Quasi-static magnetohydrodynamic turbulence at high Reynolds number

Abstract

We analyse the anisotropy of turbulence in an electrically conducting fluid submitted to a uniform magnetic field, for low magnetic Reynolds number, using the quasi-static approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of the component along the magnetic field (Moffatt, 1967). However, numerous numerical studies predict a different behaviour, wherein the final state is characterised by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using Direct Numerical Simulations (DNS) and spectral closures based on Eddy Damping Quasi-Normal Markovian (EDQNM) models. The initial temporal evolution of the decaying flow indicates that the turbulence is very similar to the so-called "two-and-a-half-dimensional" flow (Montgomery & Turner, 1982) which explains the observations in numerical studies. EDQNM models confirm this statement at higher Reynolds number.