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High-frequency wavepackets in turbulent jets

  • Kenzo Sasaki (a1), André V. G. Cavalieri (a1), Peter Jordan (a2), Oliver T. Schmidt (a3), Tim Colonius (a3) and Guillaume A. Brès (a4)...


Wavepackets obtained as solutions of the flow equations linearised around the mean flow have been shown in recent work to yield good agreement, in terms of amplitude and phase, with those educed from turbulent jets. Compelling agreement has been demonstrated, for the axisymmetric and first helical mode, up to Strouhal numbers close to unity. We here extend the range of validity of wavepacket models to Strouhal number $St=4.0$ and azimuthal wavenumber $m=4$ by comparing solutions of the parabolised stability equations with a well-validated large-eddy simulation of a Mach 0.9 turbulent jet. The results show that the near-nozzle dynamics can be correctly described by the homogeneous linear model, the initial growth rates being accurately predicted for the entire range of frequencies and azimuthal wavenumbers considered. Similarly to the lower-frequency wavepackets reported prior to this work, the high-frequency linear waves deviate from the data downstream of their stabilisation locations, which move progressively upstream as the frequency increases.


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Avital, E. J. & Sandham, N. D. 1997 A note on the structure of the acoustic field emitted by a wave packet. J. Sound Vib. 204 (3), 533539.
Beneddine, S., Sipp, D., Arnault, A., Dandois, J. & Lesshafft, L. 2016 Conditions for validity of mean flow stability analysis. J. Fluid Mech. 798, 485504.
Bowes, W. R., Bowler, D., Carnes, R., Fratarangelo, R., Rumpf, D., Heiser, W. H., Huff, D. L. & Moin, P.2009 Report on jet noise reduction. Tech. Rep., Naval Research Advisory Committee.
Brès, G. A., Ham, F. E., Nichols, J. W. & Lele, S. K. 2017 Unstructured large eddy simulations of supersonic jets. AIAA J. 55 (4), 11641184.
Brès, G. A., Jaunet, V., Le Rallic, M., Jordan, P., Colonius, T. & Lele, S. K.2015 Large eddy simulation for jet noise: the importance of getting the boundary layer right. AIAA Paper 2015-2535.
Brès, G. A., Jaunet, V., Le Rallic, M., Jordan, P., Towne, A., Schmidt, O. T., Colonius, T., Cavalieri, A. V. G. & Lele, S. K.2016 Large eddy simulation for jet noise: azimuthal decomposition and intermittency of the radiated sound. AIAA Paper 2016-3050.
Brès, G. A., Jordan, P., Colonius, T., Le Rallic, M., Jaunet, V. & Lele, S. K. 2014 Large eddy simulation of a Mach 0.9 turbulent jet. In Proceedings of the Summer Program, Center for Turbulence Research, Stanford University.
Cavalieri, A. V. G. & Agarwal, A. 2014 Coherence decay and its impact on sound radiation by wavepackets. J. Fluid Mech. 748, 399415.
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.
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (Part I). Acta Mechanica 1 (3), 215234.
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77 (2), 387413.
Crighton, D. G. & Huerre, P. 1990 Shear layer pressure fluctuations and superdirective acoustic sources. J. Fluid Mech. 220, 355368.
Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. R. Soc. Lond. A 264, 321342.
Fontaine, R. A., Elliott, G. S., Austin, J. M. & Freund, J. B. 2015 Very near-nozzle shear-layer turbulence and jet noise. J. Fluid Mech. 770, 2751.
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013 The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189202.
Gloor, M., Obrist, D. & Kleiser, L. 2013 Linear stability and acoustic characteristics of compressible, viscous, subsonic coaxial jet flow. Phys. Fluids 25 (8), 084102.
Gudmundsson, K. & Colonius, T. 2011 Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97128.
Harper-Bourne, M. 2010 Jet noise measurements: past and present. Intl J. Aeroacoust. 9 (4), 559588.
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29 (1), 245283.
Jaunet, V., Jordan, P. & Cavalieri, A. V. G. 2017 Two-point coherence of wave packets in turbulent jets. Phys. Rev. Fluids 2 (2), 024604.
Jeun, J., Nichols, J. W. & Jovanović, M. R. 2016 Input–output analysis of high-speed axisymmetric isothermal jet noise. Phys. Fluids 28 (4), 047101.
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173195.
Jordan, P., Zhang, M., Lehnasch, G. & Cavalieri, A. V. G.2017 Modal and non-modal linear wavepacket dynamics in turbulent jets. AIAA Paper 2017-3379.
Koenig, M., Sasaki, K., Cavalieri, A. V. G., Jordan, P. & Gervais, Y. 2016 Jet-noise control by fluidic injection from a rotating plug: linear and nonlinear sound-source mechanisms. J. Fluid Mech. 788, 358380.
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19 (2), 024102.
Maia, I. A., Jordan, P., Jaunet, V. & Cavalieri, A. V. G.2017 Two-point wavepacket modelling of jet noise. AIAA Paper 2017-3380.
Malik, M. R. & Chang, C.-L. 2000 Nonparallel and nonlinear stability of supersonic jet flow. Comput. Fluids 29 (3), 327365.
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.
Nichols, J. W. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225241.
Obrist, D. 2009 Directivity of acoustic emissions from wave packets to the far field. J. Fluid Mech. 640, 165186.
Petersen, R. A. & Samet, M. M. 1988 On the preferred mode of jet instability. J. Fluid Mech. 194, 153173.
Ray, P. K. & Lele, S. K. 2007 Sound generated by instability wave/shock-cell interaction in supersonic jets. J. Fluid Mech. 587, 173215.
Sandham, N. D. & Salgado, A. M. 2008 Nonlinear interaction model of subsonic jet noise. Phil. Trans. R. Soc. Lond. A 366 (1876), 27452760.
Sasaki, K., Piantanida, S., Cavalieri, V. G. & Jordan, P. 2017 Real-time modelling of wavepackets in turbulent jets. J. Fluid Mech. 821, 458481.
Sasaki, K., Tissot, G., Cavalieri, A. V. G., Jordan, P. & Biau, D.2016 Closed-loop control of wavepackets in a free shear-layer. AIAA Paper 2016-2758.
Schmidt, O. T., Towne, A., Colonius, T., Cavalieri, A. V. G., Jordan, P. & Brès, G. A. 2017 Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability. J. Fluid Mech. 825, 11531181.
Semeraro, O., Jaunet, V., Jordan, P., Cavalieri, A. V. & Lesshafft, L.2016 Stochastic and harmonic optimal forcing in subsonic jets. AIAA Paper 2016-2935.
Sinha, A., Rodríguez, D., Brès, G. A. & Colonius, T. 2014 Wavepacket models for supersonic jet noise. J. Fluid Mech. 742, 7195.
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.
Towne, A., Cavalieri, A. V. G., Jordan, P., Colonius, T., Schmidt, O., Jaunet, V. & Brès, G. A. 2017a Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825, 11131152.
Towne, A., Colonius, T., Jordan, P., Cavalieri, A. V. G. & Brès, G. A.2015 Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet. AIAA Paper 2015-2217.
Towne, A., Schmidt, O. T. & Colonius, T.2017b Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. arXiv:1708.04393.
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High-frequency wavepackets in turbulent jets

  • Kenzo Sasaki (a1), André V. G. Cavalieri (a1), Peter Jordan (a2), Oliver T. Schmidt (a3), Tim Colonius (a3) and Guillaume A. Brès (a4)...


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