A Timeline of Jet Instability Research
A chronological and topological review of past and recent progress in the analysis of jet instability
Editor
Lutz Lesshafft
Modal and transient dynamics of jet flows (2013)
X. Garnaud, L. Lesshafft, P. J. Schmid, P. Huerre
DOI: 10.1063/1.4801751
This study presents global eigenmode spectra for incompressible and subsonic jets, as well as optimal perturbations for transient temporal growth, similar to the supersonic case of Nichols & Lele (2011), but with a critical regard.
The article questions the usefulness of temporal global eigenmodes ("global modes") for the analysis of flow instability in cases where all eigenmodes are stable, although the flow is receptive to sustained forcing ("amplifier flow", Huerre & Monkewitz 1990). Jets are a prime example of this class of flows, and are chosen for a demonstration. In the parlance of the time (2013), amplifier flows were usually described as being (globally) stable, and their (spatial) amplification of perturbations was attributed to the non-normality of the linear flow operator. This mathematical argument was given by Trefethen et al. ("Hydrodynamic Stability Without Eigenvalues", Science 1993; see also the early references given in Chomaz, Annu. Rev. Fluid Mech. 2005) in order to explain the apparent paradox that (temporally) stable linear systems may exhibit significant (spatial) perturbation growth.
By the time of writing, it had become clear to us that global eigenmodes are ill-suited for a characterisation of amplifier-type instability behaviour, and that the singular modes of the resolvent operator are instead the appropriate analysis framework (see Garnaud et al. JFM 2013). While presenting a global eigenmode analysis, the paper was intended to provoke in two ways: a) it is shown that the dominant eigenmodes of constant-density jets are almost impossible to bring to numerical convergence (this point is treated more conclusively in Lesshafft, Theor. Comp. Fluid Dyn. 2018), b) the temporal framework provides an ill-conditioned basis for the description of amplifier-type flow behaviour (by comparison with the resolvent framework employed in Garnaud et al., JFM 2013).
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