Two-dimensional turbulence in the inverse cascade range.
Two-dimensional turbulence in the inverse cascade range.
复制标题
逆级联范围内的二维湍流。
DOI：
10.1103/physreve.60.5544
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
V. Yakhot
中科院分区：
文献类型：
--
作者：
V. Yakhot
强制二维纳维-斯托克斯方程的数值和物理实验表明，横向速度差由“正常”柯尔莫哥洛夫标度 <(deltav)(2n)> 比例 r(2n/3) 描述，并服从高斯统计。由于非平凡缩放是问题强非线性的标志，因此这两个结果似乎相互矛盾。本文提出了解释这些观察结果的理论。导出的压力梯度贡献的自洽表达式得出这样的结论：小尺度横向速度差由线性朗之万方程控制，并受到非局部、通用、依赖于解的高斯随机力的搅拌。这解释了实验观察到的横向速度差的高斯统计及其柯尔莫哥洛夫标度。纵向速度差 PDF 的求解基于二维湍流中能量通量的数值较小。该理论做出了一些可以通过实验检验的定量预测。
Numerical and physical experiments on forced two-dimensional Navier-Stokes equations show that transverse velocity differences are described by "normal" Kolmogorov scaling <(deltav)(2n)> proportional r(2n/3) and obey Gaussian statistics. Since nontrivial scaling is a sign of the strong nonlinearity of the problem, these two results seem to contradict each other. A theory explaining these observations is presented in this paper. The derived self-consistent expression for the pressure gradient contributions leads to the conclusion that small-scale transverse velocity differences are governed by a linear Langevin-like equation, stirred by a nonlocal, universal, solution-dependent Gaussian random force. This explains the experimentally observed Gaussian statistics of transverse velocity differences and their Kolmogorov scaling. The solution for the PDF of longitudinal velocity differences is based on the numerical smallness of the energy flux in two-dimensional turbulence. The theory makes a few quantitative predictions that can be tested experimentally.