Boffetta G, Celani A, Crisanti A, Vulpiani A
Dipartimento di Fisica Generale, Università di Torino, Via Pietro Giuria 1, 10125 Torino, Italy.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Dec;60(6 Pt A):6734-41. doi: 10.1103/physreve.60.6734.
The Lagrangian statistics of relative dispersion in fully developed turbulence is numerically investigated. A scaling range spanning many decades is achieved by generating a two-dimensional velocity field by means of a stochastic process with prescribed statistics and of a dynamical model (shell model) with fluctuating characteristic times. When the velocity field obeys Kolmogorov similarity, the Lagrangian statistics is self similar and agrees with Richardson's predictions [Proc. R. Soc. London Ser. A 110, 709 (1926)]. For intermittent velocity fields the scaling laws for the Lagrangian statistics are found to depend on the Eulerian intermittency in agreement with the multifractal description. As a consequence of the Kolmogorov law the Richardson law for the variance of pair separation is, however, not affected by intermittency corrections. Moreover, Lagrangian exponents do not depend on the particular Eulerian dynamics. A method of data analysis, based on fixed scale statistics rather than usual fixed time statistics, is shown to give much wider scaling range, and should be preferred for the analysis of experimental data.
对充分发展的湍流中相对扩散的拉格朗日统计进行了数值研究。通过具有规定统计特性的随机过程和具有波动特征时间的动力学模型（壳模型）生成二维速度场，实现了跨越多个数量级的标度范围。当速度场服从柯尔莫哥洛夫相似性时，拉格朗日统计是自相似的，并且与理查森的预测一致[《伦敦皇家学会学报》A辑110, 709 (1926)]。对于间歇性速度场，发现拉格朗日统计的标度律取决于欧拉间歇性，这与多重分形描述一致。然而，由于柯尔莫哥洛夫定律，对分离方差的理查森定律不受间歇性修正的影响。此外，拉格朗日指数不依赖于特定的欧拉动力学。一种基于固定尺度统计而非通常的固定时间统计的数据分析方法，被证明能给出更宽的标度范围，并且在分析实验数据时应优先选用。
