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Title: Transport coefficients for the shear dynamo problem at small Reynolds numbers

Abstract

We build on the formulation developed in S. Sridhar and N. K. Singh [J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients {alpha}{sub il} and {eta}{sub iml} are derived. We prove that when the velocity field is nonhelical, the transport coefficient {alpha}{sub il} vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X{sub 3} and time {tau}; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Raedler, M. Rheinhardt, and P. J. Kaepylae [Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensormore » {eta}{sub ij}({tau}). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.« less

Authors:
 [1];  [1]
  1. Raman Research Institute, Sadashivanagar, Bangalore 560 080 (India)
Publication Date:
OSTI Identifier:
21560288
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)
Additional Journal Information:
Journal Volume: 83; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevE.83.056309; (c) 2011 American Institute of Physics; Journal ID: ISSN 1539-3755
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; COORDINATES; MAGNETIC FIELDS; MATHEMATICAL SOLUTIONS; MEAN-FIELD THEORY; REYNOLDS NUMBER; SHEAR; SPECTRA; STATISTICS; STOCHASTIC PROCESSES; VELOCITY; DIMENSIONLESS NUMBERS; EVALUATION; MATHEMATICS

Citation Formats

Singh, Nishant K, Joint Astronomy Programme, Indian Institute of Science, Bangalore 560 012, and Sridhar, S. Transport coefficients for the shear dynamo problem at small Reynolds numbers. United States: N. p., 2011. Web. doi:10.1103/PHYSREVE.83.056309.
Singh, Nishant K, Joint Astronomy Programme, Indian Institute of Science, Bangalore 560 012, & Sridhar, S. Transport coefficients for the shear dynamo problem at small Reynolds numbers. United States. https://doi.org/10.1103/PHYSREVE.83.056309
Singh, Nishant K, Joint Astronomy Programme, Indian Institute of Science, Bangalore 560 012, and Sridhar, S. 2011. "Transport coefficients for the shear dynamo problem at small Reynolds numbers". United States. https://doi.org/10.1103/PHYSREVE.83.056309.
@article{osti_21560288,
title = {Transport coefficients for the shear dynamo problem at small Reynolds numbers},
author = {Singh, Nishant K and Joint Astronomy Programme, Indian Institute of Science, Bangalore 560 012 and Sridhar, S},
abstractNote = {We build on the formulation developed in S. Sridhar and N. K. Singh [J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients {alpha}{sub il} and {eta}{sub iml} are derived. We prove that when the velocity field is nonhelical, the transport coefficient {alpha}{sub il} vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X{sub 3} and time {tau}; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Raedler, M. Rheinhardt, and P. J. Kaepylae [Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor {eta}{sub ij}({tau}). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.},
doi = {10.1103/PHYSREVE.83.056309},
url = {https://www.osti.gov/biblio/21560288}, journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
issn = {1539-3755},
number = 5,
volume = 83,
place = {United States},
year = {Sun May 15 00:00:00 EDT 2011},
month = {Sun May 15 00:00:00 EDT 2011}
}