjacent to a vertical heated flat plate immersed in a thermally stratified ambient medium. The temperature on the plate surface is distributed linearly. By introducing a temperature gradient radio $a$ between the wall and the medium, we obtain a similarity solution which can describe in a smooth way the evolution between the states with isothermal and uniform-heat-flux boundary conditions. It is shown that the flow reversal in the basic flow vanishes when $a$ is larger than a critical value. A new absolute–convective instability transition of this flow is identified in the context of the coupled Orr–Sommerfeld and energy equations. Increasing $a$ decreases the domain of absolute instability, and when $a$ is large enough the absolute instability disappears. In particular, when $a\,{=}\,0$ (isothermal surface), the interval of absolute instability becomes narrower for fluids of larger Prandtl numbers, and the absolute instability does not occur for Prandtl numbers greater than 70; when $a\,{=}\,1$ (uniform-heat-flux surface) the instability remains convective in a wide Prandtl number range. Analysis of the Rayleigh equations for this problem reveals that the basic flows supporting this new instability transition have inviscid origin of convective instability. Based on the steep global mode theory, the effects of $a$ and Prandtl number on the global frequency are discussed as well.