Fine Structure of the Stokes Flow near the Central Hole of a Torus

Abstract

An alternative representation of Pell and Payne’s solution for a torus in a uniform stream is given and using this the structure of flow near the hole of the torus is examined, particularly when the size of the hole is very small. When the hole radius is about 0.092 times the radius of a base circle making the torus by rotation, a vortex ring begins to grow on the axis of symmetry of the flow. As the hole size is decreased, such eddy regions form alternately on the torus and the symmetry axis.