ABSTRACT
The interplay between the axial and the azimuthal flow in the breakdown region near the axis of slender vortices is reinvestigated. The azimuthal momentum equation for axially symmetric flow is combined with the continuity equation to yield a simple differential equation for the angular velocity. It is found to be directly proportional to the axial velocity component along the axis for inviscid incompressible flow, and to the axial mass flux for compressible flow, exhibiting a behavior analogous to the variation of the cross-section area in subsonic and supersonic stream tubes. The Stokes stresses come into play in the immediate vicinity of the stagnation point.