Batchelor, G. K., " Axial Flow in Trailing Line Vortices", J. of Flu. Mech., Vol. 20, Part 4, pgs. 645-658.

A characteristic feature of a steady trailing line-vortex from one side of a wing and of other types of line vortex is the existence of strong axial currents near the axis of symmetry. The purpose of this paper is to account in general terms for this axial flow in trailing line vortices. The link between azimuthal and axial components of motion in a steady line vortex is provided by the pressure; the radial pressure gradient balances the centrifugal force and any change in the azimuthal motion with downstream distance x produces an axial pressure gradient and consequently axial acceleration. It is suggested that the two processes of the rolling up of the vortex and and of the concentration of vorticity into a smaller cross-section should be distinguished. While the former always occurs the latter is not inevitable.