  With the help of a model of magnetohydrodynamic (MHD) turbulence tested
previously, we explore high Reynolds number regimes up to equivalent
resolutions of 6000^3 grid points in the absence of forcing and with no imposed
uniform magnetic field. For the given initial condition chosen here, with equal
kinetic and magnetic energy, the flow ends up being dominated by the magnetic
field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy
spectrum. However, the locally anisotropic magnetic field fluctuations
perpendicular to the local mean field follow a Kolmogorov law. We find that the
ratio of the eddy turnover time to the Alfven time increases with wavenumber,
contrary to the so-called critical balance hypothesis. Residual energy and
helicity spectra are also considered; the role played by the conservation of
magnetic helicity is studied, and scaling laws are found for the magnetic
helicity and residual helicity spectra. We put these results in the context of
the dynamics of a globally isotropic MHD flow which is locally anisotropic
because of the influence of the strong large-scale magnetic field, leading to a
partial equilibration between kinetic and magnetic modes for the energy and the
helicity.
