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Large-scale streaky structures in turbulent jets

  • Petrônio A. S. Nogueira (a1), André V. G. Cavalieri (a1), Peter Jordan (a2) and Vincent Jaunet (a2)


Streaks have been found to be an important part of wall-turbulence dynamics. In this paper, we extend the analysis for unbounded shear flows, in particular a Mach 0.4 round jet, using measurements taken using dual-plane, time-resolved, stereoscopic particle image velocimetry (PIV) taken at pairs of jet cross-sections, allowing the evaluation of the cross-spectral density of streamwise velocity fluctuations resolved into azimuthal Fourier modes. From the streamwise velocity results, two analyses are performed: the evaluation of wavenumber spectra (assuming Taylor’s hypothesis for the streamwise coordinate) and a spectral proper orthogonal decomposition (SPOD) of the velocity field using PIV planes in several axial stations. The methods complement each other, leading to the conclusion that large-scale streaky structures are also present in turbulent jets where they experience large growth in the streamwise direction, energetic structures extending up to eight diameters from the nozzle exit. Leading SPOD modes highlight the large-scale, streaky shape of the structures, whose aspect ratio (streamwise over azimuthal length) is approximately 15. The data were further analysed using SPOD, resolvent and transient growth analyses, good agreement being observed between the models and the leading SPOD mode for the wavenumbers considered. The models also indicate that the lift-up mechanism is active in turbulent jets, with streamwise vortices leading to streaks. The results show that large-scale streaks are a relevant part of the jet dynamics.


