Radial vorticity constraint in core flow modeling

Abstract

[1] We present a new method for estimating core surface flows by relaxing the tangentially geostrophic (TG) constraint. Ageostrophic flows are allowed if they are consistent with the radial component of the vorticity equation under assumptions of the magnetostrophic force balance and an insulating mantle. We thus derive a tangentially magnetostrophic (TM) constraint for flows in the spherical harmonic domain and implement it in a least squares inversion of GRIMM-2, a recently proposed core field model, for temporally continuous core flow models (2000.0-2010.0). Comparing the flows calculated using the TG and TM constraints, we show that the number of degrees of freedom for the poloidal flows is notably increased by admitting ageostrophic flows compatible with the TM constraint. We find a significantly improved fit to the GRIMM-2 secular variation (SV) by including zonal poloidal flow in TM flow models. Correlations between the predicted and observed length-of-day variations are equally good under the TG and TM constraints. In addition, we estimate flow models by imposing the TM constraint together with other dynamical constraints: either purely toroidal (PT) flow or helical flow constraint. For the PT case we cannot find any flow which explains the observed SV, while for the helical case the SV can be fitted. The poor compatibility between the TM and PT constraints seems to arise from the absence of zonal poloidal flows. The PT flow assumption is likely to be negated when the radial magnetostrophic vorticity balance is taken into account, even if otherwise consistent with magnetic observations.

Large-Scale Flow in the Core

“…The field models used are uncertain because of sparse, unevenly distributed, noisy data and contributions to the field from sources other than the core, particularly from the long-wavelength lithospheric field. This is further investigated by Asari and Lesur (2011) who generalize the tangentially geostrophic condition to a tangentially magnetostrophic alternative, allowing for the direct influence of magnetic field on the force balance. The secular variation models can be even less certain.…”

“…One method is to examine the range of behavior that comes from relaxing nonuniqueness assumptions and whether this can provide any dynamic information. Asari and Lesur (2011) investigated this directly by generalizing the tangentially geostrophic approach to seek tangentially magnetostrophic flows. The equation for the current density that they solved is essentially identical to the flow modeling eqn [4], and so subject to the same issues of nonuniqueness.…”

On magnetic estimation of Earth's core angular momentum variation

“…The centennial flow models by Pais et al [] have too flat a trend for the period of our current interest, be it TG or non‐TG (in their context), perhaps because these models have quite low powers for flows at largest scales, as is the case with TM27−1.0. Also in the CAM estimations from a satellite magnetic field model GRIMM2 for 2000.0 to 2010.0 [ Lesur et al , ], we see the variation which is steeper for their TG model than TM model [ Asari and Lesur , ]. The quasi‐geostrophy constraint used by Gillet et al [] is even more effective in reducing the flow space than TG, so a steep CAM trend is expected, as is the case with their actual CAM estimation.…”

“… is the unknown horizontal electrical current. is actually derived from a “non‐TM flow basis” set, obtained by eigenvalue decomposing the matrix connecting and in [ Asari and Lesur , ]. To ensure physical plausibility of resulting models, we fix λ TM at such a large value that the non‐TM flow is entirely eliminated from our models.…”

Earth Rotation Variations – Long Period

“…While it has been recognized for quite some time that the core is the only viable Observed Jackson et al (1993) Stephenson and Morrison (1984) McCarthy and Babcock (1986) Gross (2001) Jackson (1997) Pais and Hulot (2000) 1950 2000 source of the large decadal LOD variations that are observed (e.g., Lambeck, 1980;Munk and MacDonald, 1960), it was not until 1988 that Jault et al (1988) were able to model the core angular momentum (CAM) and show that it causes decadal LOD variations that agree reasonably well with those observed. Other assumptions about the core surface flow fields that have been made (Finlay et al, 2010;Holme, 2007) are that the flow is purely toroidal so that it has no radial component (Bloxham, 1990;Whaler, 1980Whaler, , 1986, that the flow is steady in time (Gubbins, 1982;Voorhies, 1986;Voorhies and Backus, 1985), that the flow is steady within a drifting reference frame (Davis and Whaler, 1996;Holme and Whaler, 2001), that the flow includes a helical component Olson, 2004, 2006), that the flow is tangentially magnetostrophic (Asari and Lesur, 2011), or that the flow is quasi-geostrophic (Canet et al, 2009;Gillet et al, 2009;Pais and Jault, 2008). The last two assumptions are required in order to reduce the inherent nonuniqueness of core surface flow determinations.…”