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 ar ise 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 criti cal circles. We rely on numerical modelling to characterize these motions f or 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 t he Ekman layer breaks down. The oscillating motions are confined to narrow shear layers and their amplitude decays exponentially away from the charact eristic surfaces. Nonlinear interactions inside the boundary layer drive th e geostrophic shear layer attached to the critical circles. This steady lay er, 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 g eostrophic velocity arising in a slowly precessing spheroid.