Wavepacket eduction in turbulent jets based on eigenmode decomposition of PIV data

Abstract

The dynamics of large scale structures in unforced turbulent jets at subsonic speeds have been related to the generation of the peak noise radiated the aft direction. The utility of instability wavepackets computed by linear stability theory or parabolised stability equations (PSE) have been demonstrated for the modeling of the near-field pressure fluctuations associated with the coherent structures. In this paper, we investigate whether the velocity field corresponding to the wavepackets also represents adequately that of the coherent structures. Previous research showed remarkable agreement in the velocity field up to the end of the potential core, but the agreement is lost gradually downstream. Locally-parallel linear stability theory (LST) of jet velocity profiles is revisited to further study the evolution of the wavepackets and the manner in which PSE 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 Kelvin-Helmholtz eigenmode responsible for the wavepacket amplification. The instability wave thus extracted is then compared, both in amplification and shape, to the PSE wavepacket and to the dominant coherent structures obtained from the proper orthogonal decomposition of the PIV measurements. The comparisons between PSE models and POD-filtered fluctuations define three spatial regions along the streamwise direction that are explained in terms of changes in the LST eigenspectrum. The noise generated by turbulent jets and its subsequent radiation to the far field is a technological problem of great importance that has received continuous attention for decades. Investigation of the associated flow physics numerically, using direct numerical simulations or large eddy simulations at Reynolds and Mach numbers of practical application remains challenging and computationally expensive even with state-of-the-art algorithms 1 and supercomputers. An intermediate approach is born from the observation 2, 3 that the highly-directional peak noise radiated in the aft direction of turbulent jets is associated with the dynamics of the large-scale coherent structures. Relatively coarse descriptions of the large-scale structures combined with acoustic projection methods are then suggested as a promising method for the prediction of the noise in the aft direct. Statistical descriptions of the coherent structures observed in jets are reminiscent of instability waves, suggesting their modeling as instability wavepackets of the mean turbulent flow. 4, 5 Most of the studies comparing wavepackets in turbulent jets with stability theory considered forced jets, for which the introduction of controllable phase-locked disturbances enables a direct comparison between experiments and theoretical