The Magnetostrophic Dynamo

Abstract:

We consider the inertia-free, inviscid model of the dynamo first proposed more than fifty years ago by Taylor as an appropriate model for the dynamical regime of the core. Estimates of the Rossby number and Ekman number for the Earth’s core show that they are both tiny, and thus suggest that this regime is appropriate for the Earth’s core. The resulting balance, termed magnetostrophic balance, must satisfy a special constraint first expounded by J. Bryan Taylor in 1963, namely that the longitudinal component of the Lorentz torque, when averaged over every cylinder coaxial with the rotation axis, must vanish. The technical nature of this constraint has hampered progress for decades. We report on our solutions for this system when mean-field dynamos are considered, in which the action of the small scales can be characterised by an alpha effect. We will reflect on the different characteristics of the solutions compared to dynamos in which viscosity plays a leading role.