ON THE INTERPRETATION OF VORTEX BREAKDOWN

Studying the numerous papers that have appeared in the recent past tha t address ''vortex breakdown,'' it may be difficult for a reader to av oid getting rather confused. It appears that various authors or even s chools have conflicting views on the correct interpretation of the phy sics of vortex breakdown. Following the investigation by Keller et al. [Z. Angew. Math. Phys. 36, 854-(1985)], in this paper, axisymmetric f orms of vortex breakdown, as originally defined by Benjamin [J. Fluid Mech. 14, 593 (1962)] are addressed. It is argued that at least,some o f the previous investigations have been concerned with different aspec ts of the same phenomena and may, in fact; not disagree. One of the mo st fundamental questions in this context concerns the properties of th e distributions of total head and circulation on the downstream side o f vortex breakdown transitions. Some previous investigators have sugge sted that the downstream how would exhibit properties that are similar to those of a wake. For this reason the phenomenon of vortex breakdow n is investigated for a class Of distributions of total head and circu lation in the domain of flow reversal that is substantially more gener al than in previous investigations. Finally, a variety of problems are discussed that are crucial for a more complete theory of vortex break down, but have not yet been solved. It is shown that for the typically small flow speeds in a domain of flow reversal produced by a vortex b reakdown wave, the departures of both vortex core size and swirl numbe r, with respect to the case of uniform total pressure in the zone of f low reversal, as discussed by Keller et al. [Z. Angew. Math. Phys. 36, 854 (1985)], remain surprisingly small. As a consequence, the possibl e appearance of large departures from a Kirchhoff-type wake must be du e to viscous diffusion at low and due to shear-layer instabilities at high Reynolds numbers. (C) 1995 American Institute of Physics.