“…Besides an increase in swirl or Reynolds numbers, vortex breakdown can be favoured by a divergent pipe, as first used in the experimental study of Sarpkaya (1971). It has been shown that the greater the divergence of the pipe, or the adverse pressure gradient, the less swirl is needed to generate breakdown (see Sarpkaya 1974;Krause 1985;Pagan & Benay 1987;Spall, Gatski & Ash 1990). The role of divergent pipes on the bifurcation structure associated with axisymmetric vortex breakdown has also been investigated theoretically in the inviscid limit by Rusak et al (2017), Rusak, Judd & Wang (1997) and .…”