Infrared properties of forced magnetohydrodynamic turbulence

Abstract

The dynamical renormalisation group (RG) is implemented to study the large-scale properties of incompressible conducting fluid stirred by random forces and currents. In contrast with Navier-Stokes turbulence, invariance properties and dimensional constraints do not always prescribe the renormalisation of the couplings. In dimensions d>d_c approximately=2.8, the system displays two non-trivial regimes: a kinetic regime where the renormalisation of the transport coefficients is due to the kinetic small scales, and a magnetic regime where it is due to the magnetic small scales. The results for the magnetic regime are not identical with predictions from the direct interaction approximation; this is due to vertex renormalisation of the Lorentz force. In dimensions 2c, with sufficiently strong external currents, there is no stable fixed point: runaway of the figurative point occurs, making the RG approach self-defeating. In two dimensions, with weak forces and currents, the absolute equilibrium results of Fyfe and Montgomery (1976) are recovered.