Wavepackets in the velocity field of turbulent jets

Abstract

We study the velocity field of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to discern the presence of instability waves in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved, PIV system, the latter being setup so as to measure three components of velocity in cross-stream planes; the field can thereby be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured, synchronously with the PIV acquisition, using a microphone ring array at polar angle, θ = 20° (measured with respect to the downstream jet axis). Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are quite different. The velocity spectrum exhibits a peak at higher azimuthal wavenumber and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown, theoretically, to be due to the radial compactness of the flow. This is confirmed by significant correlations, around 10%, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those previously reported for two-point flow-acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear Parabolised Stability Equations (PSE) (where the experimental mean velocity field is used as the base flow) to ascertain if these modes correspond to linear instability waves. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE results also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence of these unforced jets, the evolution of a certain range of frequencies and azimuthal modes can be modelled as linear instabilities of the mean velocity profile, and that these instabilities are associated with the sound radiated at low polar angles.