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...

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Asıl Yazarlar: Schekochihin, A, Iskakov, AB, Cowley, S, McWilliams, J, Proctor, M, Yousef, T
Materyal Türü: Journal article
Baskı/Yayın Bilgisi: 2007
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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&gt;&gt;1 and small magnetic Prandtl number Pm&lt;&lt;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&gt;&gt;Rm&gt;&gt;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&gt;1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At 1</re<6700.>
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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&gt;&gt;1 and small magnetic Prandtl number Pm&lt;&lt;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&gt;&gt;Rm&gt;&gt;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&gt;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
work_keys_str_mv AT schekochihina fluctuationdynamoandturbulentinductionatlowmagneticprandtlnumbers
AT iskakovab fluctuationdynamoandturbulentinductionatlowmagneticprandtlnumbers
AT cowleys fluctuationdynamoandturbulentinductionatlowmagneticprandtlnumbers
AT mcwilliamsj fluctuationdynamoandturbulentinductionatlowmagneticprandtlnumbers
AT proctorm fluctuationdynamoandturbulentinductionatlowmagneticprandtlnumbers
AT youseft fluctuationdynamoandturbulentinductionatlowmagneticprandtlnumbers