Hostname: page-component-669899f699-swprf Total loading time: 0 Render date: 2025-04-28T05:03:26.617Z Has data issue: false hasContentIssue false
  • English
  • Français

Lift-up, Kelvin–Helmholtz and Orr mechanisms in turbulent jets

Published online by Cambridge University Press:  26 May 2020

Ethan Pickering Open the ORCID record for Ethan Pickering [Opens in a new window] ,
Georgios Rigas Open the ORCID record for Georgios Rigas [Opens in a new window] ,
Petrônio A. S. Nogueira Open the ORCID record for Petrônio A. S. Nogueira [Opens in a new window] ,
André V. G. Cavalieri Open the ORCID record for André V. G. Cavalieri [Opens in a new window] ,
Oliver T. Schmidt Open the ORCID record for Oliver T. Schmidt [Opens in a new window]  and
Tim Colonius Open the ORCID record for Tim Colonius [Opens in a new window]
Ethan Pickering*
Affiliation:
Mechanical Engineering, California Institute of Technology, Pasadena, CA91125, USA
Georgios Rigas
Affiliation:
Mechanical Engineering, California Institute of Technology, Pasadena, CA91125, USA
Petrônio A. S. Nogueira
Affiliation:
Instituto Tecnológico de Aeronáutica, São José dos Campos, SP12228-900, Brazil
André V. G. Cavalieri
Affiliation:
Instituto Tecnológico de Aeronáutica, São José dos Campos, SP12228-900, Brazil
Oliver T. Schmidt
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA92093, USA
Tim Colonius
Affiliation:
Mechanical Engineering, California Institute of Technology, Pasadena, CA91125, USA
*
†Email address for correspondence: pickering@caltech.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ($St$) and non-zero azimuthal wavenumbers ($m$). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as $St/m\rightarrow 0$. Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core.

