Theory of the vortex breakdown phenomenon

The phenomenon examined is the abrupt structural change which can occur at some station along the axis of a swirling flow, notably the leading-edge vortex formed above a delta wing at incidence. Contrary to previous attempts at an explanation, the belief demonstrated herein is that vortex breakdown is not a manifestation of instability or of any other effect indicated by study of infinitesimal disturbances alone. It is instead a finite transition between two dynamically conjugate states of axisymmetric flow, analogous to the hydraulic jump in openchannel flow. A set of properties essential to such a transition, corresponding to a set shown to provide a complete explanation for the hydraulic jump, is demonstrated with wide generality for axisymmetric vortex flows; and the interpretation covers both the case of mild transitions, where an undular structure is developed without the need arising for significant energy dissipation, and the case of strong ones where a region of vigorous turbulence is generated. An important part of the theory depends on the calculus of variations; and the comprehensiveness with which certain properties of conjugate flow pairs are demonstrable by this analytical means suggests that present ideas may be useful in various other problems.