Singular Measures and Information Capacity of Turbulent Cascades
Singular Measures and Information Capacity of Turbulent Cascades
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DOI：
10.1103/physrevlett.125.104501
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发表时间：
2020-08-31
影响因子：
8.6
通讯作者：
Falkovich, Gregory
中科院分区：
文献类型：
--
作者：
Shavit, Michal;Falkovich, Gregory
弱湍流有多弱？在这里，我们用信息论的工具来分析弱相互作用波的湍流。它为比较热平衡和湍流提供了一个独特的视角。在热平衡条件下，模间的互信息是稳定的，并且很小，但对于有限盒子中的弱湍流，互信息随时间增长。我们将这种增长追溯到共振面上的概率集中，这可以一直到一个奇异的度量。令人惊讶的结论是，无论非线性多么小，任何单个幅度的统计量多么接近高斯，静止的相空间测量都远不是高斯的，正如大的相对熵所表明的那样。对于湍流模型来说，这是一个难得的好消息：已分辨的尺度携带着关于未分辨尺度的重要信息。大小尺度之间的互信息是湍流叶栅的信息量，对湍流数值模拟中子网格尺度的表示有一定的限制。
How weak is the weak turbulence? Here, we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence. The mutual information between modes is stationary and small in thermal equilibrium, yet it is shown here to grow with time for weak turbulence in a finite box. We trace this growth to the concentration of probability on the resonance surfaces, which can go all the way to a singular measure. The surprising conclusion is that no matter how small is the nonlinearity and how close to Gaussian is the statistics of any single amplitude, a stationary phase-space measure is far from Gaussian, as manifested by a large relative entropy. This is a rare piece of good news for turbulence modeling: the resolved scales carry significant information about the unresolved scales. The mutual information between large and small scales is the information capacity of turbulent cascade, setting the limit on the representation of subgrid scales in turbulence modeling.