Energy transfers in shell models for MHD turbulence

摘要

A systematic procedure to derive shell models for MHD turbulence is proposed.It takes into account the conservation of ideal quadratic invariants such asthe total energy, the cross-helicity and the magnetic helicity as well as theconservation of the magnetic energy by the advection term in the inductionequation. This approach also leads to simple expressions for the energyexchanges as well as to unambiguous definitions for the energy fluxes. Whenapplied to the existing shell models with nonlinear interactions limited to thenearest neighbour shells, this procedure reproduces well known models butsuggests a reinterpretation of the energy fluxes.