论文标题
用周期性轨道进行粗砂湍流的状态空间
Coarse graining the state space of a turbulent flow using periodic orbits
论文作者
论文摘要
我们表明，在仿真的三维纳维尔 - 正弦强迫下的三维纳维尔的模拟中产生的湍流动力学可以描述为对不稳定时间周期溶液的邻里的短暂访问。基于此描述，我们将其自由度超过$ 10^5 $自由度减少到17节点的马尔可夫链中，每个节点都对应于周期轨道的邻域。该模型准确地将系统可观察物的长期平均值作为周期轨道上的加权总和。
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.
