  We report on a series of fully resolved simulations of the flow around a
rigid sphere translating steadily near a wall, either in a fluid at rest or in
the presence of a uniform shear. Non-rotating and freely rotating spheres
subject to a torque-free condition are both considered to evaluate the
importance of spin-induced effects. The separation distance between the sphere
and wall is varied from values at which the wall influence is weak down to gaps
of half the sphere radius. The Reynolds number based on the sphere diameter and
relative velocity with respect to the ambient fluid spans the range $0.1-250$,
and the relative shear rate defined as the ratio of the shear-induced velocity
variation across the sphere to the relative velocity is varied from $-0.5$ to
$+0.5$, so that the sphere either leads the fluid or lags behind it. The
wall-induced interaction mechanisms at play in the various flow regimes are
analyzed qualitatively by examining the flow structure, especially the spanwise
and streamwise vorticity distributions. Variations of the drag and lift forces
at low-but-finite and moderate Reynolds number are compared with available
analytical and semiempirical expressions, respectively. In more inertial
regimes, empirical expressions for the two force components are derived based
on the numerical data, yielding accurate fits valid over a wide range of
Reynolds number and wall-sphere separations for both non-rotating and
torque-free spheres.
