Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer

Tissot, Gilles; Zhang, Mengqi; Lajús, Francisco C.; Cavalieri, André V. G.; Jordan, Peter

doi:10.1017/jfm.2016.735

Cited by 62 publications

(58 citation statements)

References 61 publications

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“…This is a typical manifestation of the Orr-mechanism and has similarly been observed in resolvent models of other flows (e.g. in Garnaud et al 2013;Dergham et al 2013;Jeun et al 2016;Semeraro et al 2016;Tissot et al 2017). The suboptimal modes in figure 6(d,f,h,j,l) contain two wavepackets: one in the initial shear layer region that is similar to the KH wavepackets in the optimal mode and a second further downstream in the developing jet region.…”

Section: Resolvent Spectra and Modessupporting

confidence: 72%

“…From a local stability theory point of view, the two mechanisms are distinguished by their modal and non-modal nature, see Jordan et al (2017) and Tissot et al (2017)). Tissot et al (2017) found that the critical layer, defined where the phase speed of the wavepacket is equal to the local mean velocity, plays an important role in the forced linear dynamics of jets. In accordance with our interpretation, their results suggests that the Orr-mechanism is active downstream of the potential core.…”

Section: Resolvent Spectra and Modesmentioning

confidence: 99%

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Spectral analysis of jet turbulence

et al. 2018

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Informed by LES data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic, and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract energy spectra and decompose the flow into energy-ranked coherent structures. The educed structures are generally well predicted by the resolvent analysis. Over a range of low frequencies and the first few azimuthal mode numbers, these jets exhibit a low-rank response characterized by Kelvin-Helmholtz (KH) type wavepackets associated with the annular shear layer up to the end of the potential core and that are excited by forcing in the very-near-nozzle shear layer. These modes too the have been experimentally observed before and predicted by quasi-parallel stability theory and other approximations-they comprise a considerable portion of the total turbulent energy. At still lower frequencies, particularly for the axisymmetric mode, and again at high frequencies for all azimuthal wavenumbers, the response is not low rank, but consists of a family of similarly amplified modes. These modes, which are primarily active downstream of the potential core, are associated with the Orr mechanism. They occur also as sub-dominant modes in the range of frequencies dominated by the KH response. Our global analysis helps tie together previous observations based on local spatial stability theory, and explains why quasiparallel predictions were successful at some frequencies and azimuthal wavenumbers, but failed at others.

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Section: Resolvent Spectra and Modessupporting

confidence: 72%

Section: Resolvent Spectra and Modesmentioning

confidence: 99%

Spectral analysis of jet turbulence

et al. 2018

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“…IV B, these three POD modes can be understood as the highest-gain structures that arise in response to stochastic forcing by turbulence nonlinearities. We can add that, as shown by Tissot et al [23], the connection between the turbulent forcing and the high-gain structures occurs via the critical layer and involves an Orr-like mechanism affecting downstream fluctuations. The connection between these first few modes and the far field will be discussed in Sec.…”

Section: The Amplitude Envelopesupporting

confidence: 53%

“…Indeed, good agreement is only observed between the stability predictions and the second-order, single-point statistical moments upstream of the end of the potential core. In the downstream region, on the other hand, recent studies support the idea that wave packets persist here, but are forced by turbulence [23][24][25]. Despite the low levels of the forcing modes in this region, stabilization of the dominant convective instability leads to an accrued sensitivity to nonlinear effects that act predominantly via the critical layer.…”

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confidence: 66%

Experimental study of turbulent-jet wave packets and their acoustic efficiency

et al. 2017

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This paper details the statistical and time-resolved analysis of the relationship between the near-field pressure fluctuations of unforced, subsonic free jets (0.4 M 0.6) and their far-field sound emissions. Near-field and far-field microphone measurements were taken on a conical array close to the jets and an azimuthal ring at 20• to the jet axis, respectively. Recent velocity and pressure measurements indicate the presence of linear wave packets in the near field by closely matching predictions from the linear homogenous parabolized stability equations, but the agreement breaks down both beyond the end of the potential core and when considering higher order statistical moments, such as the two-point coherence. Proper orthogonal decomposition (POD), interpreted in terms of inhomogeneous linear models using the resolvent framework allows us to understand these discrepancies. A new technique is developed for projecting time-domain pressure measurements onto a statistically obtained POD basis, yielding the time-resolved activity of each POD mode and its correlation with the far field. A single POD mode, interpreted as an optimal high-gain structure that arises due to turbulent forcing, captures the salient near-field-far-field correlation signature; further, the signatures of the next two modes, understood as suboptimally forced structures, suggest that these POD modes represent higher order, acoustically important near-field behavior. An existing Green's-function-based technique is used to make far-field predictions, and results are interpreted in terms of POD/resolvent modes, indicating the acoustic importance of this higher order behavior. The technique is extended to provide time-domain far-field predictions.

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“…These reconstruction approaches rely on the ability of a mean flow stability model to accurately describe wavepackets, which has been studied in a substantial number of articles (Cavalieri et al 2013;Rodríguez et al 2015;Beneddine et al 2016;Tissot et al 2017). This large body of work shows that the use of such a model could be, in some situations, an interesting alternative to TR-PIV.…”

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confidence: 99%

Unsteady flow dynamics reconstruction from mean flow and point sensors: an experimental study

et al. 2017

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This article presents a reconstruction of the unsteady behaviour of a round jet at a Reynolds number equal to 3300, from the sole knowledge of the time-averaged flow field and one pointwise unsteady measurement. The reconstruction approach is an application of the work of Beneddine et al. (J. Fluid Mech., vol. 798, 2016, pp. 485-504) and relies on the computation of the dominant resolvent modes of the flow, using a parabolised stability equations analysis. To validate the procedure, the unsteady velocity field of the jet has been characterised by time-resolved particle image velocimetry (TR-PIV), yielding an experimental reference. We first show that the dominant resolvent modes are proportional to the experimental Fourier modes, as predicted by Beneddine et al. (J. Fluid Mech., vol. 798, 2016, pp. 485-504). From these results, it is then possible to fully reconstruct the unsteady velocity and pressure fluctuation fields, yielding a flow field that displays good agreement with the experimental reference. Finally, it is found that the robustness of the reconstruction mainly depends on the location of the pointwise unsteady measurement, which should be within energetic regions of the flow, and this robustness as well as the quality of the reconstruction can be greatly improved by considering a few pointwise measurements instead of a single one. The effects of other experimental parameters on the reconstruction, such as the size of the interrogation window used for the TR-PIV processing and the accuracy of the positioning of the sensors, are also investigated in this paper.

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Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer

Cited by 62 publications

References 61 publications

Spectral analysis of jet turbulence

Spectral analysis of jet turbulence

Experimental study of turbulent-jet wave packets and their acoustic efficiency

Unsteady flow dynamics reconstruction from mean flow and point sensors: an experimental study

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