Abstract Computer experiments (LES) of the axisymmetric and statistically steady turbulent flow between a rotating and a fixed disk have been performed. This flow is a representative of the flow in an unshrouded rotor–stator configuration. The flow is characterized only by a local Reynolds number and a local gap ratio, provided that the distance from the rotation axis is sufficiently large so that the flow is fully turbulent. Five different cases have been considered, two of which may be classified as ‘wide-gap’ simulations, whereas the others were ‘narrow-gap’ simulations. In the latter cases, the variation of the tangential mean flow between the disks closely resembled the S-shaped mean velocity profile in a turbulent Couette flow. In the wide-gap cases, however, a nearly homogeneous core region separated the three-dimensional boundary layers adjacent to the rotor and the stator. It was observed that the degree of three-dimensionality was gradually reduced with the distance from the axis of rotation. The Reynolds shear stress vector and the mean velocity gradient vector (both in planes perpendicular to the axis of rotation) became more aligned and the structural parameter increased towards the typical limit 0.15 found in two-dimensional boundary layers. The moment coefficient Cθ deduced from the statistically averaged tangential wall-friction at the rotor compared excellently with empirical correlation formulae, whereas Cθ at the stator side was substantially lower.