JFM classification

Wakes/Jets: Jets Turbulent Flows: Compressible turbulence Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A2
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abreu, L. I., Cavalieri, A. V. G., Schlatter, P., Vinuesa, R. & Henningson, D. 2019 Reduced-order models to analyse coherent structures in turbulent pipe flow. In 11th International Symposium on Turbulence and Shear Flow Phenomena. University of Southampton.Google Scholar
Agüí, J. C. & Hesselink, L. 1988 Flow visualization and numerical analysis of a coflowing jet: a three-dimensional approach. J. Fluid Mech. 191, 19–45.CrossRefGoogle Scholar
Åkervik, E., Ehrenstein, U., Gallaire, F. & Henningson, D. S. 2008 Global two-dimensional stability measures of the flat plate boundary-layer flow. Eur. J. Mech. (B/Fluids) 27 (5), 501–513.CrossRefGoogle Scholar
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, 139–169.CrossRefGoogle Scholar
Arakeri, V. H., Krothapalli, A., Siddavaram, V., Alkislar, M. B. & Lourenco, L. M. 2003 On the use of microjets to suppress turbulence in a Mach 0.9 axisymmetric jet. J. Fluid Mech. 490, 75–98.CrossRefGoogle Scholar
Arnette, S. A., Samimy, M. & Elliott, G. S. 1993 On streamwise vortices in high Reynolds number supersonic axisymmetric jets. Phys. Fluids A 5 (1), 187–202.CrossRefGoogle Scholar
Arratia, C., Caulfield, C. P. & Chomaz, J. M. 2013 Transient perturbation growth in time-dependent mixing layers. J. Fluid Mech. 717, 90–133.CrossRefGoogle Scholar
Becker, H. A. & Massaro, T. A. 1968 Vortex evolution in a round jet. J. Fluid Mech. 31 (3), 435–448.CrossRefGoogle Scholar
Benney, D. J. 1961 A non-linear theory for oscillations in a parallel flow. J. Fluid Mech. 10 (2), 209–236.CrossRefGoogle Scholar
Benney, D. J. & Lin, C. C. 1960 On the secondary motion induced by oscillations in a shear flow. Phys. Fluids 3 (4), 656–657.CrossRefGoogle Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.CrossRefGoogle Scholar
Bernal, L. P.1981 The coherent structure of turbulent mixing layers. PhD thesis, California Institute of Technology.Google Scholar
Bernal, L. P., Breidenthal, R. E., Brown, G. L., Konrad, J. H. & Roshko, A. 1979 On the development of three dimensional small scales in turbulent mixing layers. In Proc. 2nd Int. Symp. on Turbulent Shear Flows, Imperial College, London, p. 8.1–8.6.Google Scholar
Boronin, S. A., Healey, J. J. & Sazhin, S. S. 2013 Non-modal stability of round viscous jets. J. Fluid Mech. 716, 96–119.CrossRefGoogle Scholar
Bradshaw, P., Ferriss, D. H. & Johnson, R. F. 1964 Turbulence in the noise-producing region of a circular jet. J. Fluid Mech. 19 (4), 591–624.CrossRefGoogle Scholar
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. (B/Fluids) 47, 80–96.CrossRefGoogle Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 1–24.CrossRefGoogle Scholar
Breidenthal, R. E.1978 A chemically reacting shear layer. PhD thesis, California Institute of Technology.Google Scholar
Brès, G. A., Ham, F. E., Nichols, J. W. & Lele, S. K. 2017 Unstructured large-eddy simulations of supersonic jets. AIAA J. 55 (4), 1164–1184.CrossRefGoogle Scholar
Brès, G. A., Jordan, P., Jaunet, V., Le Rallic, M., Cavalieri, A. V. G., Towne, A., Lele, S. K., Colonius, T. & Schmidt, O. T. 2018 Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets. J. Fluid Mech. 851, 83–124.CrossRefGoogle Scholar
Bridges, J. & Brown, C. 2004 Parametric testing of chevrons on single flow hot jets. In 10th AIAA/CEAS Aeroacoustics Conference, p. 2824.Google Scholar
Bridges, J., Wernet, M. & Brown, C.2003 Control of jet noise through mixing enhancement. NASA Rep. No. NASA/TM 2003-212335.Google Scholar
Browand, F. K. & Laufer, J. 1975 The roles of large scale structures in the initial development of circular jets. In Symposia on Turbulence in Liquids, p. 35. University of Missouri–Rolla.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4 (8), 1637–1650.CrossRefGoogle Scholar
Callender, B., Gutmark, E. J. & Martens, S. 2005 Far-field acoustic investigation into chevron nozzle mechanisms and trends. AIAA J. 43 (1), 87–95.CrossRefGoogle Scholar
Caraballo, E., Samimy, M., Scott, J., Narayanan, S. & DeBonis, J. 2003 Application of proper orthogonal decomposition to a supersonic axisymmetric jet. AIAA J. 41 (5), 866–877.CrossRefGoogle Scholar
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, 559–592.CrossRefGoogle Scholar
Chantry, M., Tuckerman, L. S. & Barkley, D. 2016 Turbulent–laminar patterns in shear flows without walls. J. Fluid Mech. 791, R8.CrossRefGoogle Scholar
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (Part 1). Acta Mech. 1 (3), 215–234.CrossRefGoogle Scholar
Citriniti, J. H. & George, W. K. 2000 Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the proper orthogonal decomposition. J. Fluid Mech. 418, 137–166.CrossRefGoogle Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77 (2), 397–413.CrossRefGoogle Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547–591.CrossRefGoogle Scholar
Davoust, S., Jacquin, L. & Leclaire, B. 2012 Dynamics of m = 0 and m = 1 modes and of streamwise vortices in a turbulent axisymmetric mixing layer. J. Fluid Mech. 709, 408–444.CrossRefGoogle Scholar
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, 406–430.CrossRefGoogle Scholar
Dimotakis, P. E., Miake-Lye, R. C. & Papantoniou, D. A. 1983 Structure and dynamics of round turbulent jets. Phys. Fluids 26 (11), 3185–3192.CrossRefGoogle Scholar
Eitel-Amor, G., Örlü, R. & Schlatter, P. 2014 Simulation and validation of a spatially evolving turbulent boundary layer up to Re𝜃 = 8300. Intl J. Heat Fluid Flow 47, 57–69.CrossRefGoogle Scholar
Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18 (4), 487–488.CrossRefGoogle Scholar
Farrell, B. F. 1988 Optimal excitation of perturbations in viscous shear flow. Phys. Fluids 31 (8), 2093–2102.CrossRefGoogle Scholar
