Anomalous scaling in a non-Gaussian random shell model for passive scalars |
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Authors: | Zhao Ying-Kui Chen Shi-Gang and Wang Guang-Rui |
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Institution: | 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 |
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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 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. |
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Keywords: | scaling shell model She and L\'{e}v\^{e}que (SL) model non-Gaussian passive scalar |
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