Xu Haitao, Pumir Alain, Falkovich Gregory, Bodenschatz Eberhard, Shats Michael, Xia Hua, Francois Nicolas, Boffetta Guido
International Collaboration for Turbulence Research, D-37077 Göttingen, Germany;Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany;
International Collaboration for Turbulence Research, D-37077 Göttingen, Germany;Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany;Laboratoire de Physique, Ecole Normale Supérieure de Lyon, Université de Lyon 1 and Centre National de la Recherche Scientifique, F-69007 Lyon, France;
Proc Natl Acad Sci U S A. 2014 May 27;111(21):7558-63. doi: 10.1073/pnas.1321682111. Epub 2014 May 2.
The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare "flight-crash" events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales.
由于在能量供应和耗散的截然不同的尺度之间存在能量通量,湍流的统计特性在本质上不同于处于热平衡或接近热平衡的系统中的统计特性。我们通过对在湍流中运动的小流体颗粒的能量涨落进行实验和数值研究来阐明这种差异。我们展示了细致平衡的基本性质是如何被打破的,从而对于湍流而言,向前和向后跃迁的概率并不相等。从物理角度来说,我们发现在大量的流动构型中,流体元减速比加速更快,这是在拥堵交通中驾车时大家都非常熟悉的一个特征。与快速颗粒减速相关的罕见“飞行 - 碰撞”事件的统计特征提供了一种量化湍流中不可逆性的方法。具体而言,我们发现沿着轨迹的功率涨落的三阶矩,经能量通量无量纲化后,在二维和三维空间中均呈现出作为雷诺数函数的显著幂律。这建立了系统的不可逆性与活跃尺度范围之间的关系。我们推测这里所表征的细致平衡的破坏是其他远离平衡且展现出广泛空间尺度的系统的一个普遍特征。