A DIFFICULTY WITH USING THE FROZEN FLUX HYPOTHESIS TO FIND STEADY CORE MOTIONS

摘要

Many studies have used the frozen flux hypothesis to estimate core how from geomagnetic secular variation (SV). Part of the flow remains indeterminate without some additional constraint. A theorem of Voorhies and Backus states that steady flows carl be determined uniquely. Frozen flux requires the time scale of SV, tau(B), to be much shorter than the diffusion time, tau(D), and the steady motion theorem requires the time scale for change in flow, tau(V), be much longer than tau(B). Here we argue we must also have tau(V) much less than tau(D) because truly steady flow will eventually lead to a steady equilibrium magnetic field and no SV. WE illustrate tile difficulty by a numerical example with a prescribed steady flow at the top of tile core for which frozen flux inversions never yield the correct velocity. Core motions derived using the steady motions theorem may be grossly in error. [References: 14]