Magnetostrophic balance in non-axisymmetric, non-standard dynamo models

摘要

We investigate solvability conditions for the magnetostrophic equation for dynamo models which are neither axisymmetric nor contained within an insulating sphere. Effects of topography and mantle conductivity are discussed. Simplifications that apply for axisymmetric fields contained in a perfectly insulating mantle no longer apply and we conclude that the standard manipulation of the Taylor integral is no longer helpful; it is best used in its original form #x222B;J#xD7;Bdzd. Electromagnetic and topographic core-mantle coupling are fundamentally different to viscous coupling. For the latter, the magnetostrophic equation always has a solution (due to the role of Ekman suction). For the former (in the absence of viscous coupling), a solution requires that Taylor's condition be satisfied. For the case of electromagnetic coupling, we derive the appropriate magnetic boundary conditions for various models of iower mantle conductivity. Finally, we derive the solvability condition (analogous to Taylor's condition) appropriate for a core-mantle boundary with topography.