Koopman analysis of the long-term evolution in a turbulent convection cell
Koopman analysis of the long-term evolution in a turbulent convection cell
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DOI：
10.1017/jfm.2018.297
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发表时间：
2018-07-25
影响因子：
3.7
通讯作者：
Schumacher, Joerg
中科院分区：
文献类型：
--
作者：
Giannakis, Dimitrios;Kolchinskaya, Anastasiya;Schumacher, Joerg
我们通过库普曼本征函数分析来分析封闭立方湍流瑞利-贝纳德对流室中三维流动的长期演化。这里采用从机器学习中已知的扩散核导出的数据驱动基础来表示伽辽金近似意义上的酉库普曼群的正则化生成器。得到的库普曼本征函数可以根据立方盒中的离散对称性分为子集。特别是，速度场在第一组本征函数上的投影揭示了对流单元中的四种稳定的大尺度环流（LSC）状态。我们重新捕获了对角处的优先循环滚动以及平行于侧面的滚动状态的短期切换，这在其他模拟和实验中也出现过。对角宏观流动状态可以持续长达 1000 个对流自由落体时间单位。此外，我们发现次级子集中的特定库普曼本征函数对服从增强的振荡波动，以实现 LSC 的特定稳定对角状态。还通过时空重建讨论了相应的速度场结构，例如中平面的角涡和漩涡。
We analyse the long-time evolution of the three-dimensional flow in a closed cubic turbulent Rayleigh-Benard convection cell via a Koopman eigenfunction analysis. A data-driven basis derived from diffusion kernels known in machine learning is employed here to represent a regularized generator of the unitary Koopman group in the sense of a Galerkin approximation. The resulting Koopman eigenfunctions can be grouped into subsets in accordance with the discrete symmetries in a cubic box. In particular, a projection of the velocity field onto the first group of eigenfunctions reveals the four stable large-scale circulation (LSC) states in the convection cell. We recapture the preferential circulation rolls in diagonal corners and the short-term switching through roll states parallel to the side faces which have also been seen in other simulations and experiments. The diagonal macroscopic flow states can last as long as 1000 convective free-fall time units. In addition, we find that specific pairs of Koopman eigenfunctions in the secondary subset obey enhanced oscillatory fluctuations for particular stable diagonal states of the LSC. The corresponding velocity-field structures, such as corner vortices and swirls in the midplane, are also discussed via spatiotemporal reconstructions.