Steady flows at the top of the core from geomagnetic field models:The steady motions theorem

It is demonstrated that the steady tangential velocity vs at the closed surface δK of a perfect fluid conductor bounded by a rigid, impenetrable exterior can be uniquely determined from knowledge of the normal component of the time varying magnetic flux density B n, on δK. In the context of a simple earth model consisting of an electrically insulating mantle surrounding a perfectly conducting core, the assumption of steady flow provides enough extra information to eliminate the toroidal ambiguity in B nv and to allow derivation of a unique, global flow at the top of the core from a model of the geomagnetic field.