A study of linear wavepacket models for subsonic turbulent jets using local eigenmode decomposition of PIV data

Abstract

Locally-parallel linear stability theory (LST) of jet velocity profiles is revisited to study the evolution of the wavepackets and the manner in which the parabolized stability equations (PSE) approach models them. An adjoint-based eigenmode decomposition technique is used to project cross-sectional velocity profiles measured using time-resolved particle image velocimetry (PIV) on the different families of eigenmodes present in the LST eigenspectrum. Attention is focused on the evolution of the Kelvin–Helmholtz (K–H) eigenmode and the projection of experimental fluctuations on it, since in subsonic jets the inflectional K–H instability is the only possible mechanism for linear amplification of the large-scale fluctuations, and governs the wavepacket evolution. Comparisons of the fluctuations extracted by projection onto K–H eigenmode with PSE solutions and PIV measurements are made. We show that the jet can be divided into three main regions, classified with respect to the LST eigenspectrum. Near the jet exit, there is significant amplification of the K–H mode; the PSE solution is shown to comprise almost exclusively the K–H mode, and the agreement with experiments shows that the evolution of this mode dominates the near-nozzle fluctuations. For downstream positions, the Kelvin–Helmholtz mode becomes stable and eventually merges with other branches of the eigenspectrum. The comparison between PSE, experiment and the projection onto the K–H mode for downstream positions suggests that the mechanism of saturation and decay of wavepackets is related to a combination of several marginally stable modes, which is reasonably well modeled by linear PSE, but cannot be obtained in the usual application of locally-parallel stability dealing exclusively with the K–H mode. In addition, the projection of empirical data on the K–H eigenmode at a near-nozzle cross-section is shown to be a well-founded method for the determination of the amplitudes of the linear wavepacket models.

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