Fibonacci Turbulence
Fibonacci Turbulence
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斐波那契动荡
DOI：
10.1103/physrevx.11.021063
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发表时间：
2021
影响因子：
12.5
通讯作者：
Falkovich, Gregory
中科院分区：
文献类型：
--
作者：
Vladimirova, Natalia;Shavit, Michal;Falkovich, Gregory
热平衡和湍流之间的差异从来没有像当二次不变量使平衡统计完全高斯且具有独立的起伏模式时那样显著。这发生在两类非常不同但紧密相连的系统中：不可压缩流体动力学和共振相互作用的波。这项工作首次详细分析了这种强相互作用系统中的湍流。该分析同时涉及能量和熵，并阐明了空间和时间在确定级联方向和沿其上的统计变化方面的基本作用。我们引入了一个简单而丰富的离散模型族，它具有三个相邻模的相互作用，并且证明了它具有由Fibonacci数定义的二次守恒律。根据相互作用时间随模数的变化，发现了三种类型的湍流：单正向叶栅、双叶栅和首次出现的单反叶栅情况。我们定量地描述了从热平衡到湍流叶栅的偏离如何使统计变得越来越非高斯，并找到了单模概率分布的自相似形式。我们揭示了信息(熵亏)的编码位置，并解开了模式之间的通信通道，通过成对的互信息和三元组内部的相互作用信息来量化。
Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes. That happens in two very different yet deeply connected classes of systems: incompressible hydrodynamics and resonantly interacting waves. This work presents the first detailed information-theoretic analysis of turbulence in such strongly interacting systems. The analysis involves both energy and entropy and elucidates the fundamental roles of space and time in setting the cascade direction and the changes of the statistics along it. We introduce a beautifully simple yet rich family of discrete models with triplet interactions of neighboring modes and show that it has quadratic conservation laws defined by the Fibonacci numbers. Depending on how the interaction time changes with the mode number, three types of turbulence were found: single direct cascade, double cascade, and the first-ever case of a single inverse cascade. We describe quantitatively how deviation from thermal equilibrium all the way to turbulent cascades makes statistics increasingly non-Gaussian and find the self-similar form of the one-mode probability distribution. We reveal where the information (entropy deficit) is encoded and disentangle the communication channels between modes, as quantified by the mutual information in pairs and the interaction information inside triplets.
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DOI：
10.1103/physreve.65.056305
发表时间：
2002-05
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
C. Pasquero;G. Falkovich
通讯作者：
C. Pasquero;G. Falkovich
重新审视 SABRA 模型：静力学和动力学
DOI：
10.1209/0295-5075/120/34002
发表时间：
2017
期刊：
Europhysics Letters
影响因子：
--
作者：
Rithwik Tom;Samriddhi Sankar Ray
通讯作者：
Samriddhi Sankar Ray
影响因子：
0.8
作者：
GUERRERO, JL
通讯作者：
GUERRERO, JL
影响因子：
8.6
作者：
Shavit, Michal;Falkovich, Gregory
通讯作者：
Falkovich, Gregory
影响因子：
2.4
作者：
AURELL, E;BOFFETTA, G;VULPIANI, A
通讯作者：
VULPIANI, A