中国物理B ›› 2007, Vol. 16 ›› Issue (10): 2848-2854.doi: 10.1088/1009-1963/16/10/004

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Anomalous scaling in a non-Gaussian random shell model for passive scalars

陈式刚1, 王光瑞1, 赵英奎2   

  1. (1)Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; (2)Graduate School of China Academy of Engineering Physics, Beijing 100088, China；Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • 收稿日期:2007-01-23 修回日期:2007-02-13 出版日期:2007-10-08 发布日期:2007-10-08
  • 基金资助:
    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).

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)   

  1. 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
  • Received:2007-01-23 Revised:2007-02-13 Online:2007-10-08 Published:2007-10-08
  • Supported by:
    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).

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摘要： 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 L\'{e}v\^{e}que (Phys. Rev. Lett. {\bf 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.

关键词: scaling, shell model, She and L\'{e}v\^{e}que (SL) model, non-Gaussian, passive scalar

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.

Key words: scaling, shell model, She and Lévêque (SL) model, non-Gaussian, passive scalar

中图分类号:  (Fluctuation phenomena, random processes, noise, and Brownian motion)

  • 05.40.-a
02.50.Ey (Stochastic processes) 02.50.Ng (Distribution theory and Monte Carlo studies) 47.10.-g (General theory in fluid dynamics)