Wave Propagation, Instability, and Breakdown of Vortices

The themes of wave propagation and hydrodynamic stability have played prominent roles in attempts to understand the phenomenon of vortex breakdown. Recent theoretical and experimental work provide evidence that waves and instabilities are important elements of the vortex breakdown process. Breakdown of vortex cores at high Reynolds numbers may occur in one of two forms, the apparently axisymmetric (“bubble”) or the “spiral” form. The application of soliton theory and hydrodynamic stability theory to both forms is discussed, together with a new large amplitude theory for axisymmetric waves.