ON THE EFFECT OF BOUNDARY TOPOGRAPHY ON FLOW IN THE EARTHS CORE

We examine topographical coupling between the Earth's fluid outer core and solid overlying mantle as a possible explanation of decadal perio d variations in the length-of-day. The topographical torque can be cal culated straightforwardly, provided that the flow at the core surface and the topography of the core-mantle boundary are known. Such calcula tions generally give torques which are larger than required to explain the length-of-day variations; we show however that these calculations are extremely sensitive to the flow, and so cannot be taken as provid ing any observational evidence either for or against topographical cou pling. However, observations of the magnetic field do provide useful c onstraints on the problem of topographical coupling, in particular con straining the timescale and the nature of the response of the core to topographical coupling. To examine topographical coupling in more deta il, we construct a simple model consisting of a layer of inviscid, inc ompressible, conducting fluid confined between a perfect electrically insulating boundary with small amplitude topography and a perfect elec trically conducting boundary. The layer rotates rapidly with angular v elocity OMEGA about an axis at angle theta to the layer. We show that perturbations due to the topography spread through the whole layer, ow ing to finite electrical resistivity. The resultant tangential stress at the boundary, which is determined by the perturbed pressure p and t he phase shift between p and the topography, depends strongly on the m agnetic field in the layer and its derivative at the boundary. For the toroidal magnetic fields which we consider the magnitude of the stres s can vary by several orders. The direction of the tangential stress i s also dependent on the toroidal magnetic field. The perturbations als o vary with theta. When theta almost-equal-to 0, i.e. the rotation axi s is almost parallel to the layer, two-dimensional boundary topography has the strongest effect. In this geometry, fluid inertia, which is o nly significant in a thin layer adjacent to the boundary (inertial lay er), acts via the Lorentz force to establish the phase shift. When the ta almost-equal-to pi/2, i.e. the rotation axis is almost perpendicula r to the layer, three-dimensional boundary topography has the stronges t effect. The magnitude of the coupling is the largest for the topogra phy with a lengthscale comparable to that of the system. For parameter s appropriate for the Earth's core, our results suggest that the resul tant tangential stress is roughly 10(-2) Nm-2, adequate to account for the decadal variations of the Earth'S rotation.