Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow
Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow
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DOI：
10.1017/jfm.2013.122
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发表时间：
2013-05-01
影响因子：
3.7
通讯作者：
Kerswell, Rich R.
中科院分区：
文献类型：
--
作者：
Chandler, Gary J.;Kerswell, Rich R.
我们考虑了二维湍流体的长时间模拟，该湍流体由sin 4y（x）在环面（x，y）上的帽强迫，帽是[0，2 pi]（2）的元素，目的是提取嵌入该湍流中的简单不变集或“精确回归流”。每一个经常性的流动代表了一个持续的封闭循环的动力学过程的基础上的湍流。这些被用来重建湍流统计使用周期轨道理论。该方法被认为是合理的成功，在一个低的强迫值的流量接近，但不完全在其渐近（强）湍流制度。在这里，共发现50个经常性的流动，其中大部分被埋在相空间的一部分，由湍流引起的能量和耗散p.d.f.的良好再现。然而，在较高的强迫振幅，现在在渐近湍流制度，产生的湍流数据集证明不够长，产生足够的经常性流动，使可行的预测。尽管如此，一般的方法似乎有希望提供足够的模拟数据是可用的，因为它是开放的广泛的自动化和自然生成动态重要的精确的解决方案的流动。
We consider long-time simulations of two-dimensional turbulence body forced by sin 4y (x) over cap on the torus (x, y) is an element of [0, 2 pi](2) with the purpose of extracting simple invariant sets or 'exact recurrent flows' embedded in this turbulence. Each recurrent flow represents a sustained closed cycle of dynamical processes which underpins the turbulence. These are used to reconstruct the turbulence statistics using periodic orbit theory. The approach is found to be reasonably successful at a low value of the forcing where the flow is close to but not fully in its asymptotic (strongly) turbulent regime. Here, a total of 50 recurrent flows are found with the majority buried in the part of phase space most populated by the turbulence giving rise to a good reproduction of the energy and dissipation p.d.f. However, at higher forcing amplitudes now in the asymptotic turbulent regime, the generated turbulence data set proves insufficiently long to yield enough recurrent flows to make viable predictions. Despite this, the general approach seems promising providing enough simulation data is available since it is open to extensive automation and naturally generates dynamically important exact solutions for the flow.