An exact solution to NavierStokes equations with a vortex singularity on a ray
Abstract
Exact solutions are derived for the steady axisymmetric threedimensional 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).
 Publication:

Akademiia Nauk SSSR Doklady
 Pub Date:
 1984
 Bibcode:
 1984DoSSR.276...79I
 Keywords:

 Helmholtz Vorticity Equation;
 NavierStokes Equation;
 Singularity (Mathematics);
 Steady Flow;
 Viscous Flow;
 Vortex Filaments;
 Axisymmetric Flow;
 Computational Fluid Dynamics;
 Ideal Fluids;
 Three Dimensional Flow;
 Typhoons;
 Fluid Mechanics and Heat Transfer