Abstract
Numerical simulation of the magnetic field in a rotating spherical shell was carried out to assess and improve the Reynolds-averaged turbulence model for magnetohydrodynamic flows. In the three-equation model the transport equations for the turbulent energy, its dissipation rate, and the turbulent helicity are solved in addition to the mean magnetic field. The turbulent electromotive force involved in the magnetic field equation is expressed in terms of the α dynamo and turbulent diffusivity terms. Since the model was improved considering the realizability condition for the turbulent electromotive force, steady state solutions were obtained even in the case of rapidly rotating system such as the Earth. Profiles of the magnetic field, the turbulent energy, and the turbulent helicity as well as their transport equations were examined to check the dynamo mechanism expressed in the model. The dependence on the system rotation and on model constants was examined to assess the model performance.
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