## Abstract

Mean-field theory for turbulent transport of a passive scalar (e.g., particles and gases) is discussed. Equations for the mean number density of particles advected by a random velocity field, with a finite correlation time, are derived. Mean-field equations for a passive scalar comprise spatial derivatives of high orders due to the nonlocal nature of passive scalar transport in a random velocity field with a finite correlation time. A turbulent velocity field with a random renewal time is considered. This model is more realistic than that with a constant renewal time used by Elperin et al. [Phys. Rev. E 61, 2617 (2000)], and employs two characteristic times: the correlation time of a random velocity field (Formula presented) and a mean renewal time (Formula presented). It is demonstrated that the turbulent diffusion coefficient is determined by the minimum of the times (Formula presented) and (Formula presented). The mean-field equation for a passive scalar was derived for different ratios of (Formula presented) The important role of the statistics of the field of Lagrangian trajectories in turbulent transport of a passive scalar, in a random velocity field with a finite correlation time, is demonstrated. It is shown that in the case (Formula presented) the form of the mean-field equation for a passive scalar is independent of the statistics of the velocity field, where (Formula presented) is the characteristic time of variations of a mean passive scalar field.

Original language | English |
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Pages (from-to) | 9 |

Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 64 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 2001 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics