Stagnant vortex flow

With the aid of the vorticity transport equation it is shown that in inviscid, incompressible, axially symmetric vortex flow the axial vorticity component near the axis of the vortex approaches zero if the axial velocity component approaches a stagnation point, and vice versa, the axial vorticity component is increased, if the axial flow is accelerated. This result, obtained in earlier investigations by simplifying the momentum equations for the neighborhood of the axis of the vortex, is already contained in the vorticity transport equation as formulated by von Helmholtz in 1858. In laminar flow, with viscous forces acting near the stagnation point, the angular velocity does not necessarily vanish with the axial velocity component. These questions are discussed in the following.