A Shell Model for the Hall MHD System

Abstract

A shell model has been formulated for the Hall MHD system, where the Hall term (scaled by the ion skin depth li) brings about a new singular perturbation in addition to the resistivity and viscosity effects. The model equations are derived under the constraint to conserve the energy and two helicities in the inertial range. In the limit of li → 0, the system reduces to the conventional MHD shell model.