Diffusion of passive scalar in a finite-scale random flow

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dc.creatorSchekochihin, A. A.
dc.creatorHaynes, P. H.
dc.creatorCowley, S. C.
dc.date2004-04-08
dc.date2004-12-01
dc.date.accessioned2026-07-07T10:50:42Z
dc.date.available2026-07-07T10:50:42Z
dc.descriptionWe 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/λ. 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<<k<<k_flow) is ~ k + a k^2 + ... (a>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.
dc.descriptionrevtex4, 8 pages, 4 figures; final published version
dc.identifierhttps://arxiv.org/abs/nlin/0404016
dc.identifierhttp://arxiv.org/abs/nlin/0404016
dc.identifierPhys.Rev.E70:046304,2004
dc.identifierdoi:10.1103/PhysRevE.70.046304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184620
dc.subjectChaotic Dynamics
dc.subjectAstrophysics
dc.subjectAtmospheric and Oceanic Physics
dc.subjectFluid Dynamics
dc.titleDiffusion of passive scalar in a finite-scale random flow
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