  We compute the flow induced by the steady translation of a rigid sphere along
the axis of a large cylindrical container filled with a low-viscosity fluid set
in rigid-body rotation, the sphere being constrained to spin at the same rate
as the undisturbed fluid. The parameter range covered by the simulations is
similar to that explored experimentally by Maxworthy [\textit{J. Fluid Mech.},
vol. 40, pp. 453-479 (1970)]. We describe the salient features of the flow,
especially the internal characteristics of the Taylor columns that form ahead
of and behind the body and the inertial wave pattern, and determine the drag
and torque acting on the sphere. Torque variations are found to obey two
markedly different laws under rapid- and slow-rotation conditions,
respectively. The corresponding scaling laws are predicted by examining the
dominant balances governing the axial vorticity distribution in the body
vicinity. Results for the drag agree well with the semi-empirical law proposed
for inertialess regimes by Tanzosh \& Stone [\textit{J. Fluid Mech.}, vol. 275,
pp. 225-256 (1994)]. This law is found to apply even in regimes where inertial
effects are large, provided rotation effects are also large enough. Influence
of axial confinement is shown to increase dramatically the drag in rapidly
rotating configurations, and the container length has to be approximately a
thousand times larger than the sphere for this influence to become negligibly
small. The reported simulations establish that this confinement effect is at
the origin of the long-standing discrepancy existing between Maxworthy's
results and theoretical predictions.
