Wave-packet dynamics in turbulent round jets

Despite being one of the first aeroacoustics problems to be studied, still several aspects of jet-noise eludes the understanding of the research community. While the first theoretical studies carried out on the subjet [1] identified the random turbulent eddies in the subsonic jet shear layer as the main source of noise, current literature agrees that advecting coherent structures, generally named wave-packets, play a principal role in sound radiation [2]. Despite these structures account for a limited amount of the total turbulent kinetic energy [3], their spatio-temporal coherence boosts the sound emission efficiency, resulting in a higher intensity than the disorganized smaller scales of turbulence. It is widely accepted by the aeroacoustic community, even with limited proof, that the shock-free jet noise is produced by two distinct sources: an omnidirectional incoherent source associated to fine-scale turbulence and a coherent source associated with wave-packets radiating at small angles [4]. A large effort from the aeroacoustics community is currently directed towards the identification and the modelling of the wave-packets [5]. Recently several promising attempts have been made to model the wave-packet exploiting data-driven techniques [6]: these techniques are especially well-suited to capture the intrinsic non-linear dynamic behaviour of these structures [7], paving the way to further studies which may shed light on their role in jet-noise emission. In the present talk a preliminary study on a turbulent subsonic round jet at ReD = 33000 is reported. The study aims at characterizing the jet and the turbulent features in it before attempting to extract information on the wavepackets. The velocity field has been measured in the symmetry plane of the jet with Particle Image Velocimetry (PIV) over a 20-nozzle-diameters domain in the axial direction. The flow field of the jet has been characterized both in terms of its mean velocity and of its characteristic turbulent features. The latter have been extracted using Proper Orthogonal Decomposition (POD, [8]) over the whole axial extension of the domain, thus producing modes which mostly describe the evolution of the turbulent features in this direction. Given the axial symmetry of the flow conditions, the instantaneous flow field possess circular symmetry. Therefore the azimuthal direction can be considered as an homogeneous direction, i.e. azimuthal modes are simply Fourier modes [8]. In order not to pollute the decomposition in the inhomogeneous directions (both axial and radial) and preserve the symmetries of the flow field [9], the POD is applied only on half of the measured domain along the radial direction. To increase the number of snapshots fed to the decomposition and to obtain more statistically relevant modes, the other half of the domain, mirrored along the jet axis, has been included to the ensemble of velocity field snapshots. Fig. 1 reports the top 5 most energetic POD spatial modes. As can be observed, the first mode represents a modulation of the jet velocity over the entire flow field. This modulation is likely to produce both flapping of the jet and both spreading (or shrinking, depending on the sign of the temporal mode). Most of the modes (apart from first one) shows a clear conical wavy-like structure along the axial direction, at least for y/D > 6, i.e. after the end of the potential core region, which seems to follow the jet spreading. The modes, however, do not represent a simple Fourier decomposition in the axial direction: each mode, in fact, shows a peak in the velocity at a distinct axial position, which can be interpreted as the size (in radial direction) of the most energetic feature, roughly corresponding to the jet width. It is worth remarking that, despite the modes present similar turbulent structures displaced at different axial positions, it is not possible to recover any clear frequency or time-delay relationship using Lissajous plots of temporal modes pairs. Likely, the dynamics of the turbulent features in the field depends on the combination of more than 2 modes as a consequence of the non-linearity of the phenomenon. As already stated above, the axial direction of the field is an inhomogeneous direction. However the modes reported have a strong sinusoidal behaviour in this direction, apart for a modulation which might be connected to the spreading of the jet and the change of the centerline velocity. This decomposition, therefore, suggests that this direction might be reduced to an homogeneous direction after a proper deformation of the domain, likely involving both a deformation in the radial direction and by linking the streamwise direction to the local centerline velocity. Such an approach is recommended also in [8] for jet flows. A similar decomposition is believed to provide a more compact representation of the flow field, thus allowing for more robust velocity modes which might constitute the skeleton of an efficient dynamical model for the wave-packets.