Modeling of nutation and precession: Effects of electromagnetic coupling

Buffett, B. A.; Mathews, P. M.; Herring, Thomas A.

doi:10.1029/2000jb000056

Cited by 107 publications

(224 citation statements)

References 30 publications

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“…To extrapolate from our models to the earth, we note that our poloidal field is roughly three to five times weaker than expected inside the earth; this may be quantified in one of two ways: first, by the rms value of B r on the core-mantle boundary, which for our models is 0.26 mT, three times smaller than the anticipated value of 0.69 mT from nutation studies (38); second, by the volumetric rms value of the magnetic field being 0.5 mT, two to eight times smaller than expected values of 1-4 mT (27). Because u g depends quadratically on B (principally on its poloidal component, the toroidal component being much weaker), our prescribed poloidal magnetic field will drive a geostrophic flow at least 10 times too small.…”

Section: Methodsmentioning

confidence: 99%

Electromagnetically driven westward drift and inner-core superrotation in Earth’s core

Livermore¹,

Hollerbach

Jackson

2013

Proc. Natl. Acad. Sci. U.S.A.

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A 3D numerical model of the earth's core with a viscosity two orders of magnitude lower than the state of the art suggests a link between the observed westward drift of the magnetic field and superrotation of the inner core. In our model, the axial electromagnetic torque has a dominant influence only at the surface and in the deepest reaches of the core, where it respectively drives a broad westward flow rising to an axisymmetric equatorial jet and imparts an eastward-directed torque on the solid inner core. Subtle changes in the structure of the internal magnetic field may alter not just the magnitude but the direction of these torques. This not only suggests that the quasi-oscillatory nature of inner-core superrotation [Tkal ci c H, Young M, Bodin T, Ngo S, Sambridge M (2013) The shuffling rotation of the earth's inner core revealed by earthquake doublets. Nat Geosci 6:497-502.] may be driven by decadal changes in the magnetic field, but further that historical periods in which the field exhibited eastward drift were contemporaneous with a westward inner-core rotation. The model further indicates a strong internal shear layer on the tangent cylinder that may be a source of torsional waves inside the core.geomagnetism | geodynamo T he slow westward drift of the geomagnetic field is one of the best-and longest-known features of the historical field, for which the most likely explanation is a latitudinally dependent westward flow in the outermost outer core (1, 2). Another westward-propagating and possibly related feature is equatorial waves (3), perhaps caused either by advection or instabilities on an equatorial westward jet. However, longer time series provide evidence of periods of eastward drift of the field over the past 3,000 y (4, 5). Although some geodynamo models have reproduced westward drift (6, 7), many rely on thermal winds whose structure is tied to the boundary conditions imposed by the lowermost mantle, which changes only on a timescale of 10-100 million years. A seemingly unrelated phenomenon is the superrotation (relative to the mantle) of the inner core, whose estimates vary from zero to several degrees per year (8). Links between core-surface flows and inner-core rotation are difficult to quantify because a coupling mechanism extending across the entire outer core has remained elusive. There is some evidence of such a coupling through thermal winds in polar regions (9); however, because their amplitude is linked to the mass and thermal flux at the inner-core boundary, unless the inner core is very young, the effect likely is small (10).The fluid outer core, bounded by the solid inner core and overlying mantle, likely is in a quasi-magnetostrophic balance, in which the forces of pressure, buoyancy, Coriolis, and Lorentz are almost in equilibrium (6). Two key nondimensional parameters in any model are the Ekman and Rossby numbers, measures of viscosity and inertia, respectively, believed to be ∼10 −15 and ∼10 −6in the core. However, because of the vast range of temporal and spatial scales in th...

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Section: Methodsmentioning

confidence: 99%

Electromagnetically driven westward drift and inner-core superrotation in Earth’s core

Livermore¹,

Hollerbach

Jackson

2013

Proc. Natl. Acad. Sci. U.S.A.

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“…[37] The theory which enables one to interpret the estimates obtained for the electromagnetic coupling parameters in geophysical terms is presented by Buffett et al [2002], who discuss the assumptions and approximations made; that paper may be consulted for all details. The salient points are reproduced here for convenience.…”

Section: Inclusion Of Electromagnetic Couplingsmentioning

confidence: 99%

“…Computations show that with the Coriolis force taken into account, the ratio of the imaginary part of the coupling constant to its real part keeps on decreasing in magnitude as the field strength is increased, and both parts fail to increase as fast as hB r 2 i. The reader is referred to Buffett et al [2002] for further details of the treatment and for a discussion of the approximations and assumptions made.…”

mentioning

confidence: 99%

Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth's interior

2002

Self Cite

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[1] The analytical formulation of the theories of nutation and wobble reveals the combinations of basic Earth parameters that govern the nutation-wobble response of the Earth to gravitational (tidal) forcing by heavenly bodies and makes it possible to estimate several of them through a least squares fit of the theoretical expressions to the high-precision data now available. This paper presents the essentials of the theoretical framework, the procedure that we used for least squares estimation of basic Earth parameters through a fit of theory to nutation-precession data derived from an up-to-date very long baseline interferometry data set, the results of the estimation and their geophysical interpretation, and the nutation series constructed using the estimated values of the parameters. The theoretical formulation used here differs from earlier ones in the incorporation of anelasticity and ocean tide effects into the basic structure of the dynamical equations of the theory and in the inclusion of electromagnetic couplings of the mantle and the solid inner core to the fluid outer core, though this generalization comes at the cost of making some of the system parameters complex and frequency dependent; it is also more complete, as it takes account of nonlinear terms in these equations, including effects of the time-dependent deformations produced by zonal and sectorial tides, which had been traditionally neglected in nonrigid Earth theories. Among the geophysical results obtained from our fit are estimates for the dynamic ellipticity e of the Earth (e = 0.0032845479 with an uncertainty of 12 in the last digit), for the dynamical ellipticity e f of the fluid core (3.8% higher than its hydrostatic equilibrium value, rather than $5% as hitherto), and for the two complex electromagnetic coupling constants. Our best estimates for the RMS radial magnetic fields at the core mantle boundary and at the inner core boundary, based on the estimates for these coupling constants, are~6.9 and 72 gauss, respectively, when the magnetic field configurations are restricted to certain simple classes. The field strength needed at the inner core boundary could be lower if the density of the core fluid at this boundary or the ellipticity of the solid inner core were lower than that for the Preliminary Reference Earth Model. Our estimate for the resonance frequency of the prograde free core nutation mode, with an uncertainty of $10%, constitutes the first firm detection of the resonance associated with this mode; the period found is $1025 days, double that with electromagnetic couplings ignored. (Throughout this work, ''days,'' referring to periods, stands for ''mean solar days.'') A new nutation series (MHB2000) is constructed by direct solution of the linearized dynamical equations (with our best fit values adopted for all the estimated Earth parameters) for each forcing frequency, and adding on the contributions from the nonlinear terms and other effects not included in the linearized equations. This series gives a considerably better...

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“…Effective Jan 1, 2009, the IERS recommends the use of the new International Astronomical Union (IAU) models for nutation and precession to perform this GCRF/ITRF transformation. [3,22,23,24,25,26,27 [3,5,28].…”

Section: Gcrf/itrf Transformationmentioning

confidence: 99%