Energetics of numerical geodynamo models

Global energy balances provide a useful framework for assessing the operation of numerical geodynamo models. We apply a spectral decomposition to the magnetic and kinetic energy equations to assess how the magnetic field is regenerated by convection in these models. Specific analysis of the Kuang and Bloxham model indicates that dynamo action relies on the combined effects of buoyant upwelling and shear in the zonal flow. The part of the flow that contributes most to the generation of the dipole field is associated with a narrow range of local magnetic Reynolds number around R-m approximate to O(1). Shear in the zonal flow converts the dipole field into a strong toroidal field. The equilibration of field generation is revealed in the time-dependent exchanges of kinetic and magnetic energies. We also assess the turbulent cascade of energy to small scales. Transfer of kinetic energy to small scales is represented by a turbulent viscosity, which varies substantially with the length scale of the motion. This result implies that models for turbulent viscosity should depend on the wavenumber of the motion.