A note on vortex breakdown incipience and Long’s jet

An extension of Long’s jet model is presented. This is formulated from the modified set of quasi-cylindrical (QC) equations proposed by Berger and Erlebacher (1995) [8] from an order-of-magnitude balance of the equations of motion near the vortex core breakdown. The new set of equations reveals the key role of the radial viscous term of the radial momentum equation around the vortex breakdown fold. So retaining this term, the third branch (solutions of Type III), corresponding to the full Navier–Stokes equations, and not observed by the slender Long’s model, could be obtained.