Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow
Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow
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DOI：
10.1063/1.4917279
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发表时间：
2014-06
影响因子：
4.6
通讯作者：
D. Lucas;R. Kerswell
中科院分区：
文献类型：
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作者：
D. Lucas;R. Kerswell
最近成功的动力系统的方法过渡流的动机，我们研究的效率和有效性提取简单的不变集（经常性的流）直接从混沌/湍流和这些集的潜力提供预测的某些统计流。研究了二维Kolmogorov流（含正弦体积力的二维Navier-Stokes方程）在正方形[0，2π]2圆环和沿强迫方向延伸的矩形圆环上的流动.在前一种情况下，一个数量级更多的经常性流动发现比以前[G。钱德勒和R. R. Kerswell，“Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow，”J. Fluid Mech.722，554-595（2013）]，并且示出了通过周期轨道理论对混沌的耗散和能量pdf给出改进的预测。对环流的分析表明，通过逆级联过程和二维平流非线性特征的结合，能量主要被捕获在最小波数中。在低强迫振幅下的扩展环面上，一些提取的状态模拟了空间局部混沌的统计，令人惊讶地很好地回顾了Kawahara和Kida [“Periodic motion embedded in plane Couette turbulence：Regeneration cycle and burst，”J. Fluid Mech.449，291（2001）]在低雷诺数平面Couette流中的发现。然而，在更高的强迫振幅下，成功是有限的，突出了混沌的维数增加和对更大数据集的需求。讨论了改进萃取过程的化学发展。
Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of these sets for providing predictions of certain statistics of the flow. Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a sinusoidal body force) is studied both over a square [0, 2π]2 torus and a rectangular torus extended in the forcing direction. In the former case, an order of magnitude more recurrent flows are found than previously [G. J. Chandler and R. R. Kerswell, “Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow,” J. Fluid Mech. 722, 554–595 (2013)] and shown to give improved predictions for the dissipation and energy pdfs of the chaos via periodic orbit theory. Analysis of the recurrent flows shows that the energy is largely trapped in the smallest wavenumbers through a combination of the inverse cascade process and a feature of the advective nonlinearity in 2D. Over the extended torus at low forcing amplitudes, some extracted states mimic the statistics of the spatially localised chaos present surprisingly well recalling the findings of Kawahara and Kida [“Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst,” J. Fluid Mech. 449, 291 (2001)] in low-Reynolds-number plane Couette flow. At higher forcing amplitudes, however, success is limited highlighting the increased dimensionality of the chaos and the need for larger data sets. Algorithmic developments to improve the extraction procedure are discussed.