CASCADE MODELS FOR MAGNETOHYDRODYNAMIC TURBULENCE

The complex cascade model by Gloaguen et al. [Physica D 17, 154 (1985)] for magnetohydrodynamic turbulence is studied. In the first part the Alfven effect is neglected. Stationary solutions are discussed. For purely kinetic turbulence a phenomenon, coherent structures in k spaces, is observed. For general magnetohydrodynamic turbulence, energy spectra are, in general, close to k(-5/3), and inertial-range statistics, in particular structure functions, are similar to those observed in hydrodynamic (fluid) turbulence. In the second part the Alfven effect is included. For the simplest case of a constant large-scale field B-0, energy spectra are k(-1.25), flatter than the expected Iroshnikov-Kraichnan law k(-3/2), and the inertial-range statistics are exactly Gaussian. Hence, the model has to be refined. Assuming B-0 to be the actual fluctuating field, intermittency is reintroduced, and the spectrum is close to k(-3/2), though it tends to become flatter for high k, such that a uniformly valid inertial-range power-law spectrum may not exist.