Vortex–Wave Interactions/Self‐Sustained Processes in High Prandtl Number Natural Convection in A Vertical Channel with Moving Sidewalls
Vortex–Wave Interactions/Self‐Sustained Processes in High Prandtl Number Natural Convection in A Vertical Channel with Moving Sidewalls
复制标题
具有移动侧壁的垂直通道中高普朗特数自然对流的涡波相互作用/自持过程
DOI：
10.1111/j.1467-9590.2011.00543.x
复制
发表时间：
2012
影响因子：
2.7
通讯作者：
P. Hall
中科院分区：
文献类型：
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作者：
P. Hall
当充满流体的垂直通道保持温差时，自然对流就发生了。水平温度梯度驱动垂直方向的单向流动。这种流动被沿相等方向和相反方向移动的侧壁所增强。人们对剪切流和对流中可能发生的一般湍流结构很感兴趣，在这里我们给出了与流向涡结构相互作用的波场相关的基本结构。本文考虑了高格拉什夫数极限，并展示了自维持过程是如何以类似于Hall和Smith[1]（以下简称HS1）和Hall和Sherwin[2]（以下简称HS2）讨论的方式与波系统相互作用时发生的。这些波以中性的小振幅模式出现在与重力方向一致的大振幅涡旋上。然后，波通过非线性效应驱动涡旋结构，从而关闭自维持过程。该过程的简化相互作用方程与Couette流或Blasius流的相应方程有很大的不同，并推导了其解的初始形式。结果适用于没有侧壁运动的自然对流，也确实适用于没有加热的库埃特流。我们的分析解释了已知发生在库埃特流中的次谐波自维持过程的起源。
Natural convection takes place when a temperature difference is maintained across a vertical channel filled with fluid. The horizontal temperature gradient drives a unidirectional flow in the vertical direction. This flow is augmented by sidewalls moving in equal and opposite directions. There is much interest in the generic turbulent structures that can occur both in shear flows and convection and here we give the basic structure associated with wavefields interacting with streamwise vortex structures. The high Grashof number limit is considered and it is shown how a self‐sustained process can occur with vortices interacting with a wave system in a manner similar to that discussed by Hall and Smith [ 1 ], hereafter referred to as HS1 and Hall and Sherwin [ 2 ], hereafter referred to as HS2. The waves occur as neutral modes of small amplitude riding on top of large amplitude vortices aligned with the direction of gravity. The waves then drive the vortex structure through nonlinear effects thus closing the self‐sustained process. The simplified interaction equations for the process differ significantly from the corresponding equations in Couette or Blasius flow and we derive the initial form of their solution. The results apply to natural convection without the motion of the sidewalls and indeed to Couette flow when there is no heating. Our analysis explains the origin of subharmonic self‐sustained processes which are known to occur in Couette flow.