Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear

Rogachevskii, I.; Kleeorin, N.

doi:10.1103/physreve.68.036301

Cited by 144 publications

(158 citation statements)

References 38 publications

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“…The existence of this "W × J-effect" has been confirmed in the framework of the second-order correlation approximation by Rädler and Stepanov (2006). The simple model of an "W × J-dynamo" proposed by Rogachevskii and Kleeorin (2003) (see also Rogachevskii and Kleeorin 2004) works with the coefficients determining this and the accompanying effects as calculated in the spectral τ -approximation. It turned out however that it fails to work with the coefficients resulting from the second-order correlation approximation for purely hydrodynamic background turbulence, and this applies independently of q Kitchatinov 2006, Rädler andStepanov 2006).…”

Section: 22mentioning

confidence: 80%

Mean-field electrodynamics: critical analysis of various analytical approaches to the mean electromotive force

Rädler

Rheinhardt

2007

Geophysical & Astrophysical Fluid Dynamics

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There are various analytical approaches to the mean electromotive force E = u × b crucial in mean-field electrodynamics, with u and b being velocity and magnetic field fluctuations. In most cases the traditional approach, restricted to the second-order correlation approximation, has been used. Its validity is only guaranteed for a range of conditions, which is narrow in view of many applications, e.g., in astrophysics. With the intention to have a wider range of applicability other approaches have been proposed which make use of the so-called τ -approximation, reducing correlations of third order in u and b to such of second order. After explaining some basic features of the traditional approach a critical analysis of the approaches of that kind is given. It is shown that they lead in some cases to results which are in clear conflict with those of the traditional approach. It is argued that this indicates shortcomings of the τ -approaches and poses serious restrictions to their applicability. These shortcomings do not result from the basic assumption of the τ -approximation. Instead, they seem to originate in some simplifications made in order to derive E without really solving the equations governing u and b. A starting point for a new approach is described which avoids the conflict.

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Section: 22mentioning

confidence: 80%

Mean-field electrodynamics: critical analysis of various analytical approaches to the mean electromotive force

Rädler

Rheinhardt

2007

Geophysical & Astrophysical Fluid Dynamics

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“…Another suggestion is that, if even transient growth makes non axisymmetric mean magnetic fields strong enough, they themselves might drive motions which could lead to subcritical dynamo action (Rincon et al 2008). Yet another possibility that has been suggested is the shear-current effect (Rogachevskii & Kleeorin 2003, 2004. In this mechanism, it is thought that the mean shear gives rise to anisotropic turbulence, which causes an extra component of the mean electromotive force (EMF), leading to the generation of the cross-shear component of the mean magnetic field from the component parallel to the shear flow.…”

Section: Introductionmentioning

confidence: 99%

The shear dynamo problem for small magnetic Reynolds numbers

Sridhar

Singh

2010

J. Fluid Mech.

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We study large-scale kinematic dynamo action due to turbulence in the presence of a linear shear flow, in the low conductivity limit. Our treatment is non perturbative 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 (Rm) but could have arbitrary fluid Reynolds number. The equation for the magnetic fluctuations is expanded perturbatively in the small quantity, Rm. Our principal results are as follows: (i) The magnetic fluctuations are determined to lowest order in Rm by explicit calculation of the resistive Green's function for the linear shear flow; (ii) The mean electromotive force is then calculated and an integro-differential 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, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the spacetime integrals; (iii) The contribution of the "D" terms is such that their contribution to the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. Therefore, to lowest order in Rm but to all orders in the shear strength, the "D" terms cannot give rise to a shear-current assisted dynamo effect; (iv) Casting the integro-differential 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 velocity spectrum tensor, which is the fundamental dynamical quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field; (vi) The "C" terms couple different components of the mean magnetic field, so they can, in principle, give rise to a shear-current type effect. We discuss the application to a slowly varying magnetic field, where it can be shown that forced non helical velocity dynamics at low fluid Reynolds number does not result in a shear-current assisted dynamo effect.

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“…This was one of the first examples showing cyclic dynamo action somewhat reminiscent of the solar dynamo , and it was believed to be a prototype of magnetically driven dynamos ( ). This phenomenon may be superficially similar to a magnetically dominated version of the shear-current effect (Rogachevskii & Kleeorin 2003. With the test-field method one is now in a good position to identify the governing mechanism by determining all components of the α and η t tensors.…”

Section: Dynamos Driven By Magnetic Instabilitiesmentioning

confidence: 99%

Advances in Theory and Simulations of Large-Scale Dynamos

Brandenburg

2009

Space Sci Rev

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Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted.

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Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear

Cited by 144 publications

References 38 publications

Mean-field electrodynamics: critical analysis of various analytical approaches to the mean electromotive force

Mean-field electrodynamics: critical analysis of various analytical approaches to the mean electromotive force

The shear dynamo problem for small magnetic Reynolds numbers

Advances in Theory and Simulations of Large-Scale Dynamos

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