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Alkislar, M. B., Krothapalli, A. & Butler, G. W. 2007 The effect of streamwise vortices on the aeroacoustics of a Mach 0.9 jet. J. Fluid Mech. 578, 139169.10.1017/S0022112007005022
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499525.10.1017/S002211208600099X
Bogey, C., Marsden, O. & Bailly, C. 2011 Large-eddy simulation of the flow and acoustic fields of a Reynolds number 105 subsonic jet with tripped exit boundary layers. Phys. Fluids 23, 035104.10.1063/1.3555634
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. (B/Fluids) 47, 8096; (Enok Palm Memorial Volume).10.1016/j.euromechflu.2014.03.005
Breakey, D. E. S., Jordan, P., Cavalieri, A. V. G., Nogueira, P. A., Léon, O., Colonius, T. & Rodríguez, D. 2017 Experimental study of turbulent-jet wave packets and their acoustic efficiency. Phys. Rev. Fluids 2, 124601.10.1103/PhysRevFluids.2.124601
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4 (8), 16371650.10.1063/1.858386
Cavalieri, A., Jordan, P. & Lesshafft, L. 2019 Wave-packet models for jet dynamics and sound radiation. Appl. Mech. Rev 71 (2), 020802.
Cavalieri, A. V. G. & Agarwal, A. 2014 Coherence decay and its impact on sound radiation by wavepackets. J. Fluid Mech. 748, 399415.10.1017/jfm.2014.186
Cavalieri, A. V. G., Jordan, P., Agarwal, A. & Gervais, Y. 2011 Jittering wave-packet models for subsonic jet noise. J. Sound Vib. 330 (18–19), 44744492.
Cavalieri, A. V. G., Rodríguez, D., Jordan, P., Colonius, T. & Gervais, Y. 2013 Wavepackets in the velocity field of turbulent jets. J. Fluid Mech. 730, 559592.10.1017/jfm.2013.346
Cossu, C., Pujals, G. & Depardon, S. 2009 Optimal transient growth and very large-scale structures in turbulent boundary layers. J. Fluid Mech. 619, 7994.10.1017/S0022112008004370
Crighton, D. G. 1975 Basic principles of aerodynamic noise generation. Prog. Aerosp. Sci. 16 (1), 3196.10.1016/0376-0421(75)90010-X
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547591.10.1017/S0022112071001745
Del Alamo, J. C. & Jimenez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205213.10.1017/S0022112006000607
Dergham, G., Sipp, D. & Robinet, J.-C. 2013 Stochastic dynamics and model reduction of amplifier flows: the backward facing step flow. J. Fluid Mech. 719, 406430.10.1017/jfm.2012.610
Eitel-Amor, G., Örlü, R. & Schlatter, P. 2014 Simulation and validation of a spatially evolving turbulent boundary layer up to Re 𝜃 = 8300. Intl J. Heat Fluid Flow 47, 5769.10.1016/j.ijheatfluidflow.2014.02.006
Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18 (4), 487488.10.1063/1.861156
Farrell, B. F. & Ioannou, P. J. 2012 Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow. J. Fluid Mech. 708, 149196.10.1017/jfm.2012.300
Gustavsson, L. H. 1991 Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 224, 241260.10.1017/S002211209100174X
Gutmark, E. J. & Grinstein, F. F. 1999 Flow control with noncircular jets. Annu. Rev. Fluid Mech. 31 (1), 239272.10.1146/annurev.fluid.31.1.239
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.10.1017/S0022112095000978
Hanifi, A., Schmid, P. J. & Henningson, D. S. 1996 Transient growth in compressible boundary layer flow. Phys. Fluids 8 (3), 826837.10.1063/1.868864
Hellström, L. H. O., Ganapathisubramani, B. & Smits, A. J. 2015 The evolution of large-scale motions in turbulent pipe flow. J. Fluid Mech. 779, 701715.10.1017/jfm.2015.418
Hellström, L. H. O., Marusic, I. & Smits, A. J. 2016 Self-similarity of the large-scale motions in turbulent pipe flow. J. Fluid Mech. 792, R1.10.1017/jfm.2016.100
Hellström, L. H. O., Sinha, A. & Smits, A. J. 2011 Visualizing the very-large-scale motions in turbulent pipe flow. Phys. Fluids 23 (1), 011703.10.1063/1.3533016
Hultgren, L. S. & Gustavsson, L. H. 1981 Algebraic growth of disturbances in a laminar boundary layer. Phys. Fluids 24 (6), 10001004.10.1063/1.863490
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.10.1017/S0022112006003946
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708738.10.1017/jfm.2016.226
Jaunet, V., Jordan, P. & Cavalieri, A. V. 2017 Two-point coherence of wave packets in turbulent jets. Phys. Rev. Fluids 2 (2), 024604.10.1103/PhysRevFluids.2.024604
Jiménez-González, J. I. & Brancher, P. 2017 Transient energy growth of optimal streaks in parallel round jets. Phys. Fluids 29 (11), 114101.10.1063/1.4986150
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45 (1), 173195.10.1146/annurev-fluid-011212-140756
Jung, D., Gamard, S. & George, W. K. 2004 Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 1. The near-field region. J. Fluid Mech. 514, 173204.10.1017/S0022112004000163
