Spiral vortex breakdown as a global mode

By F. Gallaire, M. Ruith, Eckart Meiburg, Jean-Marc Chomaz, P. Huerre. Journal of Fluid Mechanics, 2006

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Nonmodal Stability Theory (2007, methodology): “…response, i.e., the Green’s function, of the flow and its subsequent analysis regarding propagation direction was introduced by Delbende et al. (1998) and has since been applied to a variety of open flows (see Brandt et al. 2003, Gallaire et al. 2006, Le Gal & Croquette 2000, Ravier et al. 2006).”
Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes (2016, methodology): “The vortex breakdown bubble of the Grabowski vortex (Grabowski & Berger 1976) has been studied by DNS (Ruith et al. 2003), by weakly nonlinear analysis (Meliga, Gallaire & Chomaz 2012a) and by global temporal stability and sensitivity analyses (Gallaire et al. 2006; Qadri, Mistry & Juniper 2013).”
An experimental investigation of swirling jets (2005, result): “Further support for this point of view comes from recent work at LadHyX by Ruith et al. (2004) which suggests that the observations of an unstable region downstream of the breakdown region in Ruith et al. (2003) can be interpreted as being the result of the breaking of the symmetry of the vortex b”
Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction (2011, methodology): “Gallaire et al. (2006) performed a linear stability analysis based on numerical simulations of a swirling jet at Re= 200 that were conducted by Ruith et al. (2003).”