Three-dimensional Stokes flow in a cylindrical container

Abstract

Consider a cylindrical container of circular section filled with a viscous fluid. We consider flow in such a cylinder driven by the motion of flat belts across the partially open end walls of the container. The flow field is determined by the use of a vector eigenfunction expansion. The critical points that are exhibited in the plane of symmetry include elliptic points, foci, and saddles. As the parameters are varied one can have bifurcations in which one type of critical point bifurcates to a collection of others. An example of a limiting surface is also demonstrated. Since the flow fields considered have little symmetry, the three-dimensional streamlines are for the most part not closed. As a consequence the flow fields tend to globalize structures that would otherwise have been isolated. This feature can have important consequences for mixing.