Finite-Correlation-Time Effects in the Kinematic Dynamo Problem

Most of the theoretical results on the kinematic amplification of small-scale magnetic fluctuations by turbulence have been confined to the model of white-noise-like advecting turbulent velocity field. In this work, the statistics of the passive magnetic field in the diffusion-free regime are consid...

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Үндсэн зохиолчид: Schekochihin, A, Kulsrud, R
Формат: Journal article
Хэвлэсэн: 2000
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author Schekochihin, A
Kulsrud, R
author_facet Schekochihin, A
Kulsrud, R
author_sort Schekochihin, A
collection OXFORD
description Most of the theoretical results on the kinematic amplification of small-scale magnetic fluctuations by turbulence have been confined to the model of white-noise-like advecting turbulent velocity field. In this work, the statistics of the passive magnetic field in the diffusion-free regime are considered for the case when the advecting flow is finite-time correlated. A new method is developed that allows one to systematically construct the correlation-time expansion for statistical characteristics of the field. The expansion is valid provided the velocity correlation time is smaller than the characteristic growth time of the magnetic fluctuations. This expansion is carried out up to first order in the general case of a d-dimensional arbitrarily compressible advecting flow. The growth rates for all moments of the magnetic field are derived. The effect of the first-order corrections is to reduce these growth rates. It is shown that introducing a finite correlation time leads to the loss of the small-scale statistical universality, which was present in the limit of the delta-correlated velocity field. Namely, the shape of the velocity time-correlation profile and the large-scale spatial structure of the flow become important. The latter is a new effect, that implies, in particular, that the approximation of a locally-linear shear flow does not fully capture the effect of nonvanishing correlation time. Physical applications of this theory include the small-scale kinematic dynamo in the interstellar medium and protogalactic plasmas.
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spelling oxford-uuid:aa74da38-5e59-44ca-bc80-8ab7f9683bde2022-03-27T03:15:10ZFinite-Correlation-Time Effects in the Kinematic Dynamo ProblemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:aa74da38-5e59-44ca-bc80-8ab7f9683bdeSymplectic Elements at Oxford2000Schekochihin, AKulsrud, RMost of the theoretical results on the kinematic amplification of small-scale magnetic fluctuations by turbulence have been confined to the model of white-noise-like advecting turbulent velocity field. In this work, the statistics of the passive magnetic field in the diffusion-free regime are considered for the case when the advecting flow is finite-time correlated. A new method is developed that allows one to systematically construct the correlation-time expansion for statistical characteristics of the field. The expansion is valid provided the velocity correlation time is smaller than the characteristic growth time of the magnetic fluctuations. This expansion is carried out up to first order in the general case of a d-dimensional arbitrarily compressible advecting flow. The growth rates for all moments of the magnetic field are derived. The effect of the first-order corrections is to reduce these growth rates. It is shown that introducing a finite correlation time leads to the loss of the small-scale statistical universality, which was present in the limit of the delta-correlated velocity field. Namely, the shape of the velocity time-correlation profile and the large-scale spatial structure of the flow become important. The latter is a new effect, that implies, in particular, that the approximation of a locally-linear shear flow does not fully capture the effect of nonvanishing correlation time. Physical applications of this theory include the small-scale kinematic dynamo in the interstellar medium and protogalactic plasmas.
spellingShingle Schekochihin, A
Kulsrud, R
Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
title Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
title_full Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
title_fullStr Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
title_full_unstemmed Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
title_short Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
title_sort finite correlation time effects in the kinematic dynamo problem
work_keys_str_mv AT schekochihina finitecorrelationtimeeffectsinthekinematicdynamoproblem
AT kulsrudr finitecorrelationtimeeffectsinthekinematicdynamoproblem