Fluid instabilities in precessing spheroidal cavities

We study by direct numerical simulation the motion of incompressible fluid contained in an ellipsoid of revolution with ellipticity 0.1 or less which rotates about its axis of symmetry and whose rotation axis is executing precessional motion. A solution to this problem for an inviscid fluid given by Poincare (1910) predicts motion of uniform vorticity. The simulations show how the orientation of the average vorticity of a real fluid is influenced by both pressure and viscous torques exerted by the boundaries. Axisymmetric shear layers appear which agree well with those observed experimentally by Malkus (1968). Shear caused by deviations from a velocity field with uniform vorticity triggers an instability consisting of waves propagating around the average rotation axis of the fluid. The Ekman layers at the boundaries may also become unstable.