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


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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    • "Topographic core–mantle coupling has been of interest for understanding the axial torques (Hide 1969; Anufriev & Braginsky 1975, 1977a,b; Moffatt 1978; Jault & Le Mouël 1989; Jault & Le Mouël 1990, 1991; Kuang & Bloxham 1993; Kuang & Chao 2001) and the equatorial torques (Hide et al. 1996; Hulot et al. 1996) that the fluid core exerts on the mantle. Comparatively fewer studies have examined the explicit role that CMB topography plays in altering the convective dynamics of the core (Bell & Soward 1996; Bassom & Soward 1996; Herrmann & Busse 1998; Westerburg & Busse 2003). "
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    ABSTRACT: We present the first investigation that explores the effects of an isolated topographic ridge on thermal convection in a planetary core-like geometry and using core-like fluid properties (i.e. using a liquid metal-like low Prandtl number fluid). The model's mean azimuthal flow resonates with the ridge and results in the excitation of a stationary topographic Rossby wave. This wave generates recirculating regions that remain fixed to the mantle reference frame. Associated with these regions is a strong longitudinally dependent heat flow along the inner core boundary; this effect may control the location of melting and solidification on the inner core boundary. Theoretical considerations and the results of our simulations suggest that the wavenumber of the resonant wave, LR, scales as Ro-1/2, where Ro is the Rossby number. This scaling indicates that small-scale flow structures [wavenumber ?] in the core can be excited by a topographic feature on the core-mantle boundary. The effects of strong magnetic diffusion in the core must then be invoked to generate a stationary magnetic signature that is comparable to the scale of observed geomagnetic structures [?].
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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.
    Preview · Article · Feb 2008 · Geophysical Journal International
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    • "For example, it is well known that interactions between the Earth's core and mantle cause very strong decadal variations in LOD. However , compared to other effects, these processes in the Earth's interior seem to be inferior for the excitation of long-period polar motion (Hide et al. 1996). There is some evidence that the relative motion between core and mantle contributes to the so-called Markowitz-wobble, which is an oscillation with a period of about 30 yr (Dumberry & Bloxman 2002). "
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    ABSTRACT: This paper focuses on the contribution of inter-annual hydrological mass redistributions to the excitation of polar motion. Variations in hydrological angular momenta are computed from the Land Dynamics Model (LaD) for the period between 1986 January and 2004 May. For validation, the numerical results for the hydrological excitations are compared with respective time-series derived from geodetic observations. In order to provide a comparable reference, the latter are reduced by atmospheric and oceanic effects which are the prominent contributors to polar motion excitation on subdiurnal to decadal timescales. Both the hydrological and the geodetic excitation series are low-pass filtered by means of a Vondrák filter in order to remove the dominant annual oscillations. For the comparison of hydrological and geodetic excitations, wavelet scalograms and cross-scalograms along with the respective normed coherency are computed. Analyses reveal that the hydrological mass redistributions deduced from LaD contribute to polar motion excitation at retrograde periods around 4 yr, although the signal energy is smaller in the hydrological excitations than that in the residual geodetic excitations.
    Preview · Article · Apr 2007 · Geophysical Journal International
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