The instability of streaks in near-wall turbulence
The instability of streaks in near-wall turbulence
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近壁湍流中条纹的不稳定性
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发表时间：
1998
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通讯作者：
A. Pinelli
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作者：
G. Kawahara;J. Jiménez;M. Uhlmann;A. Pinelli
最近对近壁湍流自持机制的几个方面进行了研究（参见 Jimenez & Moin 1991；Hamilton, Kim & Waleffe 1995；Waleffe 1997；Schoppa & Hussain 1997；Jimenez & Pinelli 1998）。众所周知，近壁区域存在两种关键结构：流向涡和条纹。流向涡流通过其引起的横流平流使平均流变形而产生条纹。流向上几乎均匀的条纹变得不稳定，沿流向弯曲并导致流向涡度的产生。最后，产生的流向涡量非线性地演化为流向涡。以这种方式，流向涡流和条纹依次彼此产生以维持近壁湍流。本报告将讨论的条纹的不稳定性预计将成为自我维持循环的一个关键因素。如果条纹不是不稳定的，那么流向涡流应该在粘度的作用下衰减，条纹也应该衰减。这种衰变意味着再生循环的终止。因此，控制条纹不稳定性可以减少阻力或增强近壁湍流中的热量和动量传递。条纹的控制似乎比流向涡流的控制更容易，因为与流向涡流相比，条纹在流向方向上具有更大的长度尺度。由于壁上的条纹流取决于翼展方向以及壁法线方向，因此我们不能将 Squire 变换应用于条纹不稳定，因此我们必须考虑不稳定的三维机制。 Waleffe (1995, 1997) 和 Waleffe & Kim (1997) 在数值上检验了低雷诺数下平面库埃特流中条纹的线性稳定性。他们采用由假设的流向滚动变形的流向速度场作为基流，以证明经常通过实验和数值观察到的正弦模式实际上是通过不稳定机制增长的。他们指出，不稳定源自拐点，即条纹流展向变化中的尾流不稳定。雷迪等人。 (1998) 系统地研究了平面 Poiseuille 流和平面 Couette 流中相同的不稳定性，以研究亚临界转变。另一方面，对于湍流通道流，Schoppa 和 Hussain (1997, 1998) 通过使用直接数值模拟检查了条纹模型流中嵌入的小扰动（仅在一面壁上）的时间演化。他们发现了正弦模式的指数增长，并讨论了不稳定的机制。他们指出，连续不稳定并不是
Several aspects of the self-sustaining mechanism of near-wall turbulence have been studied recently (see Jimenez & Moin 1991; Hamilton, Kim & Waleffe 1995; Waleffe 1997; Schoppa & Hussain 1997; Jimenez & Pinelli 1998). It is well-known that there are two key structures, streamwise vortices and streaks, in the near-wall region. Streamwise vortices generate streaks through the deformation of the mean flow by their induced cross-flow advection. The streaks, which are nearly uniform in the streamwise direction, become unstable, bending along the streamwise direction and leading to the production of streamwise vorticity. Finally, the produced streamwise vorticity evolves nonlinearly into streamwise vortices. In this manner streamwise vortices and streaks generate each other sequentially to sustain near-wall turbulence. The instability of streaks, to be discussed in this report, is expected to be a crucial ingredient in the self-sustaining cycle. If the streaks were not unstable, then the streamwise vortices should decay under the action of viscosity and so also should the streaks. This decay would mean a termination of the regeneration cycle. Therefore, controlling the streak instability could reduce drag or enhance heat and momentum transfer in near-wall turbulent flows. The control of streaks seems to be easier than that of streamwise vortices since streaks have much larger length scale in the streamwise direction compared to that of streamwise vortices. Because streaky flows over a wall depend on the spanwise direction as well as the wall-normal direction, we cannot apply Squire’s transformation to the streak instability, and thus we must consider the three-dimensional mechanism for the instability. Waleffe (1995, 1997) and Waleffe & Kim (1997) examined numerically the linear stability of streaks in a plane Couette flow at a low Reynolds number. They employed the streamwise velocity field deformed by assumed streamwise rolls as a base flow to demonstrate that sinuous modes, which have often been observed experimentally and numerically, actually grow via the instability mechanism. They stated that the instability originates from inflection points, i.e. wake-like instability, in the spanwise variation of streaky flows. Reddy et al. (1998) investigated the same instability systematically in plane Poiseuille flow as well as in plane Couette flow to study subcritical transition. For a turbulent channel flow, on the other hand, Schoppa & Hussain (1997, 1998) examined the time-evolution of small disturbances embedded in a model flow for streaks (on only one wall) by using direct numerical simulations. They found an exponential growth of sinuous modes and discussed the mechanism of the instability. They remarked that the streak instability is not the