MAGNETOSTROPHIC BALANCE IN NON-AXISYMMETRICAL, NONSTANDARD DYNAMO MODELS

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 a re discussed. Simplifications that apply for axisymmetric fields conta ined in a perfectly insulating mantle no longer apply and we conclude that the standard manipulation of the Taylor integral is no longer hel pful; it is best used in its original form integral J x B dz dphi. Ele ctromagnetic and topographic core-mantle coupling are fundamentally di fferent to viscous coupling. For the latter, the magnetostrophic equat ion 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 coupl ing, we derive the appropriate magnetic boundary conditions for variou s models of lower mantle conductivity. Finally, we derive the solvabil ity condition (analogous to Taylor's condition) appropriate for a core -mantle boundary with topography.