A closed torus in Stokes flow
Abstract
Axisymmetrical Stokes flows about a closed torus, formed from the rotation of two equal touching circles about their common tangent, are studied for the cases when the torus rotates steadily about its axis of symmetry in a quiescent fluid or is at rest in a uniform axial stream. The resistance coefficients for the body are determined and compared with those of a sphere, disk and hemispherical cup. For streaming motion past the torus, the flow is shown to separate from the body and a dividing streamline in each cusp separates fluid which flows past the body from fluid which is trapped in closed eddytype motion. Within these regions of flow, the fluid rotates in an infinite set of toroidal vortices.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 November 1976
 Bibcode:
 1976QJMAM..29..381D
 Keywords:

 Rotating Fluids;
 Separated Flow;
 Stokes Flow;
 Toruses;
 Vortices;
 Axisymmetric Flow;
 Bessel Functions;
 Disks (Shapes);
 Hemispheres;
 Laplace Equation;
 Ring Structures;
 Spheres;
 Streamlining;
 Uniform Flow;
 Fluid Mechanics and Heat Transfer