Mode selection in swirling jet experiments: a linear stability analysis

By F. Gallaire, Jean-Marc Chomaz. Journal of Fluid Mechanics, 2003

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Application of the dynamic mode decomposition to experimental data (2011, background): “In this configuration, a low Reynolds number axisymmetric water jet enters, without swirl, into a quiescent pool of water (Fig. 4). An axisymmetric vortex sheet develops, which subsequently rolls up according to a Kelvin‐Helmholtz-type instability ( Gallaire and Chomaz 2003 ).”
Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction (2011, methodology): “2003; Liang & Maxworthy 2005; Gallaire et al. 2006). There are several experimental techniques to confirm that the flow has transitioned to a global mode via a supercritical Hopf bifurcation. According to Huerre & Monkewitz (1990), near critical conditions, the amplitude of the global mode |A| is go”
Spiral vortex breakdown as a global mode (2006, unknown): “As mentioned in Gallaire & Chomaz (2003) , the Hilbert transform degrades the tails of the wave packet considerably when its spectrum does not vanish at k = 0. As a result, the determination of ω0,i when it is close to zero becomes less accurate.”
An experimental investigation of swirling jets (2005, methodology): “Furthermore, using the stability calculations of Gallaire & Chomaz (2003b), we find agreement that the calculated phase speed of their m =+1 and +2 modes in a temporal stability study is close to the rotation rate of the vortex core at the inlet.”