Helical shell models for MHD

Abstract : A shell model for magnetohydrodynamics (MHD) is derived directly from the dynamical system driving the evolution of three helical modes interacting in a triad. The use of helical modes implies that two shell variables are required for the velocity as well as for the magnetic field. The advantage of the method is the automatic conservation of all the ideal quadratic MHD invariants. The number of coupling constants is however larger than in traditional shell models. This difficulty is worked around by introducing an averaging procedure that allows to derive the shell model coupling constants directly from the MHD equations. The resulting shell model is used to explore the influence of a helical forcing on the global properties of MHD turbulence close to the onset of the dynamo regime.