Elucidation and control of coherent structures and large-scale turbulence structures based on saddle solutions

这项工作的目的是利用Navier-Stokes方程的不稳定周期和定常行波解来阐明或控制相干结构和大尺度湍流结构。在平面Couette系统中，通过层流吸引子和湍流吸引子之间盆地边界上周期轨道的不稳定流形来描述过渡到湍流的动态流动行为，而减阻是通过限制在近壁区的控制输入来实现的。在方管流动中发现了行波解，用来证明相干结构和湍流驱动的二次流之间的直接关联。

The aim of this work is to elucidate or control coherent structures and large-scale turbulence structures using unstable periodic and steady traveling-wave solutions to the Navier-Stokes equation. In a plane Couette system dynamical flow behavior in transition to turbulence has been characterized in terms of the unstable manifold of the periodic orbit on the basin boundary between laminar and turbulent attractors, while a drag reduction has been accomplished by use of control input confined to the near-wall regions. The traveling-wave solution has been discovered in square-duct flow to be used for demonstration of direct relevance between coherent structures and turbulence-driven secondary flow.