We study a simple magnetohydrodynamical approach in which hydrodynamics and MHD turbulence are coupled in a shell model, with given dynamo constraints in the large scales. We consider the case of a low Prandtl number fluid for which the inertial range of the velocity field is much wider than that of the magnetic field. Random reversals of the magnetic field are observed and it shown that the magnetic field has a nontrivial evolution—linked to the nature of the hydrodynamics turbulence.

• Received 1 May 2009

DOI:https://doi.org/10.1103/PhysRevLett.105.024501