STATISTICAL-MECHANICS OF SHELL MODELS FOR 2-DIMENSIONAL TURBULENCE
STATISTICAL-MECHANICS OF SHELL MODELS FOR 2-DIMENSIONAL TURBULENCE
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DOI：
10.1103/physreve.50.4705
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发表时间：
1994-12-01
影响因子：
2.4
通讯作者：
VULPIANI, A
中科院分区：
文献类型：
--
作者：
AURELL, E;BOFFETTA, G;VULPIANI, A
我们研究壳模型，保存类似物的能量和拟能，因此被设计为模拟流体湍流的二维（2D）。主要结果是，观察到的状态被很好地描述为一个正式的统计平衡，非常类似于Onsager [Nuovo Cimento Suppl. 6，279（1949）]，Hopf [J. Rat.机械肛门1，87（1952）]和Lee [Q. 10，69（1952）]。在强迫和耗散的存在下，我们观察到一个向前通量的拟能和一个向后通量的能量。这些通量可以理解为系统中从一个源到两个汇的平均扩散漂移，该系统接近局部平衡，且拉格朗日乘子（“壳温”）随尺度缓慢变化。这清楚地表明，最简单的壳模型不足以再现二维紊流的主要特征。与二维Navier-Stokes方程和Euler方程的相应预测相比，在这些壳模型中，从涡度拟能的前向级联和从正式统计平衡的一个分支得到的功率谱的维数预测是一致的。这种巧合以前曾导致错误的结论，即壳模型表现出前向级联拟能。我们还研究了模型的动力学性质和扰动的增长。
We study shell models that conserve the analogs of energy and enstrophy and hence are designed to mimic fluid turbulence in two-dimensions (2D). The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager [Nuovo Cimento Suppl. 6, 279 (1949)], Hopf [J. Rat. Mech. Anal. 1, 87 (1952)], and Lee [Q. Appl. Math. 10, 69 (1952)]. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (‘‘shell temperatures’’) changing slowly with scale. This is clear evidence that the simplest shell models are not adequate to reproduce the main features of two-dimensional turbulence. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy and from one branch of the formal statistical equilibrium coincide in these shell models in contrast to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence has previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy. We also study the dynamical properties of the models and the growth of perturbations.