Diffusion of passive scalar in a finite-scale random flow
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-sca...
| Main Authors: | , , |
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| Format: | Journal article |
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2004
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| _version_ | 1797091703911350272 |
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| author | Schekochihin, A Haynes, P Cowley, S |
| author_facet | Schekochihin, A Haynes, P Cowley, S |
| author_sort | Schekochihin, A |
| collection | OXFORD |
| description | 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<<k<<k_flow) (a="" +="" ...="" a="" is="" k="" k^2="" ~="">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.</k<<k_flow)> |
| first_indexed | 2024-03-07T03:36:46Z |
| format | Journal article |
| id | oxford-uuid:bc8f9a11-f1dc-4685-886e-b707d75e8423 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:36:46Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:bc8f9a11-f1dc-4685-886e-b707d75e84232022-03-27T05:25:12ZDiffusion of passive scalar in a finite-scale random flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bc8f9a11-f1dc-4685-886e-b707d75e8423Symplectic Elements at Oxford2004Schekochihin, AHaynes, PCowley, SWe 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<<k<<k_flow) (a="" +="" ...="" a="" is="" k="" k^2="" ~="">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.</k<<k_flow)> |
| spellingShingle | Schekochihin, A Haynes, P Cowley, S Diffusion of passive scalar in a finite-scale random flow |
| title | Diffusion of passive scalar in a finite-scale random flow |
| title_full | Diffusion of passive scalar in a finite-scale random flow |
| title_fullStr | Diffusion of passive scalar in a finite-scale random flow |
| title_full_unstemmed | Diffusion of passive scalar in a finite-scale random flow |
| title_short | Diffusion of passive scalar in a finite-scale random flow |
| title_sort | diffusion of passive scalar in a finite scale random flow |
| work_keys_str_mv | AT schekochihina diffusionofpassivescalarinafinitescalerandomflow AT haynesp diffusionofpassivescalarinafinitescalerandomflow AT cowleys diffusionofpassivescalarinafinitescalerandomflow |