Alpha-effect current and kinetic helicities for magnetically driven turbulence and solar dynamo

Abstract

Recent numerical simulations lead to the result that turbulence is much more magnetically driven than believed. In particular the role of magnetic buoyancy appears quite important for the generation of α-effect and angular momentum transport (Brandenburg & Schmitt 1998). We present results obtained for a turbulence field driven by a (given) Lorentz force in a non-stratified but rotating convection zone. The main result confirms the numerical findings of Brandenburg & Schmitt that in the northern hemisphere the α-effect and the kinetic helicity are positive (and negative in the northern hemisphere), this being just opposite to what occurs for the current helicity which is negative in the northern hemisphere (and positive in the southern hemisphere). There has been an increasing number of papers presenting observations of current helicity at the solar surface, all showing that it is negative in the northern hemisphere and positive in the southern hemisphere (see Rudiger et al. 2000, also for a review). Mass conservation requires that Notice, that density has been assumed as homogeneous and density fluctuations vary in time. We do not adopt the inelastic approximation. For the turbulent energy equation we simply adopt a polytropic relation. In the sense of the ‘ -approximation’, the spectrum of the given magnetic fluctuations field has been approximated by with The turbulence may develop under the influence of a large-scale magnetic field B and the gravity g. For the current helicity we find