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
Linear impulse response in hot round jets (2007)
Lutz Lesshafft, Patrick Huerre
DOI: 10.1063/1.2437238
Two main questions are treated in this article:
- What physical mechanism causes absolute instability in low-density jets?
- How are shear-layer and jet-column instability modes properly characterised and distinguished?
The analysis is local, and entirely based on spatio-temporal modes, i.e. modes that have complex frequencies as well as complex wavenumbers. We consider those spatio-temporal modes that appear in the linear impulse response, i.e. the linear wavepacket that evolves out of a singular perturbation impulse in a parallel flow. According to Huerre (2000), these are the modes that travel at a real group velocity, and which can therefore be identified as the absolute modes in a co-moving frame of reference. Consequently, we recover the same family of instability modes as Jendoubi & Strykowski (1994).
The answers to the two questions above are as follows:
- Absolute instability is caused by a destabilising effect of the baroclinic torque, which in the case of a light jet acts in phase with the standard shear instability. (In a heavy jet, the baroclinic effect is out of phase with the shear instability and therefore is stabilising, not shown in the paper).
- Shear-layer and jet-column modes are cleanly distinguished in the context of the linear impulse response wavepacket, as long as the shear layer thickness and the jet radius are well separated. Shear-layer modes achieve significantly higher growth rates, but only at group velocities around half the jet velocity; they are therefore convected away from the source and are not responsible for absolute instability. Jet-column modes dominate the impulse response wavepacket at low group velocities, including vg=0. The absolute mode is always of the jet-column type.
In my understanding, the distinction between shear-layer and jet-column modes cannot be made in the context of temporal or spatial analysis. Some confusion exists in the literature on this point, because these terms are often used in a vague sense. In the context of global analysis, where the separation between jet radius and shear layer thickness necessarily disappears downstream, this distinction is largely irrelevant anyway...
The baroclinic torque mechanism re-appears in a similar study on axisymmetric wakes by Meliga et al. (JFM 2008), and in the later global instability studies by Bharadwaj & Das (JFM 2017) and by Chakravarthy et al. (JFM 2018) on light jets and plumes.
Note that there is a sign error in equation (16) of this paper. This is a typo, the signs in the instability code were correct.
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