Geometry of the turbulence in wall-bounded shear flows: periodic orbits
Geometry of the turbulence in wall-bounded shear flows: periodic orbits
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DOI：
10.1088/0031-8949/2010/t142/014007
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发表时间：
2010-12-01
期刊：
影响因子：
2.9
通讯作者：
Gibson, J. F.
中科院分区：
文献类型：
--
作者：
Cvitanovic, P.;Gibson, J. F.
中等雷诺数湍流的动力学理论通过一组精确解（平衡、相对平衡、周期轨道等）将无限维Navier-Stokes状态空间三角化，形成一个刚性的主干，使我们能够描述和预测湍流流体的正弦运动。我们报告的一组不稳定的周期轨道的确定密切递归的湍流。几个平衡，密切类似于经常观察到的，但不稳定的相干结构用于构建一个低维的状态空间投影从极高维的数据集。湍流可以被看作是一系列接近不稳定周期轨道的通道，即湍流典型的时间递归动力学相干结构。
The dynamical theory of moderate Reynolds number turbulence triangulates the infinite-dimensional Navier-Stokes state space by sets of exact solutions (equilibria, relative equilibria, periodic orbits, etc), which form a rigid backbone that enables us to describe and predict the sinuous motions of a turbulent fluid. We report on the determination of a set of unstable periodic orbits from close recurrences of the turbulent flow. A few equilibria that closely resemble frequently observed but unstable coherent structures are used for constructing a low-dimensional state-space projection from the extremely high-dimensional data sets. The turbulent flow can then be visualized as a sequence of close passages to unstable periodic orbits, i.e the time-recurrent dynamical coherent structures typical of a turbulent flow.