  We present azimuthal velocity profiles measured in a Taylor-Couette
apparatus, which has been used as a model of stellar and planetary accretion
disks. The apparatus has a cylinder radius ratio of $\eta = 0.716$, an
aspect-ratio of $\Gamma = 11.74$, and the plates closing the cylinders in the
axial direction are attached to the outer cylinder. We investigate angular
momentum transport and Ekman pumping in the Rayleigh-stable regime. The regime
is linearly stable and is characterized by radially increasing specific angular
momentum. We present several Rayleigh-stable profiles for shear Reynolds
numbers $Re_S \sim O(10^5) \,$, both for $\Omega_i > \Omega_o > 0$
(quasi-Keplerian regime) and $\Omega_o > \Omega_i > 0$ (sub-rotating regime)
where $\Omega_{i,o}$ is the inner/outer cylinder rotation rate. None of the
velocity profiles matches the non-vortical laminar Taylor-Couette profile. The
deviation from that profile increased as solid-body rotation is approached at
fixed $Re_S$. Flow super-rotation, an angular velocity greater than that of
both cylinders, is observed in the sub-rotating regime. The velocity profiles
give lower bounds for the torques required to rotate the inner cylinder that
were larger than the torques for the case of laminar Taylor-Couette flow. The
quasi-Keplerian profiles are composed of a well mixed inner region, having
approximately constant angular momentum, connected to an outer region in
solid-body rotation with the outer cylinder and attached axial boundaries.
These regions suggest that the angular momentum is transported axially to the
axial boundaries. Therefore, Taylor-Couette flow with closing plates attached
to the outer cylinder is an imperfect model for accretion disk flows,
especially with regard to their stability.
