Spherical probes and quantized vortices: Hydrodynamic formalism and simple applications

The velocity field of an ideal fluid in the presence of a moving spherical boundary and a vortex line of arbitrary configuration is found, and the hydrodynamic force acting on the sphere determined. Using this formalism, one may compute the motion of the sphere and the vortex line in the general case where the sphere has inertia and is subject to externally applied forces. The resulting algorithm can be utilized to study the complicated hydrodynamic interactions between charge carriers and quantized vortices in superfluid helium. As simple examples of the application of the hydrodynamic formalism, the force exerted on a moving sphere by an instantaneously rectilinear vortex is evaluated, and the interaction of a vortex ring with a fixed sphere is considered.