利用周期轨道粗粒化湍流的状态空间
Coarse graining the state space of a turbulent flow using periodic orbits
摘要：
我们表明，在正弦强迫下的三阶周期域中的三维纳维-斯托克斯方程的模拟中出现的湍流动力学可以被描述为对不稳定的时间周期解的邻域的瞬态访问。基于这种描述，我们减少了原来的系统与更多的$10^5$自由度到一个17节点的马尔可夫链，其中每个节点对应于一个周期轨道的邻域。该模型准确地再现长期平均系统的观测值作为加权和周期轨道。
英文摘要：
We show that turbulent dynamics that arise in simulations of the three-dimensional Navier--Stokes equations in a triply-periodic domain under sinusoidal forcing can be described as transient visits to the neighborhoods of unstable time-periodic solutions. Based on this description, we reduce the original system with more than $10^5$ degrees of freedom to a 17-node Markov chain where each node corresponds to the neighborhood of a periodic orbit. The model accurately reproduces long-term averages of the system's observables as weighted sums over the periodic orbits.
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