The topographic torque associated with a tangentially geostrophic motion at the core surface and inferences on the flow inside the core

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Abstract
In the last few years seismologists have proposed core-mantle topographies. At the same time much effort has been devoted by geomagneticians to calculate the fluid flow (and the related pressure field) at the top of the core, based on the observation of the secular variation of the geomagnetic field. A ‘‘topographic torque'', which results from the action of the pressure field at the core surface, has long been invoked to allow for exchanges of angular momentum between the core and the mantle. In this paper, we show that this torque can be computed if forces at the top of the core are in geostrophic balance. The deep nature of this topographic torque can be understood only if one goes beyond the case of a pseudo-static equilibrium and considers explicitly the acceleration term in the equation of motion. We show that the pressure field acts in such a way as to accelerate a zonal flow consisting of cylindrical annuli. These annuli rotate like rigid bodies, with an angular velocity which depends on the distance to the rotation axis. Furthermore, we show that a gravity torque may also act on these same cylinders.