Diffusion of passive scalar in a finite-scale random flow

Details Diffusion of passive scalar in a finite-scale random flow Diffusion of passive scalar in a finite-scale random flow

2004-04-08

arxiv.org/abs/nlin/0404016v2

Phys.Rev.E70:046304,2004

Nonlinear Sciences

Chaotic Dynamics

revtex4, 8 pages, 4 figures; final published version

Scientific paper

10.1103/PhysRevE.70.046304

We consider a solvable model of the decay of scalar variance in a single-scale random velocity field. We show that if there is a separation between the flow scale k_flow^{-1} and the box size k_box^{-1}, the decay rate lambda ~ (k_box/k_flow)^2 is determined by the turbulent diffusion of the box-scale mode. Exponential decay at the rate lambda is preceded by a transient powerlike decay (the total scalar variance ~ t^{-5/2} if the Corrsin invariant is zero, t^{-3/2} otherwise) that lasts a time t~1/\lambda. Spectra are sharply peaked at k=k_box. The box-scale peak acts as a slowly decaying source to a secondary peak at the flow scale. The variance spectrum at scales intermediate between the two peaks (k_box<0). The mixing of the flow-scale modes by the random flow produces, for the case of large Peclet number, a k^{-1+delta} spectrum at k>>k_flow, where delta ~ lambda is a small correction. Our solution thus elucidates the spectral make up of the ``strange mode,'' combining small-scale structure and a decay law set by the largest scales.

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