Topographic Core‐Mantle Coupling and Polar Motion On Decadal Time‐Scales

Department of Physics (Atmospheric, Oceanic and Planetary Physics), University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU
Geophysical Journal International (Impact Factor: 2.56). 04/1996; 125(2):599 - 607. DOI: 10.1111/j.1365-246X.1996.tb00022.x

ABSTRACT Associated with non-steady magnetohydrodynamic (MHD) flow in the liquid metallic core of the Earth, with typical relative speeds of a fraction of a millimetre per second, are fluctuations in dynamic pressure of about 103 N m−2. Acting on the non-spherical core-mantle boundary (CMB), these pressure fluctuations give rise to a fluctuating net topographic torque Lt(t) (i=1, 2, 3)—where t denotes time—on the overlying solid mantle. Geophysicists now accept the proposal by one of us (RH) that Li-(t) makes a significant and possibly dominant contribution to the total torque Li*(t) on the mantle produced directly or indirectly by core motions. Other contributions are the ‘gravitational’ torque associated with fluctuating density gradients in the core, the ‘electromagnetic’ torque associated with Lorentz forces in the weakly electrically conducting lower mantle, and the ‘viscous’ torque associated with shearing motions in the boundary layer just below the CMB. the axial component L3*(t) of Li* (t) contributes to the observed fluctuations in the length of the day [LOD, an inverse measure of the angular speed of rotation of the solid Earth (mantle, crust and cryosphere)], and the equatorial components (Li* (t)) L* (t) contribute to the observed polar motion, as determined from measurements of changes in the Earth's rotation axis relative to its figure axis.
In earlier phases of a continuing programme of research based on a method for determining Li(t) from geophysical data (proposed independently about ten years ago by Hide and Le Mouël), it was shown that longitude-dependent irregular CMB topography no higher than about 0.5 km could give rise to values of L3(t) sufficient to account for the observed magnitude of LOD fluctuations on decadal time-scales. Here, we report an investigation of the equatorial components (L1(t), L2(t)) = L(t) of Li(t) taking into account just one topographic feature of the CMB—albeit possibly the most pronounced—namely the axisymmetric equatorial bulge, with an equatorial radius exceeding the polar radius by 9.5 ± 0.1 km (the mean radius of the core being 3485 2 km, 0.547 times that of the whole Earth). A measure of the local horizontal gradient of the fluctuating pressure field near the CMB can be obtained from the local Eulerian flow velocity in the ‘free stream’ below the CMB by supposing that nearly everywhere in the outer reaches of the core—the ‘polosphere’ (Hide 1995)—geostrophic balance obtains between the pressure gradient and Coriolis forces. the polospheric velocity fields used were those determined by Jackson (1989) from geomagnetic secular variations (GSV) data on the basis of the geostrophic approximation combined with the assumption that, on the time-scales of the GSV, the core behaves like a perfect electrical conductor and the mantle as a perfect insulator.
In general agreement with independent calculations by Hulot, Le Huy & Le Mouël (1996) and Greff-Lefftz & Legros (1995), we found that in magnitude L (t) for epochs from 1840 to 1990 typically exceeds L3(t) by a factor of about 10, roughly equal to the ratio of the height of the equatorial bulge to that strongly implied for irregular topography by determinations of L3(t) (see Hide et al. 1993). But L (t) still apparently falls short in magnitude by a factor of up to about 5 in its ability t o account for the amplitude of the observed time-series of polar motion on decadal time-scales (DPM), and it is poorly correlated with that time-series. So we conclude that unless uncertainties in the determination of the DPM time-series from observations-which we also discuss-have been seriously underestimated, the action of normal pressure forces associated with core motions on the equatorial bulge of the core-mantle boundary makes a significant but not dominant contribution to the excitation of decadal polar motion. Other geophysical processes such as the movement of groundwater and changes in sea-level must also be involved.

