Steady core flow in an azimuthally drifting reference frame

Flows at the top of the Earth's core generating the observed geomagnetic se cular variation (SV) can be deduced in the frozen-flux approximation with v arious non-uniqueness-reducing assumptions such as tangential geostrophy an d steadiness. Steady Hows are attractive because they require only a small number of parameters to explain the gross features of the SV. However, they art: unable to reproduce the fine detail contained in the SV, and cannot b e used to explain observed decadal changes in the length of day. Here we fi nd flows steady in a local reference frame within the core, but the frame i s allowed to rotate relative to the mantle. Previous investigations have st udied steady drift with respect to the mantle, introducing just a single ex tra parameter into the calculation; here we also allow the drift to vary wi th time. We then minimize a linear combination of the fit to time-varying c oefficients expressing the SV, a measure of the complexity of the flow and the drift acceleration. The resulting non-linear inverse problem is solved in a two-stage iterative process-for a given drift, we solve for the best-f itting steady flow, and then adjust the drift to improve the fit. We seek s olutions for the intervals 1900-1980 and 1840-1990; over both epochs, allow ing the reference frame of a steady flow to drift gives a strikingly improv ed fit. For flows with a relatively high misfit, the frame drift is westwar ds at a rate similar to the observed 'westward drift' rate of the geomagnet ic field at the Earth's surface (approximately 0.2 yr(-1)). Requiring a tig hter fit, and hence a more complex flow, gives rise to two solutions, one w ith 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 ale similar to those deduced previously by any of the nonuniqueness-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 additional misfit reducti on over a uniform drift, by assuming that the variation in drift reflects v ariation in solid body rotation of the whole core, it can explain decadal l ength-of-day changes almost as well as. and prior to 1900 perhaps better th an, fully time-dependent tangentially geostrophic flows with vastly more fr ee parameters. We examine the significance of these models in terms of larg e-scale wave motion in the core.