SIMPLE-MODELS OF NON-GAUSSIAN STATISTICS FOR A TURBULENTLY ADVECTED PASSIVE SCALAR

被引:28
作者
HOLZER, M
PUMIR, A
机构
[1] ECOLE NORMALE SUPER, PHYS STAT LAB, F-75231 PARIS, FRANCE
[2] CORNELL UNIV, ATOM & SOLID STATE PHYS LAB, ITHACA, NY 14853 USA
来源
PHYSICAL REVIEW E | 1993年 / 47卷 / 01期
关键词
D O I
10.1103/PhysRevE.47.202
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We study the probability distribution of a passive scalar undergoing turbulent mixing in the presence of a mean scalar gradient. Kerstein's model, which describes the turbulent mixing process as a collection of instantaneous local rearrangements of the scalar, is argued to be a plausible approximation when the size of the system is much larger than the velocity correlation length, and after the description has been coarse grained over a correlation volume. In the physical range of parameters, we find numerically that the fluctuations of the scalar theta are close to exponentially distributed when a linear mean scalar gradient is imposed. The phenomenological mean-field-like theory of Pumir, Shraiman, and Siggia [Phys. Rev. Lett. 66, 2984 (1991)] is derived heuristically beginning with the Kerstein model. This theory predicts strictly exponential tails for the probability distribution of the scalar fluctuations P(theta), i.e., P(theta) approximately exp(Absolute value of theta). We also consider a simplified version of the Kerstein model which is analytically fully tractable and gives qualitatively similar results numerically. Under conditions of spatial homogeneity and imposed linear mean scalar gradient, this simplified model and the full Kerstein model are described by the same mean-field theory. However, for the simplified model, the large-Absolute value of theta asymptotic behavior of P(theta) is Poisson-like, i.e., P(theta) approximately exp[-\theta\ln\theta/(const)\].
引用
收藏
页码:202 / 219
页数:18
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