Conical vortices: A class of exact solutions of the Navier-Stokes equations

Abstract

A two-parameter family of exact axially symmetric solutions of the Navier-Stokes equations for vortices contained within conical boundaries is found. The solutions depend upon the same similarity variable, equivalent to the polar angle φ measured from the symmetry axis, as flows previously discussed by Long and by Serrin, but are distinct from the cases they treated. The conical bounding stream surfaces of the present solution can be located at any angle φ = φ0, where 0