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(-1 )(flow ) and the box size k(-1 )(box ) , the decay rate lambda proportional, variant ( k(box) / k(flow) )(2) is determined by the tu...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1826279450758610944 |
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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(-1 )(flow ) and the box size k(-1 )(box ) , the decay rate lambda proportional, variant ( 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 approximately t(-5/2) if the Corrsin invariant is zero, t(-3/2) otherwise) that lasts a time t approximately 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<< (a="" )="" +...="" approximately="" is="" k(2)="" k(flow)="" k+a="">0) . The mixing of the flow-scale modes by the random flow produces, for the case of large Péclet number, a k(-1+delta) spectrum at k>> k(flow) , where delta proportional 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<<> |
| first_indexed | 2024-03-06T23:58:54Z |
| format | Journal article |
| id | oxford-uuid:753d0027-c215-410a-8876-c9d4e26db26d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:58:54Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:753d0027-c215-410a-8876-c9d4e26db26d2022-03-26T20:08:05ZDiffusion of passive scalar in a finite-scale random flow.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:753d0027-c215-410a-8876-c9d4e26db26dEnglishSymplectic 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(-1 )(flow ) and the box size k(-1 )(box ) , the decay rate lambda proportional, variant ( 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 approximately t(-5/2) if the Corrsin invariant is zero, t(-3/2) otherwise) that lasts a time t approximately 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<< (a="" )="" +...="" approximately="" is="" k(2)="" k(flow)="" k+a="">0) . The mixing of the flow-scale modes by the random flow produces, for the case of large Péclet number, a k(-1+delta) spectrum at k>> k(flow) , where delta proportional 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<<> |
| 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 |