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Title:  The shear dynamo problem for small magnetic Reynolds numbers 
Authors:  Sridhar, S. Singh, Nishant K. 
Keywords:  Dynamo theory MHD and electrohydrodynamics 
Issue Date:  Dec2010 
Publisher:  Cambridge University Press 
Citation:  Journal of Fluid Mechanics, 2010, Vol. 664, p265 
Abstract:  We study largescale kinematic dynamo action due to turbulence in the presence of a linear shear flow in the lowconductivity limit. Our treatment is nonperturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Rem), but could have arbitrary fluid Reynolds number. The equation for the magnetic fluctuations is expanded perturbatively in the small quantity, Rem. Our principal results are as follows: (i) the magnetic fluctuations are determined to the lowest order in Rem by explicit calculation of the resistive Green's function for the linear shear flow; (ii) the mean electromotive force is then calculated and an integrodifferential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the 'C' and 'D' terms, respectively, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the spacetime integrals; (iii) the contribution of the D term is such that its contribution to the time evolution of the crossshear components of the mean field does not depend on any other components except itself. Therefore, to the lowest order in Rem, but to all orders in the shear strength, the D term cannot give rise to a shearcurrentassisted dynamo effect; (iv) casting the integrodifferential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors; (v) the integral kernels are expressed in terms of the velocityspectrum tensor, which is the fundamental dynamical quantity that needs to be specified to complete the integrodifferential equation description of the time evolution of the mean magnetic field; (vi) the C term couples different components of the mean magnetic field, so they can, in principle, give rise to a shearcurrenttype effect. We discuss the application to a slowly varying magnetic field, where it can be shown that forced nonhelical velocity dynamics at low fluid Reynolds number does not result in a shearcurrentassisted dynamo effect. 
Description:  Restricted Access. An openaccess version is available at arXiv.org (one of the alternative locations) 
URI:  http://hdl.handle.net/2289/3975 
ISSN:  00221120 (Online) 14697645 
Alternative Location:  http://adsabs.harvard.edu/abs/2010JFM...664..265S http://arxiv.org/abs/0910.2141 http://dx.doi.org/10.1017/S0022112010003745 
Copyright:  2010 Cambridge University Press 
Appears in Collections:  Research Papers (A&A)

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