Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
This paper is a detailed report on a programme of simulations used to settle a long-standing issue in the dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dep...
| Main Authors: | , , , , , |
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| Format: | Journal article |
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2007
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| _version_ | 1826306147015983104 |
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| author | Schekochihin, A Iskakov, AB Cowley, S McWilliams, J Proctor, M Yousef, T |
| author_facet | Schekochihin, A Iskakov, AB Cowley, S McWilliams, J Proctor, M Yousef, T |
| author_sort | Schekochihin, A |
| collection | OXFORD |
| description | This paper is a detailed report on a programme of simulations used to settle a long-standing issue in the dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rm_c vs. the hydrodynamic Reynolds number Re is obtained for 1<re<6700. for="" in="" is="" larger="" limit="" pm="" pm<<1,="" rm_c="" than="" the="" times="" ~3="">1. The stability curve Rm_c(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate is ~Rm^{1/2} in the limit Re>>Rm>>1, as should be the case if the dynamo is driven by the inertial-range motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm>1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At 1</re<6700.> |
| first_indexed | 2024-03-07T06:43:31Z |
| format | Journal article |
| id | oxford-uuid:fa1a7e83-c42b-49c3-a4ed-09ca8390d02e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:43:31Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:fa1a7e83-c42b-49c3-a4ed-09ca8390d02e2022-03-27T13:03:05ZFluctuation dynamo and turbulent induction at low magnetic Prandtl numbersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fa1a7e83-c42b-49c3-a4ed-09ca8390d02eSymplectic Elements at Oxford2007Schekochihin, AIskakov, ABCowley, SMcWilliams, JProctor, MYousef, TThis paper is a detailed report on a programme of simulations used to settle a long-standing issue in the dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rm_c vs. the hydrodynamic Reynolds number Re is obtained for 1<re<6700. for="" in="" is="" larger="" limit="" pm="" pm<<1,="" rm_c="" than="" the="" times="" ~3="">1. The stability curve Rm_c(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate is ~Rm^{1/2} in the limit Re>>Rm>>1, as should be the case if the dynamo is driven by the inertial-range motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm>1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At 1</re<6700.> |
| spellingShingle | Schekochihin, A Iskakov, AB Cowley, S McWilliams, J Proctor, M Yousef, T Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers |
| title | Fluctuation dynamo and turbulent induction at low magnetic Prandtl
numbers |
| title_full | Fluctuation dynamo and turbulent induction at low magnetic Prandtl
numbers |
| title_fullStr | Fluctuation dynamo and turbulent induction at low magnetic Prandtl
numbers |
| title_full_unstemmed | Fluctuation dynamo and turbulent induction at low magnetic Prandtl
numbers |
| title_short | Fluctuation dynamo and turbulent induction at low magnetic Prandtl
numbers |
| title_sort | fluctuation dynamo and turbulent induction at low magnetic prandtl numbers |
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