Abstract:
Two assumptions are often made when computing Earth's core surface flows from geomagnetic data: the frozen-flux assumption and the tangentially geostrophic assumption. These assumptions impose some integral constraints on the geomagnetic field on secular timescales. It has been shown in the first paper of this series that all known integral constraints could actually be deduced from a single set of curvilinear integral constraints on the secular variation along level curves of $ζ=Br /cos θ$ at the core surface. In the present paper, these particular constraints are further proved to be sufficient conditions for the geomagnetic secular variation to be generated by a tangentially geostrophic flow under the frozen-flux assumption. This result means that no other independent constraint can be found and makes it possible to attempt building geomagnetic models consistent with both the frozen-flux and the tangentially geostrophic assumptions. Also, the complete set of tangentially geostrophic flow solutions of the induction equation under the frozen-flux assumption is exhibited. These solutions are amenable to direct numerical computation.
