Small scale exact coherent structures at large Reynolds numbers in plane Couette flow
Small scale exact coherent structures at large Reynolds numbers in plane Couette flow
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DOI：
10.1088/1361-6544/aa9462
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发表时间：
2018-02-01
期刊：
影响因子：
1.7
通讯作者：
Zammert, Stefan
中科院分区：
文献类型：
--
作者：
Eckhardt, Bruno;Zammert, Stefan
平面库埃特流和其他几种剪切流中向湍流的转变与鞍点分岔有关，其中出现了纳维-斯托克斯方程的完全三维非线性解，即所谓的精确相干态 (ECS)。随着雷诺数的增加，状态会发生二次分岔，并且它们的时间演化变得越来越复杂。相反，它们的空间复杂性仍然有限，因此这些状态不能增加空间复杂性，也不能级联到更高雷诺数所预期的更小尺度。我们在这里介绍了随着雷诺数增加而以越来越小的规模存在的缩放 ECS 系列。我们特别关注平面库埃特流的两个这样的族，一个集中在中平面附近，另一个集中在墙壁附近。我们讨论它们的缩放和定位属性以及分叉图。所有解都集中在壁法线方向上。在翼展方向和下游方向，它们要么是周期性的，要么是局部的。位于壁附近的缩放 ECS 系列让人想起附着的涡流，并表明自相似 ECS 如何有助于边界层轮廓的形成。
The transition to turbulence in plane Couette flow and several other shear flows is connected with saddle node bifurcations in which fully three-dimensional, nonlinear solutions to the Navier-Stokes equation, so-called exact coherent states (ECS), appear. As the Reynolds number increases, the states undergo secondary bifurcations and their time-evolution becomes increasingly more complex. Their spatial complexity, in contrast, remains limited so that these states cannot contribute to the spatial complexity and cascade to smaller scales expected for higher Reynolds numbers. We here present families of scaling ECS that exist on ever smaller scales as the Reynolds number is increased. We focus in particular on two such families for plane Couette flow, one centered near the midplane and the other close to a wall. We discuss their scaling and localization properties and the bifurcation diagrams. All solutions are localized in the wall-normal direction. In the spanwise and downstream direction, they are either periodic or localized as well. The family of scaling ECS localized near a wall is reminiscent of attached eddies, and indicates how self-similar ECS can contribute to the formation of boundary layer profiles.