Gravitational torque on the inner core and decadal polar motion

Abstract

S U M M A R YA 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 Y 1 2 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.

The Magnetic Field of Planet Earth

“…But because equatorial torques do not break the Taylor constraint, their consequence on the core surface flow cannot be easily identified. Nonetheless their magnitude can be roughly estimated and shown to also be compatible with the weak and poorly resolved decade Hulot et al 1996;Dumberry 2008a). …”

“…These are a special type of Alfvén wave that propagate along the cylindrically radial component of the magnetic field perpendicular to Earth's rotation axis (see e.g. Dumberry 2008b where an accessible introductory account is given). Figure 21 shows schematically the geometrical form of torsional oscillations.…”

Librations of the Galilean satellites: The influence of global internal liquid layers

“…(A.18) since it is also valid for a non-homogenous internal layer, as has been shown by e.g. Dumberry (2008) in the particular case of the gravitational torque on the inner core of the Earth due to the outer core, mantle and crust.…”

“…From the angular momentum equations for the ocean (12) and for the liquid 21 core (14), we then have, in the Poincaré approximation (ḣ o andḣ f 0),…”

Earth Rotation Variations – Long Period

“…But when Mound (2005) examined this mechanism, he concluded that while torsional oscillations may excite both decadal LOD and polar motion variations, when the oscillations are constrained to match the observed LOD amplitude, the resulting electromagnetic torque on the inner core is too weak to excite decadal polar motions to their observed level. Dumberry (2008) further studied the influence of the inner core on polar motion by examining the gravitational coupling between the inner core and density heterogeneities in the mantle. He found that his model is capable of producing decadal polar motions having amplitudes as large as those observed and that are polarized about a longitudinal axis.…”