Three-dimensional solutions for the geostrophic flow in the Earth's core

摘要: In his seminal work, Taylor (1963) argued that the geophysically relevant limit for dynamo action within outer core is one of negligibly small inertia and viscosity in magnetohydrodynamic equations. Within this limit, he showed existence a necessary condition, now well known as Taylor's constraint, which requires cylindrically-averaged Lorentz torque must everywhere vanish; magnetic fields satisfy condition are termed states. further requirement constraint being continuously satisfied through time prescribes evolution geostrophic flow, azimuthal flow. We show original prescription satisfying given second order ordinary differential equation, only valid subset An incomplete treatment boundary conditions renders equation generally incorrect. Here, by taking proper account boundaries, we describe generalisation method enables correct evaluation instantaneous flow any 3D state. present first full-sphere examples flows driven non-axisymmetric Although axisymmetry admits mild logarithmic singularity on rotation axis, fully case absent indeed appears to be regular.