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741773.10.1017/S0022112067001740
Kozlov, V. V., Grek, G. R., Lofdahl, L. L., Chernorai, V. G. & Litvinenko, M. V. 2002 Role of localized streamwise structures in the process of transition to turbulence in boundary layers and jets. J. Appl. Mech. Tech. Phys. 43 (2), 224236.10.1023/A:1014745424327
Lajús, F. C., Cavalieri, A. V. & Deschamps, C. J. 2015 Spatial stability characteristics of non-circular jets. In 21st AIAA/CEAS Aeroacoustics Conference, p. 2537. American Institute of Aeronautics and Astronautics.
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (2), 243251.10.1017/S0022112080000122
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19 (2), 024102.10.1063/1.2437238
Lesshafft, L., Semeraro, O., Jaunet, V., Cavalieri, A. VG. & Jordan, P.2019 Resolvent-based modelling of coherent wavepackets in a turbulent jet. Phys. Rev. Fluids (in press).10.1103/PhysRevFluids.4.063901
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643668.10.1017/S0022112092000612
Marant, M. & Cossu, C. 2018 Influence of optimally amplified streamwise streaks on the Kelvin–Helmholtz instability. J. Fluid Mech. 838, 478500.10.1017/jfm.2017.925
Marusic, I., Baars, W. J. & Hutchins, N. 2017 Scaling of the streamwise turbulence intensity in the context of inner–outer interactions in wall turbulence. Phys. Rev. Fluids 2 (10), 100502.10.1103/PhysRevFluids.2.100502
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.10.1017/S002211201000176X
Mollo-Christensen, E. 1967 Jet noise and shear flow instability seen from an experimenter’s viewpoint (similarity laws for jet noise and shear flow instability as suggested by experiments). J. Appl. Mech. 34, 17.10.1115/1.3607624
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147156.10.1017/S002211200700777X
Pujals, G., Cossu, C. & Depardon, S. 2010 Forcing large-scale coherent streaks in a zero-pressure-gradient turbulent boundary layer. J. Turbul. 11, N25.
Pujals, G., García-Villalba, M., Cossu, C. & Depardon, S. 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21 (1), 015109.10.1063/1.3068760
Scarano, F. 2001 Iterative image deformation methods in PIV. Meas. Sci. Technol. 13 (1), R1.
Schmid, P. J. & Henningson, D. S. 2012 Stability and Transition in Shear Flows, vol. 142. Springer Science & Business Media.
Schmidt, O. T., Towne, A., Rigas, G., Colonius, T. & Brès, G. A. 2018 Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953982.10.1017/jfm.2018.675
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57108.10.1017/S002211200100667X
Semeraro, O., Jaunet, V., Jordan, P., Cavalieri, A. V. & Lesshafft, L. 2016 Stochastic and harmonic optimal forcing in subsonic jets. In 22nd AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics.
Sinha, A., Gudmundsson, K., Xia, H. & Colonius, T. 2016 Parabolized stability analysis of jets from serrated nozzles. J. Fluid Mech. 789, 3663.10.1017/jfm.2015.719
Sinha, A., Rodríguez, D., Brès, G. A. & Colonius, T. 2014 Wavepacket models for supersonic jet noise. J. Fluid Mech. 742, 7195.10.1017/jfm.2013.660
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 2754.10.1017/S0022112083000634
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.10.1146/annurev-fluid-122109-160753
Tam, C. K. W. & Burton, D. E. 1984 Sound generated by instability waves of supersonic flows. Part 2. Axisymmetric jets. J. Fluid Mech. 138 (-1), 273295.10.1017/S0022112084000124
Tinney, C. E., Glauser, M. N. & Ukeiley, L. S. 2008 Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition. J. Fluid Mech. 612, 107141.10.1017/S0022112008002978
Tissot, G., Zhang, M., Lajús, F. C., Cavalieri, A. V. G. & Jordan, P. 2017 Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer. J. Fluid Mech. 811, 95137.10.1017/jfm.2016.735
Tomkins, C. D. & Adrian, R. J. 2005 Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J. Fluid Mech. 545, 141162.10.1017/S0022112005006397
Towne, A., Schmidt, O. T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821867.10.1017/jfm.2018.283
Trefethen, L. N. 2000 Spectral Methods in MATLAB, vol. 10. Society for Industrial Mathematics.10.1137/1.9780898719598
Waleffe, F. 1995 Hydrodynamic stability and turbulence: beyond transients to a self-sustaining process. Stud. Appl. Maths 95 (3), 319343.10.1002/sapm1995953319
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids 39 (6), 10961100.10.1007/s00348-005-0016-6
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Large-scale streaky structures in turbulent jets

  • Petrônio A. S. Nogueira (a1), André V. G. Cavalieri (a1), Peter Jordan (a2) and Vincent Jaunet (a2)


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