Baiesi Marco, Maes Christian
Instituut voor Theoretische Fysica, K.U.Leuven, Celestijnenlaan 200D, B-3001, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Nov;72(5 Pt 2):056314. doi: 10.1103/PhysRevE.72.056314. Epub 2005 Nov 11.
Insight into the problem of two-dimensional turbulence can be obtained by an analogy with a heat conduction network. It allows the identification of an entropy function associated with the enstrophy dissipation and that fluctuates around a positive (mean) value. While the corresponding enstrophy network is highly nonlocal, the direction of the enstrophy current follows from the Second Law of Thermodynamics. An essential parameter is the ratio of the intensity of driving as a function of wave number , to the dissipation strength , where is the viscosity. The enstrophy current flows from higher to lower values of , similar to a heat current from higher to lower temperature. Our probabilistic analysis of the enstrophy dissipation and the analogy with heat conduction thus complements and visualizes the more traditional spectral arguments for the direct enstrophy cascade. We also show a fluctuation symmetry in the distribution of the total entropy production which relates the probabilities of direct and inverse enstrophy cascades.
通过与热传导网络进行类比，可以深入了解二维湍流问题。这使得能够识别与涡量耗散相关的熵函数，该熵函数围绕一个正值（平均值）波动。虽然相应的涡量网络具有高度的非局部性，但涡量流的方向遵循热力学第二定律。一个重要参数是作为波数函数的驱动强度与耗散强度的比值，其中 是粘性系数。涡量流从较高的 值流向较低的 值，类似于热流从较高温度流向较低温度。因此，我们对涡量耗散的概率分析以及与热传导的类比，补充并直观展示了关于直接涡量级联的更传统的频谱论证。我们还展示了总熵产生分布中的涨落对称性，它关联了直接和反向涡量级联的概率。
