Mean-field theory for a passive scalar advected by a turbulent velocity field with a random renewal time.
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 tau(c), and a mean renewal time tau. It is demonstrated that the turbulent diffusion coefficient is determined by the minimum of the times tau(c) and tau. The mean-field equation for a passive scalar was derived for different ratios of tau/tau(c). 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 tau(c)<<tau<<tau(N) the form of the mean-field equation for a passive scalar is independent of the statistics of the velocity field, where tau(N) is the characteristic time of variations of a mean passive scalar field.
Elperin
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T
The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, P. O. Box 653, Israel.
Kleeorin
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N
Rogachevskii
I
I
Sokoloff
D
D