The Stewartson layer of a rotating disk of finite radius

It is shown that if a disk of finite radius and the surrounding medium rotate coaxially with slightly different angular velocities, an axial layer in the form of a cylindrical shell exists at the edge of the disk. This shell of thickness O(E1/3) has length O(E-1) in axial direction, where E is the Ekman number. Its most characteristic element is the axial velocity of O(E1/6) which is larger than everywhere else in the field. We calculate the velocity components and the pressure in this layer.