Influence of core flows on the decade variations of the polar motion

We address the possibility for the core flows that generate the geomagnetic field to contribute significantly to the decade variations of the mean pole position (generally called the Markowitz wobble). This assumption is made plausible by the observation that the flow at the surface of the core-estimated from the geomagnetic secular variation models-experiences important changes on this time scale. We discard the viscous and electromagnetic core-mantle couplings and consider only the pressure torque γ pf resulting from the fluid flow overpressure acting on the non-spherical core-mantle boundary (CMB) at the bottom of the mantle, and the gravity torque γ gf due to the density heterogeneity driving the core flow. We show that forces within the core balance each other on the time scale considered and, using global integrals over the core, the mantle and the whole Earth, we write Euler's equation for the mantle in terms of two more useful torques γ Pgeo and γ. The “geostrophic torque”, γ Pgeo incorporates γ pf and part of γ gf , while γ is another fraction of γ gf . We recall how the geostrophic pressure pgeo , and thus γ Pgeo for a given topography, can be derived from the flow at the CMB and compute the motion of the mean pole from 1900 to 1990, assuming in a first approach that the unknown γ can be neglected. The amplitude of the computed pole motion is three to ten times less than the observed one and out of the phase with it. In order to estimate the possible contribution of γ we then use a second approach and consider the case in which the reference state for the Earth is assumed to be the classical axisymmetric ellipsoidal figure with an almost constant ellipticity within the core. We show that (γ P geo + γ) is then equal to a pseudo-electromagnetic torque γ L 3 , the torque exerted on the core by the component of the Lorentz force along the axis of rotation (this torque exists even though the mantle is assumed insulating). This proves that, at least in this case and probably in the more general case of a bumpy CMB, γ is not negligible compared with γ Pgeo . Eventually, we estimate the order of magnitude of γ L 3 , show that it is likely to be small and conclude with further possibilities for the Markowitz wobble to be excited from within the core.