Measurements have been performed with a laser‐Doppler velocimeter of the radial dependence of azimuthal velocity components, using liquid H2O, in cylindrical containers with aspect ratiosA(i.e., the ratio of heightlto radiusb) ranging from 0.212 to 1.64. The reciprocal Ekman number ranged from 980 to 60 000. The radius was fixed at 5.25 cm. The rotating disk was located at the top. Our data are in fair agreement with numerical results of Tomlan and Hudson. Oscillations, observed during steady flow, are inertial waves with frequencies and amplitudes depending on aspect ratio and disk angular velocity. Spin‐down parameters fit a theoretical solution given previously. Observed oscillations during spin‐down have been accounted for through a heuristic argument involving convection of boundary‐layer fluid downward along the axis near the just‐stopped disk.