A scalar model for MHD turbulence

A model for homogeneous MHD turbulence is proposed. Nonlinear interactions acts between nearest neighbours in a discretized wavenumbers space and conservation properties (total energy and v-b correlation) are verified. The model can be truncated at will. With three modes, a bifurcation analysis is given. In the turbulent case (dissipation and kinetic forcing are present) one obtains time fluctuations at all scales and time-averaged power law spectra, the small scales exhibit intermittency effects. Typical MHD phenomena such as the dynamo effect or the increase of v-b correlation in the decaying cases are also observed.