The mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow

The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean--field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-like dynamo. In view of this application the second--order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the $\alpha$--effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.Comment: 16 pages, 2 figures, in PRE pres

General second-rank correlation tensors for homogeneous magnetohydrodynamic turbulence

The properties and structure of second-order (Cartesian) correlation tensors are derived for the general case of two solenoidal random vector fields. The theory is intended to describe homogeneous magnetohydrodynamic turbulence, with no assumed rotational or reflectional symmetries. Each correlation tensor can be written in terms of four scalar generating functions and the relationship of these functions to the potentials that generate the poloidal and toroidal components of the underlying vector fields is derived. The physical nature of the scalar functions is investigated and their true or pseudoscalar character is ascertained. In our general discussion we clarify several misleading statements dating back to Robertson’s original paper in the field [Proc. Camb. Philos. Soc. 36, 209 (1940)]. It is also shown that using the one-dimensional correlation function, it is possible to obtain spectral information on the induced electric field in directions perpendicular to the measurement direction

On the effects of turbulence on a screw dynamo

In an experiment in the Institute of Continuous Media Mechanics in Perm (Russia) an non--stationary screw dynamo is intended to be realized with a helical flow of liquid sodium in a torus. The flow is necessarily turbulent, that is, may be considered as a mean flow and a superimposed turbulence. In this paper the induction processes of the turbulence are investigated within the framework of mean--field electrodynamics. They imply of course a part which leads to an enhanced dissipation of the mean magnetic field. As a consequence of the helical mean flow there are also helical structures in the turbulence. They lead to some kind of $\alpha$--effect, which might basically support the screw dynamo. The peculiarity of this $\alpha$--effect explains measurements made at a smaller version of the device envisaged for the dynamo experiment. The helical structures of the turbulence lead also to other effects, which in combination with a rotational shear are potentially capable of dynamo action. A part of them can basically support the screw dynamo. Under the conditions of the experiment all induction effects of the turbulence prove to be rather weak in comparison to that of the main flow. Numerical solutions of the mean--field induction equation show that all the induction effects of the turbulence together let the screw dynamo threshold slightly, at most by one per cent, rise. The numerical results give also some insights into the action of the individual induction effects of the turbulence.Comment: 15 pages, 7 figures, in GAFD prin

Alpha-effect dynamos with zero kinetic helicity

A simple explicit example of a Roberts-type dynamo is given in which the alpha-effect of mean-field electrodynamics exists in spite of point-wise vanishing kinetic helicity of the fluid flow. In this way it is shown that alpha-effect dynamos do not necessarily require non-zero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition numerical solutions of the original dynamo equations are given, that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity.Comment: 6 pages, 3 figures, accepted for PR

Comment on ``The linear instability of magnetic Taylor-Couette flow with Hall effect''

In the paper we comment on (R\"udiger & Shalybkov, Phys. Rev. E. 69, 016303 (2004) (RS)), the instability of the Taylor--Couette flow interacting with a homogeneous background field subject to Hall effect is studied. We correct a falsely generalizing interpretation of results presented there which could be taken to disprove the existence of the Hall--drift induced magnetic instability described in Rheinhardt and Geppert, Phys. Rev. Lett. 88, 101103. It is shown that in contrast to what is suggested by RS, no additional shear flow is necessary to enable such an instability with a non--potential magnetic background field, whereas for a curl--free one it is. In the latter case, the instabilities found in RS in situations where neither a hydrodynamic nor a magneto--rotational instability exists are demonstrated to be most likely magnetic instead of magnetohydrodynamic. Further, some minor inaccuracies are clarified.Comment: 3 pages, 1 figure; accepted by Physical Review

Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence

The turbulent magnetic diffusivity tensor is determined in the presence of rotation or shear. The question is addressed whether dynamo action from the shear-current effect can explain large-scale magnetic field generation found in simulations with shear. For this purpose a set of evolution equations for the response to imposed test fields is solved with turbulent and mean motions calculated from the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate turbulent transport coefficients. The diagonal components of the turbulent magnetic diffusivity tensor are found to be very close together, but their values increase slightly with increasing shear and decrease with increasing rotation rate. In the presence of shear, the sign of the two off-diagonal components of the turbulent magnetic diffusion tensor is the same and opposite to the sign of the shear. This implies that dynamo action from the shear--current effect is impossible, except perhaps for high magnetic Reynolds numbers. However, even though there is no alpha effect on the average, the components of the alpha tensor display Gaussian fluctuations around zero. These fluctuations are strong enough to drive an incoherent alpha--shear dynamo. The incoherent shear--current effect, on the other hand, is found to be subdominant.Comment: 12 pages, 13 figures, improved version, accepted by Ap

Electromotive Force and Large-Scale Magnetic Dynamo in a Turbulent Flow with a Mean Shear

An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the alpha-effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a new ''shear-current" effect. A contribution to the electromotive force related with the symmetric parts of the gradient tensor of the mean magnetic field (the kappa-effect) is found in a nonrotating turbulent flows with a mean shear. The kappa-effect and turbulent magnetic diffusion reduce the growth rate of the mean magnetic field. It is shown that a mean magnetic field can be generated when the exponent of the energy spectrum of the background turbulence (without the mean velocity shear) is less than 2. The ''shear-current" effect was studied using two different methods: the Orszag third-order closure procedure and the stochastic calculus. Astrophysical applications of the obtained results are discussed.Comment: 12 pages, REVTEX4, submitted to Phys. Rev.