KELVINS THEOREM APPLIED TO THE EARTHS CORE

We examine the consequences of adopting simplifying assumptions of a h ighly electrically conducting core and an insulating mantle for the ma gnetic field at the top of the core. These approximations form a zerot h-order model for the Earth, but may be quite accurate. We find that i n addition to the well-known invariants which apply to patches of radi al magnetic flux on the core surface which are bounded by contours on which the radial field vanishes, additional constraints apply to the s ame patches. These constraints are precisely those related to Kelvin's theorem, which is well-known in rotating systems when magnetic fields are absent. In principle, the constraints can be tested by repeated o bservations of the field through time.