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A difficulty with using the Frozen Flux Hypothesis to find steady core motions
Author(s) -
Gubbins David,
Kelly Peter
Publication year - 1996
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/96gl01392
Subject(s) - flux (metallurgy) , flow (mathematics) , mechanics , core (optical fiber) , physics , earth's magnetic field , scale (ratio) , steady state (chemistry) , magnetic field , materials science , chemistry , quantum mechanics , optics , metallurgy
Many studies have used the frozen flux hypothesis to estimate core flow 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 can be determined uniquely. Frozen flux requires the time scale of SV, τ B , to be much shorter than the diffusion time, τ D , and the steady motion theorem requires the time scale for change in flow, τ V , be much longer than τ B . Here we argue we must also have τ V ≪ τ D because truly steady flow will eventually lead to a steady equilibrium magnetic field and no SV. We illustrate the difficulty by a numerical example with a prescribed steady flow at the top of the core for which frozen flux inversions never yield the correct velocity. Core motions derived using the steady motions theorem may be grossly in error.