We study the steady free-surface flow of a viscous liquid layer contained in a cylinder with a rotating bottom and a fixed lateral wall. When the disk rotates at large speed, the free surface deforms strongly and three-dimensional instability patterns (rotating polygons) or sloshing motions can arise. In order to get some insight on their formation mechanisms, a study of the axisymmetric base flow is carried out numerically. The flow structure consists of a well-known central fluid column entrained in a motion of solid-body rotation at the disk angular velocity. The fluid region situated at the periphery reveals a complex structure as it is found to be surrounded by four boundary layers. This leads us to discuss the relevance of existing base-flow models used for instability studies of this flow configuration.