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Available from: J. O. Dickey, Sep 26, 2015
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    • "The conclusion of all these studies is that surface processes cannot excite a polar motion of the amplitude and form of the Markowitz wobble. The polar motion resulting from an exchange of angular momentum between the core and the mantle by electromagnetic (Greff-Lefftz & Legros 1995) and topographic coupling (Greff-Lefftz & Legros 1995; Hide et al. 1996; Hulot et al. 1996) at the core–mantle boundary (CMB) is also incapable of explaining the Markowitz wobble. "
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    ABSTRACT: SUMMARYA decadal polar motion with an amplitude of approximately 25 milliarcsecs (mas) is observed over the last century, a motion known as the Markowitz wobble. The origin of this motion remains unknown. In this paper, we investigate the possibility that a time-dependent axial misalignment between the density structures of the inner core and mantle can explain this signal. The longitudinal displacement of the inner core density structure leads to a change in the global moment of inertia of the Earth. In addition, as a result of the density misalignment, a gravitational equatorial torque leads to a tilt of the oblate geometric figure of the inner core, causing a further change in the global moment of inertia. To conserve angular momentum, an adjustment of the rotation vector must occur, leading to a polar motion. We develop theoretical expressions for the change in the moment of inertia and the gravitational torque in terms of the angle of longitudinal misalignment and the density structure of the mantle. A model to compute the polar motion in response to time-dependent axial inner core rotations is also presented. We show that the polar motion produced by this mechanism can be polarized about a longitudinal axis and is expected to have decadal periodicities, two general characteristics of the Markowitz wobble. The amplitude of the polar motion depends primarily on the Y12 spherical harmonic component of mantle density, on the longitudinal misalignment between the inner core and mantle, and on the bulk viscosity of the inner core. We establish constraints on the first two of these quantities from considerations of the axial component of this gravitational torque and from observed changes in length of day. These constraints suggest that the maximum polar motion from this mechanism is smaller than 1 mas, and too small to explain the Markowitz wobble.
    Geophysical Journal International 02/2008; 172(3):903 - 920. DOI:10.1111/j.1365-246X.2007.03653.x · 2.56 Impact Factor
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    • "This result was also confirmed by Jault and Le Mouël (1989) (they attached to Hide's method more detailed reasoning by allowing for the role of inertial force on the outer core fluid to complete the angular momentum budget in the core and mantle (see Section 2.1.1)). The calculation of the equatorial topographic torque by Hide's method has also been attempted, which indicates that its typical magnitude is smaller by several factors than that corresponding to the Markowitz wobble (Greff-Lefftz and Legros, 1995; Hide et al., 1996; Hulot et al., 1996). "
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    ABSTRACT: With the prospect of studying the relevance of the topographic core-mantle coupling to the variations of the Earth's rotation and also its applicability to constraining the core surface flow, we investigate the variability of the topographic torque estimated by using core surface flow models accompanied by (a) uncertainty due to the non-uniqueness problem in the flow inversion, and (b) variance originating in that of geomagnetic secular variation models employed in the inversion. Various flow models and their variances are estimated by inverting prescribed geomagnetic models at the epoch 1980. The subsequent topographic torque is then calculated by using a core-mantle boundary topography model obtained by seismic tomography. The calculated axial and equatorial torques are found subject to the variability of order 10 19 and 10 20 Nm, respectively, on which (b) is more effective than (a). The variability of the torque is attributed even to (a) and (b) of the large-scale flows (degrees 2 and 3). Yet, it still seems unlikely for the decadal polar motion with the observed amplitude to be excited exclusively by the equatorial topographic torque associated with any of reasonable core surface flow models. It is also confirmed that, with the topography model adopted here, the axial topographic torque on a rigid annulus in the core (coaxial with the Earth's rotation axis) associated with any of reasonable flow models is larger by two orders of magnitude than the plausible inertial torque on such cylinders. This implies that any core surface flow model consistent with the topographic coupling does not exist, unless the topography model is appropriately modified. Nevertheless, the topographic coupling might provide not only a weak constraint for explaining the decadal LOD variations, but also the possibility to probe the core surface flow and the core dynamics.
    Physics of The Earth and Planetary Interiors 01/2006; 154(1):85-111. DOI:10.1016/j.pepi.2005.09.002 · 2.90 Impact Factor
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    • "In addition, such coupling would excite variations of LOD with larger amplitudes than are observed (see also Hinderer et al., 1990). Hide et al. (1996) found that the topographic torque is too small by a factor of 5 to excite the decadal Ám. Normally, a selfconsistent model is necessary to explain simultaneously the decadal variations in both ÁLOD and Ám. "
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    ABSTRACT: In this work, we review the processes in the Earth's core that influence the Earth's rotation on the decadal time scale. While core–mantle coupling is likely to be responsible for the decadal length-of-day variations, this hypothesis is controversial with respect to polar-motion variations. The electromagnetic-coupling torques are strongly dependent on the assumed electrical conductivity of the lower mantle, while the topographic torques are influenced by the topography of the core–mantle boundary (CMB). Because no comprehensive theoretical framework for determining the topographic and material parameters of the CMB region is currently available, the modeled results about the coupling torques can only be verified by their consistency with the observed variations of the Earth's rotation and the geomagnetic field. A second path of investigation is to consider the relative angular momentum of the core. Recently, the axial angular-momentum balance has been found to coincide with observed variations in the geomagnetic field and the length of day. However, with respect to polar-motion variations, the angular-momentum balance is not yet closed. We also discuss the role of an irregular motion of the figure axis of the oblate inner core with respect to the outer core and mantle in the excitation of polar motion. In particular, we assume that the associated changes of the Earth's inertia tensor cause the observed decadal variations in polar motion. From this assumption, we can derive the temporal variation of the orientation of the figure axis of the inner core from polar-motion data. Finally, we calculate the gravity variations caused by this relative inner-core motion and compare them with the accuracy of current and planned satellite missions.
    Journal of Geodynamics 10/2003; 36(3-36):343-358. DOI:10.1016/S0264-3707(03)00054-1 · 2.22 Impact Factor
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