The flow in a cylindrical container with a rotating end wall at small but finite Reynolds number

Similarity solutions of the first kind are intermediate asymptotic solutions for the Stokes flow field and for the first-order inertial correction to the Stokes flow field in small aspect ratio geometries with both no-slip and free-slip boundary conditions opposite the rotating end wall. These results differ from the semi-infinite cylindrical container, where similarity solutions of the second kind are intermediate asymptotic representations of the Stokes and first-order flow fields. Lanczos factors are used to show that for Reynolds numbers less than 1, the boundary discontinuity has a limited influence on the flow field with a no-slip boundary condition opposite the rotating end wall but the boundary discontinuity is important in determining the flow field with a free-slip boundary condition opposite the rotating end wall.