Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the P\`eclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to non-local and non-instantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.Comment: 13 pages, 10 figures, published on PR

Mean-field effects in the Galloway-Proctor flow

The coefficients defining the mean electromotive force in a Galloway-Proctor flow are determined. This flow shows a two-dimensional pattern and is helical. The pattern wobbles in its plane. Apart from one exception a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes and Tobias (2006, Phys. Rev. Lett., 96, 034503). An analytic theory of the alpha effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an alpha effect but no gamma effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for alpha and show that gamma is in general nonzero. Both alpha and gamma show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the wobbling motion. Some results for the magnetic diffusivity eta_t and a related quantity are given, too. Finally a result for alpha in the case of a randomly varying flow without the aforementioned circular motion is presented. This flow may be a more appropriate model for studying the alpha effect and related effects in flows that are statistical isotropic in a plane.Comment: 12 pages, 14 figures, submitted to MNRA

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

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

Nonlinear magnetic diffusivity and alpha tensors in helical turbulence

The effect of a dynamo-generated mean magnetic field of Beltrami type on the mean electromotive force is studied. In the absence of the mean magnetic field the turbulence is assumed to be homogeneous and isotropic, but it becomes inhomogeneous and anisotropic with this field. Using the testfield method the dependence of the alpha and turbulent diffusivity tensors on the magnetic Reynolds number Rm is determined for magnetic fields that have reached approximate equipartition with the velocity field. The tensor components are characterized by a pseudoscalar alpha and a scalar turbulent magnetic diffusivity etat. Increasing Rm from 2 to 600 reduces etat by a factor ~5, suggesting that the quenching of etat is, in contrast to the 2-dimensional case, only weakly dependent on Rm. Over the same range of Rm, however, alpha is reduced by a factor ~14, which can qualitatively be explained by a corresponding increase of a magnetic contribution to the alpha effect with opposite sign. The level of fluctuations of alpha and etat is only 10% and 20% of the respective kinematic reference values.Comment: 4 pages, 3 figs, ApJL (accepted version

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

Cooling of Neutron Stars with Strong Toroidal Magnetic Fields

We present models of temperature distribution in the crust of a neutron star in the presence of a strong toroidal component superposed to the poloidal component of the magnetic field. The presence of such a toroidal field hinders heat flow toward the surface in a large part of the crust. As a result, the neutron star surface presents two warm regions surrounded by extended cold regions and has a thermal luminosity much lower than in the case the magnetic field is purely poloidal. We apply these models to calculate the thermal evolution of such neutron stars and show that the lowered photon luminosity naturally extends their life-time as detectable thermal X-ray sources

Dipole-Quadrupole Degeneracy in Kinematic Dynamo Models With Homogeneous Conductivity

We discuss and prove dipole-quadrupole degeneracy in kinematic dynamos with homogeneous conductivity and certain very natural symmetry properties. In the case of 2 -dynamos, symmetric and antisymmetric modes have the same conditions of excitation and the same real growth rates. For non-vanishing velocity field, i. e. 2 !-dynamos (including a possible poloidal flow), symmetric and antisymmetric modes exchange their r oles if the velocity field is reversed. We give a formal definition of symmetric and antisymmetric modes and introduce the parity operator for vector fields