Steady core flow in an azimuthally drifting reference frame

Abstract

Flow at the top of the Earth's core generating the observed geomagnetic secular variation (SV) can be deduced in the frozen-flux approximation with varios non-uniqueness-reducing assumptions such as tangential geostrophy and steadiness. Steady flows are attreactive because they require only a small number of parameters to explain the gross feature of the SV. However, they are unable to reproduce the fine detail contained in theSV, and cannot be used to explained observed decadal changes in the length of day. Here we find flows steady in a local references frame within the core, but the frame is allowed to rotate relative to the mantle. Previous investigations have studied steady drift with respect to the mantle, introducing just a single extra parameter into the calculation; here we also allow the drift to vary with time. We then minimize a linear combination of the fit to time-varying coefficients expressing the SV, a measure of the complexity of the flow and the drift acceleretion. The resulting non-linear inverse problem is solved in a two-stage iterative process-for a given drift, we solve for the best-fitting steady flow, and then adjust the drift to improve the fit. We seek solutions for the intervals 1900-1980 and 1840-1990; over both epochs, allowing the reference frame of a steady flow to drift gives a strikingly improved fit. For flows with a relativly high misfit, the frame drift is westwards at a rate similar to the observed 'westward drift' rate of the geomagnetic field at the Earth's surface (approximately 0.2° yr-1). Requiring a tighter fit, and hence a more complex flow, gives rise to two solutions, one with a westward frame drift with respect to the mantle, the other eastward, and the relative drift rates gradually increase to a maximum of 0.9° yr-1 as the misfit decreases. Flows in the mantle reference frame are similar to tyhose deduced previously by any of the non-uniqueness-reducing assumptions. However, in the drifting frame, the flows are almost completely dominated by the drift between the two reference frames. Although the time dependence of the drift is weak and results in only a small additionalmisfit reduction over a uniform drift, by assuming that the variation in drift reflects variation in solid body rotation of the whole core, it can explain decadal length-of-day changes almost as well as, and prior to 1900 perhaps better than, fully time-dependent tengentially geostrophic flows with vastly more free parameters. We examine the significance of these models in terms of large-scale wave motion in the core.