A shell model for free decaying MHD-turbulence and the role of the magnetic Prandtl number

T. Antonov¹ - S. Lozhkin¹ - P. Frick¹ - D. Sokoloff²

¹ Institute of Continuous Media Mechanics Korolyov 1, 614061, Per
² Science Research Computing Center, Moscow State University 119899, Moscow

Abstract
The shell model of MHD turbulence is used to investigate the evolution of the magnetic and velocity fields in free decaying turbulence for various magnetic Prandtl numbers and types of initial conditions. The exponential growth of magnetic energy (small-scale dynamo) with following saturation at the equipartition level at the timescales of several dozens of turnover times is demonstrated. Some dependence on the magnetic Prandtl number is revealed which is yet not as strong as to prohibit the small-scale dynamo action in stars and galaxies. The evolution of the magnetic and velocity fields is investigated on the timescale of thousands turnover times. For most realizations a coherent state with high alignment between magnetic and velocity field has been developed. In the case of establishment of a coherent state the dissipation rate is found to be substantially reduced. At the same time there are few realizations, which display different behavior, characterized by a lower level of cross-helicity. Figs 4, Refs 13.