Critical magnetic Prandtl number for small-scale dynamo.
We report a series of numerical simulations showing that the critical magnetic Reynolds number Rm(c) for the nonhelical small-scale dynamo depends on the Reynolds number Re. Namely, the dynamo is shut down if the magnetic Prandtl number Pr(m)=Rm/Re is less than some critical value Pr(m,c)< ap...
| Main Authors: | , , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2004
|
| _version_ | 1826296447501336576 |
|---|---|
| author | Schekochihin, A Cowley, S Maron, J McWilliams, J |
| author_facet | Schekochihin, A Cowley, S Maron, J McWilliams, J |
| author_sort | Schekochihin, A |
| collection | OXFORD |
| description | We report a series of numerical simulations showing that the critical magnetic Reynolds number Rm(c) for the nonhelical small-scale dynamo depends on the Reynolds number Re. Namely, the dynamo is shut down if the magnetic Prandtl number Pr(m)=Rm/Re is less than some critical value Pr(m,c)< approximately 1 even for Rm for which dynamo exists at Pr(m)> or =1. We argue that, in the limit of Re-->infinity, a finite Pr(m,c) may exist. The second possibility is that Pr(m,c)-->0 as Re--> infinity, while Rm(c) tends to a very large constant value inaccessible at current resolutions. If there is a finite Pr(m,c), the dynamo is sustainable only if magnetic fields can exist at scales smaller than the flow scale, i.e., it is always effectively a large-Pr(m) dynamo. If there is a finite Rm(c), our results provide a lower bound: Rm(c) greater, similar 220 for Pr(m)< or =1/8. This is larger than Rm in many planets and in all liquid-metal experiments. |
| first_indexed | 2024-03-07T04:16:28Z |
| format | Journal article |
| id | oxford-uuid:c994a8ce-7060-4579-93f1-b278a3ba2453 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:16:28Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:c994a8ce-7060-4579-93f1-b278a3ba24532022-03-27T07:00:17ZCritical magnetic Prandtl number for small-scale dynamo.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c994a8ce-7060-4579-93f1-b278a3ba2453EnglishSymplectic Elements at Oxford2004Schekochihin, ACowley, SMaron, JMcWilliams, JWe report a series of numerical simulations showing that the critical magnetic Reynolds number Rm(c) for the nonhelical small-scale dynamo depends on the Reynolds number Re. Namely, the dynamo is shut down if the magnetic Prandtl number Pr(m)=Rm/Re is less than some critical value Pr(m,c)< approximately 1 even for Rm for which dynamo exists at Pr(m)> or =1. We argue that, in the limit of Re-->infinity, a finite Pr(m,c) may exist. The second possibility is that Pr(m,c)-->0 as Re--> infinity, while Rm(c) tends to a very large constant value inaccessible at current resolutions. If there is a finite Pr(m,c), the dynamo is sustainable only if magnetic fields can exist at scales smaller than the flow scale, i.e., it is always effectively a large-Pr(m) dynamo. If there is a finite Rm(c), our results provide a lower bound: Rm(c) greater, similar 220 for Pr(m)< or =1/8. This is larger than Rm in many planets and in all liquid-metal experiments. |
| spellingShingle | Schekochihin, A Cowley, S Maron, J McWilliams, J Critical magnetic Prandtl number for small-scale dynamo. |
| title | Critical magnetic Prandtl number for small-scale dynamo. |
| title_full | Critical magnetic Prandtl number for small-scale dynamo. |
| title_fullStr | Critical magnetic Prandtl number for small-scale dynamo. |
| title_full_unstemmed | Critical magnetic Prandtl number for small-scale dynamo. |
| title_short | Critical magnetic Prandtl number for small-scale dynamo. |
| title_sort | critical magnetic prandtl number for small scale dynamo |
| work_keys_str_mv | AT schekochihina criticalmagneticprandtlnumberforsmallscaledynamo AT cowleys criticalmagneticprandtlnumberforsmallscaledynamo AT maronj criticalmagneticprandtlnumberforsmallscaledynamo AT mcwilliamsj criticalmagneticprandtlnumberforsmallscaledynamo |