MRI-driven turbulent transport: the role of dissipation, channel modes and their parasites

¹ Laboratoire d'Astrophysique, UJF CNRS, BP 53, 38041 Grenoble Cedex 9, France e-mail: Pierre-Yves.Longaretti@obs.ujf-grenoble.fr
² Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK

Received: 18 January 2010
Accepted: 8 April 2010

Abstract

Context. In the recent years, MRI-driven turbulent transport has been found to depend in a significant way on fluid viscosity ν and resistivity η through the magnetic Prandtl number Pm = ν/η. In particular, the transport decreases with decreasing Pm; if persistent at very large Reynolds numbers, this trend may lead to question the role of MRI-turbulence in YSO disks, whose Prandtl number is usually very small.

Aims. In this context, the principal objective of the present investigation is to characterize in a refined way the role of dissipation. Another objective is to characterize the effect of linear (channel modes) and quasi-linear (parasitic modes) physics in the behavior of the transport.

Methods. These objectives are addressed with the help of a number of incompressible numerical simulations. The horizontal extent of the box size has been increased in order to capture all relevant (fastest growing) linear and secondary parasitic unstable modes.

Results. The major results are the following: i- the increased accuracy in the computation of transport averages shows that the dependence of transport on physical dissipation exhibits two different regimes: for Pm 1, the transport has a power-law dependence on the magnetic Reynolds number rather than on the Prandtl number; for Pm > 1, the data are consistent with a primary dependence on Pm for large enough (10³) Reynolds numbers. ii- The transport-dissipation correlation is not clearly or simply related to variations of the linear modes growth rates. iii- The existence of the transport-dissipation correlation depends neither on the number of linear modes captured in the simulations, nor on the effect of the parasitic modes on the saturation of the linear modes growth. iv- The transport is usually not dominated by axisymmetric (channel) modes.