TURBULENT TRANSPORT OF MAGNETIC-FIELDS .5. DISTRIBUTION OF MAGNETIC ENERGY IN A SIMPLE ALPHA-DYNAMO

In this paper we analyse the stationary mean energy density tensor [formula omitted] for the α2-sphere. This model is one of the simplest possible turbulent dynamos, originally due to Krause and Steenbeck (1967): a conducting sphere of radius R with homogeneous, isotropic and stationary turbulent convection, no differential rotation and negligible resistivity. The stationary solution of the (linear) equation for Tij is found analytically. Only Trr, Tθθ and Tφφ, are unequal to zero, and we present their dependence on the radial distance r. The stationary solution depends on two coefficients describing the turbulent state: the diffusion coefficient [formula omitted] and the vorticity coefficient [formula omitted] where u(r,t) is the turbulent velocity and τc its correlation time. But the solution is independent of the dynamo coefficient [formula omitted] although a does occur in the equation for Tij. This result confirms earlier conclusions that helicity is not required for magnetic field generation. In the stationary state, magnetic energy is generated by the vorticity and transported to the boundary, where it escapes at the same rate. The solution presented contains one free parameter that is connected with the distribution of B over spatial scales at the boundary, about which Tij gives no information. We regard this investigation as a first step towards the analysis of more complicated, solar-type dynamos. © 1990, Taylor & Francis Group, LLC. All rights reserved.