Turbulent transport coefficients and residual energy in mean-field dynamo theory

Abstract

The turbulent electromotive force in the mean-field equation needs to be modeled to predict a large-scale magnetic field in magnetohydrodynamic turbulence at high Reynolds number. Using a statistical theory for inhomogeneous turbulence, model expressions for transport coefficients appearing in the turbulent electromotive force are derived including the α coefficient and the turbulent diffusivity. In particular, as one of the dynamo effects, the pumping effect is investigated and a model expression for the pumping term is obtained. It is shown that the pumping velocity is closely related to the gradient of the turbulent residual energy, or the difference between the turbulent kinetic and magnetic energies. The production terms in the transport equation for the turbulent electromotive force are also examined and the validity of the model expression is assessed by comparing with earlier results concerning the isotropic α coefficient. The mean magnetic field in a rotating spherical shell is calculated using a turbulence model to demonstrate the pumping effect.

Cross helicity and related dynamo

“…This implies that the magnetic fluctuation effect in the turbulent magnetic diffusivity may be suppressed due to the magnetic pressure, in particular in the case of incompressible MHD flow. This result is consistent with the traditional mean-field theories (Ra¨dler et al 2003, Brandenburg and Subramanian 2005, Ra¨dler and Rheinhardt 2007, Hamba and Sato 2008. …”

“…Actually higher-order contributions in the TSDIA were examined without resorting to the Elsasser formulation. It was found that the magnetic fluctuation contribution is canceled by the higher-order contributions (Hamba and Sato 2008). However, it is also probable that, if we proceed to further higher-order 130 N.…”

“…As we have just derived above, the magneticfield fluctuation contributes to the turbulent electromotive force antiparallel to the mean electric-current density (see (49)). The higher-order contribution of the magneticfield fluctuation may reduce this magnetic fluctuation contribution (Hamba and Sato 2008). Let us consider the mean electric-current density J, which corresponds to the sheared mean magnetic-field configuration as in figure 5.…”

Constitutive theory of inhomogeneous turbulent flow based on two-scale Lagrangian formalism

“…TSDIA is inconsistent with some classes of coordinate transformations. At least it has been pointed out so far that TSDIA results do not transform in a correct way under the time-dependent rotation [25]. More general criticism may be made from the view point of the covariance principle [26][27][28].…”

“…direct derivations of mean-vorticity effects in the vortex and MHD dynamos are actually avoided but instead are estimated so that the transformation rule Ω → Ω + 2ω p holds. Regarding the MHD dynamo, Ref [25]. has carefully pointed out the breaking of Euclidean invariance and made theoretical improvements by employing the corotational derivative instead of non-covariant Lagrangian derivative (see Eqs.…”