On the interpretation of vortex breakdown

Abstract

Studying the numerous papers that have appeared in the recent past that address ‘‘vortex breakdown,’’ it may be difficult for a reader to avoid getting rather confused. It appears that various authors or even schools have conflicting views on the correct interpretation of the physics of vortex breakdown. Following the investigation by Keller et al. [Z. Angew. Math. Phys. 36, 854 (1985)], in this paper, axisymmetric forms of vortex breakdown, as originally defined by Benjamin [J. Fluid Mech. 14, 593 (1962)] are addressed. It is argued that at least some of the previous investigations have been concerned with different aspects of the same phenomena and may, in fact, not disagree. One of the most fundamental questions in this context concerns the properties of the distributions of total head and circulation on the downstream side of vortex breakdown transitions. Some previous investigators have suggested that the downstream flow would exhibit properties that are similar to those of a wake. For this reason the phenomenon of vortex breakdown is investigated for a class of distributions of total head and circulation in the domain of flow reversal that is substantially more general than in previous investigations. Finally, a variety of problems are discussed that are crucial for a more complete theory of vortex breakdown, 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 breakdown wave, the departures of both vortex core size and swirl number, with respect to the case of uniform total pressure in the zone of flow reversal, as discussed by Keller et al. [Z. Angew. Math. Phys. 36, 854 (1985)], remain surprisingly small. As a consequence, the possible appearance of large departures from a Kirchhoff-type wake must be due to viscous diffusion at low and due to shear-layer instabilities at high Reynolds numbers.