Advances in Theory and Simulations of Large-Scale Dynamos

Abstract

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.

Dynamo Models of the Solar Cycle

“…In the context of solar cycle models, one could also expect the Lorentz force to reduce the amplitude of differential rotation until the effective dynamo number falls back to its critical value, at which point the dynamo again saturates 11 . The third class of quenching mechanism listed above has not yet been investigated in detail, but numerical simulations of MHD turbulence indicate that the effects of the small-scale turbulent magnetic field on the -effect can be profound (see Pouquet et al, 1976;Durney et al, 1993;Brandenburg, 2009;Cattaneo and Hughes, 2009).…”

“…The issue hinges on helicity conservation and flux through boundaries, and subtleties of flow-field interaction in MHD turbulence. For recent entry points into this very active area of current research, see , Blackman and Field (2000), Dobler (2001), andBrandenburg (2009).…”

The solar dynamo

“…Results exhibited a self-similar inverse cascade of magnetic helicity from small to large scales, 5 which was later demonstrated in idealized numerical simulations of MHD turbulence [60,61]. However, MHD convection simulations have demonstrated that rotation alone is not sufficient to promote the generation of large-scale fields by means of an inverse cascade of magnetic helicity; rather, results are sensitive to boundary conditions, geometry and the strength and orientation of rotational shear (reviewed by Tobias et al [62] and Brandenburg [63]). …”

ISSI Workshop on Solar Magnetism: Concluding Remarks

“…One way to introduce some non-linearity is to implement the so-called α-quenching, which is supposed to represent the feedback of the magnetic field on the small-scale motions that are responsible for the α-effect, but it is not clear how that quenching should be implemented (see Brandenburg 2009). …”