2007/01/11 by Plunian, F., Stepanov, R.
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Plasma Physics (physics.plasm-ph)
paper · doi:10.48550/arxiv.physics/0701141
We derive a new shell model of magnetohydrodynamic (MHD) turbulence in which the energy transfers are not necessary local. Like the original MHD equations, the model conserves the total energy, magnetic helicity, cross-helicity and volume in phase space (Liouville's theorem) apart from the effects of external forcing, viscous dissipation and magnetic diffusion. In the absence of magnetic field the model exhibits a statistically stationary kinetic energy solution with a Kolmogorov spectrum. The dynamo action from a seed magnetic field by the turbulent flow and the non linear interactions are studied for a wide range of magnetic Prandtl numbers in both kinematic and dynamic cases. The non locality of the energy transfers are clearly identified.