Kurien S, Sreenivasan K R
Physics Department and Mason Laboratory, Yale University, New Haven, Connecticut 06520-8286, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Nov;64(5 Pt 2):056302. doi: 10.1103/PhysRevE.64.056302. Epub 2001 Oct 22.
Two recent papers [V. Yakhot, Phys. Rev. E 63, 026307, (2001) and R. J. Hill, J. Fluid Mech. 434, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of dynamic equations for structure functions of arbitrary order in turbulence. These equations are not closed. Yakhot proposed a "mean-field theory" to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and expressions for the peak in the probability density function of transverse velocity increments, and for its behavior for intermediate amplitudes. At high Reynolds numbers, some relevant experimental data on pressure gradient and dissipation terms are presented that are needed to provide closure, as well as on other aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory.
最近的两篇论文[V. 亚霍特，《物理评论E》63卷，026307，（2001年）以及R. J. 希尔，《流体力学杂志》434卷，379页，（2001年）]通过两种不同的方法推导出了一组湍流中任意阶结构函数的动力学方程，这两种方法都以纳维 - 斯托克斯方程作为共同的出发点。这些方程是不封闭的。亚霍特提出了一种“平均场理论”来封闭局部各向同性湍流的方程，并得到了结构函数的标度指数以及横向速度增量概率密度函数峰值的表达式，以及其在中间幅度下的行为。在高雷诺数下，给出了一些关于压力梯度和耗散项的相关实验数据，这些数据对于理论的封闭以及理论所预测的其他方面是必要的。理论与数据之间的比较显示出不同程度的一致性，并揭示了理论实施中固有的差距。
