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Register a new userThe helicity constraint in turbulent dynamos with shear
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The evolution of magnetic fields is studied using simulations of forced helical turbulence with strong imposed shear. After some initial exponential growth, the magnetic field develops a large scale travelling wave pattern. The resulting field structure possesses magnetic helicity, which is conserved in a periodic box by the ideal MHD equations and can hence only change on a resistive time scale. This constrains strongly the growth time of the large scale magnetic field, but less strongly the length of the cycle period. Comparing with the case without shear, the time scale for large scale field amplification is shortened by a factor Q, which depends on the relative importance of shear and helical turbulence, and which controls also the ratio of toroidal to poloidal field. The results of the simulations can be reproduced qualitatively and quantitatively with a mean-field alpha-Omega dynamo model with alpha-effect and the turbulent magnetic diffusivity coefficients that are less strongly quenched than in the corresponding alpha^2-dynamo.
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Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modelled in terms of an alphaOmega dynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the alpha-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Rm) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on Rm.
The motivation for considering distributed large scale dynamos in the solar context is reviewed in connection with the magnetic helicity constraint. Preliminary accounts of 3-dimensional direct numerical simulations (in spherical shell segments) and simulations of 2-dimensional mean field models (in spherical shells) are presented. Interesting similarities as well as some differences are noted.
We present nonlinear mean-field alpha-Omega dynamo simulations in spherical geometry with simplified profiles of kinematic alpha effect and shear. We take magnetic helicity evolution into account by solving a dynamical equation for the magnetic alpha effect. This gives a consistent description of the quenching mechanism in mean-field dynamo models. The main goal of this work is to explore the effects of this quenching mechanism in solar-like geometry, and in particular to investigate the role of magnetic helicity fluxes, specifically diffusive and Vishniac-Cho (VC) fluxes, at large magnetic Reynolds numbers (Rm). For models with negative radial shear or positive latitudinal shear, the magnetic alpha effect has predominantly negative (positive) sign in the northern (southern) hemisphere. In the absence of fluxes, we find that the magnetic energy follows an Rm^-1 dependence, as found in previous works. This catastrophic quenching is alleviated in models with diffusive magnetic helicity fluxes resulting in magnetic fields comparable to the equipartition value even for Rm=10^7. On the other hand, models with a shear-driven Vishniac-Cho flux show an increase of the amplitude of the magnetic field with respect to models without fluxes, but only for Rm<10^4. This is mainly a consequence of assuming a vacuum outside the Sun which cannot support a significant VC flux across the boundary. However, in contrast with the diffusive flux, the VC flux modifies the distribution of the magnetic field. In addition, if an ill-determined scaling factor in the expression for the VC flux is large enough, subcritical dynamo action is possible that is driven by the action of shear and the divergence of current helicity flux.
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.
Identifying generic physical mechanisms responsible for the generation of magnetic fields and turbulence in differentially rotating flows is fundamental to understand the dynamics of astrophysical objects such as accretion disks and stars. In this paper, we discuss the concept of subcritical dynamo action and its hydrodynamic analogue exemplified by the process of nonlinear transition to turbulence in non-rotating wall-bounded shear flows. To illustrate this idea, we describe some recent results on nonlinear hydrodynamic transition to turbulence and nonlinear dynamo action in rotating shear flows pertaining to the problem of turbulent angular momentum transport in accretion disks. We argue that this concept is very generic and should be applicable to many astrophysical problems involving a shear flow and non-axisymmetric instabilities of shear-induced axisymmetric toroidal velocity or magnetic fields, such as Kelvin-Helmholtz, magnetorotational, Tayler or global magnetoshear instabilities. In the light of several recent numerical results, we finally suggest that, similarly to a standard linear instability, subcritical MHD dynamo processes in high-Reynolds number shear flows could act as a large-scale driving mechanism of turbulent flows that would in turn generate an independent small-scale dynamo.
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