An Isaac Newton Institute Workshop

MAGNETOHYDRODYNAMICS OF STELLAR INTERIORS <br> Supported by the European Commission, Sixth Framework Programme - <br> Marie Curie Conferences and Training Courses - MSCF-CT-2003-503674

Numerical simulations of small scale dynamo activity; spectra and critical magnetic Reynolds numbers.

Authors: Nils Erland L. Haugen (Dep. of Physics, NTNU, Trondheim, Norway), Axel Brandenburg (NORDITA, Copenhagen, Denmark)

Abstract

There is as yet no consensus on the appearance of the large Reynolds number energy spectrum of non-helical MHD turbulence without background field. We use direct numerical simulations with up to 1024^3 meshpoints, together with simulations with hyperdiffusion, in an attempt to see this large Reynolds number limit. We show that the energy spectra consist of a sub-inertial range, around the forcing wavenumber, where the magnetic energy is in sub-equipartition. At larger wavenumbers there is first a range where the magnetic energy is in super-equipartition, followed by a possible equipartition range with a k^(-5/3) slope, before we see a small bottleneck and the diffusive range at the smallest scales. We also investigate the critical magnetic Reynolds number (Rmc) for dynamo action. We find Rmc to be at a minimum for magnetic Prandtl numbers slightly above unity. For magnetic Prandtl numbers smaller than unity we find Rmc=Re^alpha, where alpha is 1/3 for magnetic Prandtl numbers larger than 1/8, and possibly 1 for smaller magnetic Prandtl numbers.