Numerical study of the motions within a slowly precessing sphere at low Ekman number

A geostrophic circulation and a pair of oblique oscillating shear layers arise in a spherical fluid cavity contained in a slowly precessing rigid body. Both are caused by the breakdown of the Ekman boundary layer at two critical circles. We rely on numerical modelling to characterize these motions for very small Ekman numbers. Both the O(E-1/5) amplitude of the velocity in the oscillating shear layer and the width (also O(E-1/5)) of these oblique layers are the result of influx into the interior from the regions where the Ekman layer breaks down. The oscillating motions are confined to narrow shear layers and their amplitude decays exponentially away from the characteristic surfaces. Nonlinear interactions inside the boundary layer drive the geostrophic shear layer attached to the critical circles. This steady layer, again of O(E-1/5) thickness, contains O(E-3/10) velocities. Our results are in good agreement with the experimental measurement by Malkus of the geostrophic velocity arising in a slowly precessing spheroid.