Anomalous scaling in a non-Gaussian random shell model for passive scalars
Zhao Ying-Kui(赵英奎)a)b)†, Chen Shi-Gang(陈式刚)b), and Wang Guang-Rui(王光瑞)b)
a Graduate School of China Academy of Engineering Physics, Beijing 100088, China; b Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Abstract In this paper, we have introduced a shell-model of Kraichnan's passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and $\delta$ correlated in time, and its introduction is inspired by She and Lévêque (Phys. Rev. Lett.72, 336 (1994)). For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents $H(p)$ of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of $p$ up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the $H(p)$ advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.
Received: 23 January 2007
Revised: 13 February 2007
Accepted manuscript online:
PACS:
05.40.-a
(Fluctuation phenomena, random processes, noise, and Brownian motion)
Fund: Project supported by the Major Program of the National Natural
Science Foundation (Grant No~10335010) and the National Natural Science Foundation-the Science Foundation of China Academy
of Engineering Physics NSAF (Grant No~10576005).
Cite this article:
Zhao Ying-Kui(赵英奎), Chen Shi-Gang(陈式刚), and Wang Guang-Rui(王光瑞) Anomalous scaling in a non-Gaussian random shell model for passive scalars 2007 Chinese Physics 16 2848
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