The presence of swirling motion, i.e.,  is shown not to influence the axial motion given by  provided . If  is very large, the presence of swirl completely alters the motion on the axial plane. For , the azimuthal solution can be solved in terms of the circulation , where . The solution can be described in terms of the self-similar solution of the second kind, , where  is an unknown constant and  is an eigenvalue. The function  satisfies
subjected to the boundary conditions  and  as .