Chaotic advection in a Rayleigh-Bénard flow.
Chaotic advection in a Rayleigh-Bénard flow.
复制标题
瑞利-贝纳德流中的混沌平流。
DOI：
10.1103/physreva.43.774
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
Wiggins
中科院分区：
文献类型：
--
作者：
Camassa;Wiggins
我们考虑与时间相关的流中被动示踪剂的传输问题，该流对应于瑞利-贝纳德对流辊的均匀振荡不稳定开始时略高于 scrRt 的瑞利数 scrR。通过使用流函数对流动进行建模，我们展示了如何在没有分子扩散性的情况下构建和识别流动中的不变结构，这些结构充当流体粒子运动的“模板”。这种方法和对称性考虑使我们能够编写明确的公式来描述有限次数的示踪剂传输。在振荡小振幅的极限下，即当 (scrR-scrRt)1/2 很小时，我们表明穿过滚动边界输送的流体量随振幅线性增长，这与 Solomon 和 Gollub 的实验和数值结果一致 [Phys. Rev. A 38, 6280 (1988)]。分子扩散性的存在给问题带来了（长）时间尺度。我们讨论了该理论在这种情况下的适用性，通过引入一个简单的规则来确定何时扩散率的影响可以忽略不计，并对这种情况下的流动进行数值模拟以提供一个例子。
We consider the problem of transport of a passive tracer in the time-dependent flow corresponding to a Rayleigh number scrR slightly above the scrRt at the onset of the even oscillatory instability for Rayleigh-Benard convection rolls. By modeling the flow with a stream function, we show how to construct and identify invariant structures in the flow that act as a ‘‘template’’ for the motion of fluid particles, in the absence of molecular diffusivity. This approach and symmetry considerations allow us to write explicit formulas that describe the tracer transport for finite times. In the limit of small amplitude of the oscillation, i.e., when (scrR-scrRt)1/2 is small, we show that the amount of fluid transported across a roll boundary grows linearly with the amplitude, in agreement with the experimental and numerical findings of Solomon and Gollub [Phys. Rev. A 38, 6280 (1988)]. The presence of molecular diffusivity introduces a (long) time scale into the problem. We discuss the applicability of the theory in this situation, by introducing a simple rule for determining when the effects of diffusivity are negligible, and perform numerical simulations of the flow in this case to provide an example.