Elucidation and control of near-wall turbulence-A new approach by saddle solutions

在这个研究项目中，最近发现有吸引力的鞍解（不稳定的平衡或周期解）重新计算平面Couette，平面Poiffille和自治壁系统，比较它们的性能。结果表明，尽管驱动方式不同，壁面剪切流仍存在普适的鞍解。这些解决方案已被证明是分为两个家庭，其中之一是上支解决方案，其特点是占主导地位的流向涡运动和另一个是下支解决方案，其特点是占主导地位的条纹结构。前者代表了近壁湍流的良好结构和统计特性，而后者则表现出远小于湍流状态的壁面剪切速率。在平面Couette流动的数值实验中，利用混沌控制理论，对壁面剪切率小得多的下分支解（不稳定周期解）进行了稳定化，实现了一种混沌控制， ...更多信息 湍流中表面摩擦阻力显著减小。对平面Couette系统的下支解进行了线性稳定性分析，证明了该解只有一个不稳定特征值。在亚临界雷诺数下，下分支解及其稳定流形形成层流和湍流吸引子之间的盆边界。它已被证明，湍流可以分层，如果一个小振幅的控制输入施加在流动过程中的瞬态方法的下解，因此盆地边界。在平面Couette流中考察了代表近壁湍流的上分支解（不稳定周期解）的性质，表明该解再现了近壁湍流的普遍统计规律，即，普朗特墙定律此外，在高对称性的双箱湍流中也发现了同样的上支解，证实了该解的统计特性与湍流状态下的统计特性是一致的。发现上支解也再现了各向同性湍流的普遍统计规律，即，Kolmogorov相似定律少

In this research project, recently found appealing saddle solutions (unstable equilibrium or periodic solutions) were recomputed in plane Couette, plane Poiseuille, and autonomous wall systems to compare their properties. It has been shown that in spite of diffrernce in the way of driving the systems, there exist universal saddle solutions in wall-bounded shear flow. These solutions have been shown to be classified into two families, one of which is an upper-branch solution characterized by dominant streamwise vortical motion and the other of which is a lower-branch solution characterized by dominant streaky structures. The former represents well structures and statistics for near-wall turbulence, while the latter exhibits wall shear rate much less than that for a turbulent state. In numerical experiments of plane Couette flow, the lower-branch solution (unstable periodic solution) with much less wall shear rate has been stabilized by the use of a chaos control theory to accomplish a s … More ignificant reduction of skin friction drag in turbulent flow. The linear stability analysis of the lower-branch solution for the plane Couette system has been performed to demonstrate that the solution has only one unstable eigenvalue. At subcritical Reynolds numbers the lower-branch solution and its stable manifold form the basin boundary between laminar and turbulent attractors. It has been shown that turbulent flow can be laminarized if a small-amplitude control input is imposed on the flow during its transient approach to the lower solution and so to the basin boundary. The properties of the upper-branch solution (unstable periodic solution) representing near-wall turbulence was examined in plane Couette flow to show that the solution reproduces the universal statistical law of near-wall turbulence, i.e., the Prandtl wall law. Furthermore, the same kind of an upper-branch solution has been discovered in periodic-box turbulence with the high-symmetry to confirm that the statistics of the solution is in good agreement with that in a turbulent state. It has been found that the upper-branch solution also reproduces the universal statistical law of isotropic turbulence, i.e., the Kolmogorov similarity law. Less