Global stability of time-dependent flows. Part 2. Modulated fluid layers
Global stability of time-dependent flows. Part 2. Modulated fluid layers
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随时间变化的流量的全局稳定性。
DOI：
10.1017/s0022112074000747
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发表时间：
1974
影响因子：
3.7
通讯作者：
G. Homsy
中科院分区：
文献类型：
--
作者：
G. Homsy
利用能量方法给出了一大类调制Bénard问题的两个稳定性判据。这两个判据都给出了适用于任意幅度扰动的稳定极限。其中第一个被称为强全球稳定，它要求所有扰动的能量在时间上单调和指数地衰减。该判据的应用导致了瑞利数的预测，在瑞利数以下，Bous-Sinesq方程的扩散停滞解是唯一的。第二个标准只要求干扰在许多调制周期内渐近衰减到零，这是一个较弱的稳定性概念。使用这两个准则的计算结果给出了可获得线性渐近稳定性结果的各种具体情况的计算结果，并且可以看到能量极限和线性极限往往彼此接近。
The method of energy is used to develop two stability criteria for a large class of modulated Bénard problems. Both criteria give stability limits which hold for disturbances of arbitrary amplitude. The first of these, designated as strong global stability, requires the energy of all disturbances to decay monotonically and exponentially in time. Application of this criterion results in a prediction of Rayleigh numbers below which the diffusive stagnant solution to the Bous-sinesq equations is unique. The second criterion requires only that disturbances decay asymptotically to zero over many cycles of modulation, and is a weaker concept of stability. Computational results using both criteria are given for a wide range of specific cases for which linear asymptotic stability results are available, and it is seen that the energy and linear limits often lie close to one another.