An exact solution to Navier-Stokes equations with a vortex singularity on a ray

Exact solutions are derived for the steady axisymmetric three-dimensional problem concerning a viscous incompressible flow with a singularity of the vortex filament type on a ray. The treatment is extended to the limiting case of an ideal liquid, and a simple method is proposed for finding limiting flows. The following two examples are considered: an infinite flow with a vortex singularity on a ray (this flow illustrates the Helmholtz theorem) and a problem concerning a vortex filament resting against a plane (the velocity field of this flow provides a qualitative description of flow in the center of a typhoon).