  We examine the dynamics of a rotating viscous fluid following an abrupt
change in the angular velocity of the solid bounding surface. We include the
effects of a density stratification and compressibility which are important in
astrophysical objects such as neutron stars. We confirm and extend the
conclusions of previous studies that stratification restricts the Ekman pumping
process to a relatively thin layer near the boundary, leaving much of the
interior fluid unaffected. We find that finite compressibility further inhibits
Ekman pumping by decreasing the extent of the pumped layer and by increasing
the time for spin-up. The results of this paper are important for interpreting
the spin period discontinuities (``glitches'') observed in rotating neutron
stars.