Farrell, B. F. & Ioannou, P. J. 1993 Optimal excitation of three-dimensional perturbations in viscous constant shear flow. Phys. Fluids A 5 (6), 1390–1400.CrossRefGoogle Scholar
Freund, J. B. & Colonius, T. 2009 Turbulence and sound-field pod analysis of a turbulent jet. Intl J. Aeroacoust. 8 (4), 337–354.CrossRefGoogle Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013a Modal and transient dynamics of jet flows. Phys. Fluids 25 (4), 044103.CrossRefGoogle Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013b The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.CrossRefGoogle Scholar
Greska, B., Krothapalli, A., Seiner, J., Jansen, B. & Ukeiley, L. 2005 The effects of microjet injection on an f404 jet engine. In 11th AIAA/CEAS Aeroacoustics Conference, p. 3047.Google Scholar
Gudmundsson, K. & Colonius, T. 2011 Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97–128.CrossRefGoogle Scholar
Hack, M. J. P. & Moin, P. 2017 Algebraic disturbance growth by interaction of Orr and lift-up mechanisms. J. Fluid Mech. 829, 112–126.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16 (1), 365–422.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number. J. Fluid Mech. 643, 333–348.CrossRefGoogle Scholar
Jaunet, V., Jordan, P. & Cavalieri, A. V. G. 2017 Two-point coherence of wave packets in turbulent jets. Phys. Rev. F 2 (2), 024604.Google Scholar
Jeun, J., Nichols, J. W. & Jovanović, M. R. 2016 Input–output analysis of high-speed axisymmetric isothermal jet noise. Phys. Fluids 28 (4), 047101.CrossRefGoogle Scholar
Jiménez, J. 2013 How linear is wall-bounded turbulence? Phys. Fluids 25 (11), 110814.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jimenez, J., Cogollos, M. & Bernal, L. P. 1985 A perspective view of the plane mixing layer. J. Fluid Mech. 152, 125–143.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Jimenez-Gonzalez, J. I. & Brancher, P. 2017 Transient energy growth of optimal streaks in parallel round jets. Phys. Fluids 29 (11), 114101.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.CrossRefGoogle Scholar
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, 173–204.CrossRefGoogle Scholar
Kantharaju, J., Courtier, R., Leclaire, B. & Jacquin, L. 2020 Interactions of large-scale structures in the near field of round jets at high Reynolds numbers. J. Fluid Mech. 888, A8.CrossRefGoogle Scholar
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50 (1), 133–160.CrossRefGoogle Scholar
Klebanoff, P. S. 1971 Effect of freestream turbulence on the laminar boundary layer. Bull. Am. Phys. Soc. 16 (11), 1323.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–773.CrossRefGoogle Scholar
Konrad, J. H.1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. PhD thesis, California Institute of Technology.Google Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (2), 243–251.CrossRefGoogle Scholar
Lesshafft, L., Semeraro, O., Jaunet, V., Cavalieri, A. V. G. & Jordan, P. 2019 Resolvent-based modelling of coherent wavepackets in a turbulent jet. Phys. Rev. F 4 (6), 063901.Google Scholar
Liepmann, D. 1991 Streamwise vorticity and entrainment in the near field of a round jet. Phys. Fluids A 3 (5), 1179–1185.CrossRefGoogle Scholar
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643–668.CrossRefGoogle Scholar
Lin, C. C.1981 The evolution of streamwise vorticity in the free shear layer. PhD thesis, Univ. Calif., Berkeley.Google Scholar
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139–178.CrossRefGoogle Scholar
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Propagation (ed. Yaglom, A. M. & Tatarski, V. I.), pp. 166–178. Nauka.Google Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic Press.Google Scholar
Malik, M. & Chang, C. L. 1997 PSE applied to supersonic jet instability. In 35th Aerospace Sciences Meeting and Exhibit, p. 758.Google Scholar
Marant, M. & Cossu, C. 2018 Influence of optimally amplified streamwise streaks on the Kelvin–Helmholtz instability. J. Fluid Mech. 838, 478–500.CrossRefGoogle Scholar
Martin, J. E. & Meiburg, E. 1991 Numerical investigation of three-dimensionally evolving jets subject to axisymmetric and azimuthal perturbations. J. Fluid Mech. 230, 271–318.CrossRefGoogle Scholar
Mattsson, K. & Nordström, J. 2004 Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys. 199 (2), 503–540.CrossRefGoogle Scholar
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
Metcalfe, R. W., Orszag, S. A., Brachet, M. E., Menon, S. & Riley, J. J. 1987 Secondary instability of a temporally growing mixing layer. J. Fluid Mech. 184, 207–243.CrossRefGoogle Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 21, 159–199.CrossRefGoogle Scholar
Miksad, R. W. 1972 Experiments on the nonlinear stages of free-shear-layer transition. J. Fluid Mech. 56 (4), 695–719.CrossRefGoogle Scholar
Mizuno, Y. & Jiménez, J. 2013 Wall turbulence without walls. J. Fluid Mech. 723, 429–455.CrossRefGoogle Scholar
Moffatt, H. K. 1965 The interaction of turbulence with strong wind shear. In Atmospheric Turbulence and Radio Waves Propagation, Proc. Intern. Collq. Moscow, 1965, pp. 139–156.Google Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157 (2), 787–795.CrossRefGoogle Scholar
Mollo-Christensen, E. 1967 Jet noise and shear flow instability seen from an experimenter’s viewpoint. Trans. ASME J. Appl. Mech. 34, 1–7.CrossRefGoogle Scholar
Monokrousos, A., Åkervik, E., Brandt, L. & Henningson, D. S. 2010 Global three-dimensional optimal disturbances in the blasius boundary-layer flow using time-steppers. J. Fluid Mech. 650, 181–214.CrossRefGoogle Scholar
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, 147–156.CrossRefGoogle Scholar
Morra, P., Semeraro, O., Henningson, D. S. & Cossu, C. 2019 On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows. J. Fluid Mech. 867, 969–984.CrossRefGoogle Scholar
Morris, P. J. 1976 The spatial viscous instability of axisymmetric jets. J. Fluid Mech. 77 (3), 511–529.CrossRefGoogle Scholar
Neu, J. C. 1984 The dynamics of stretched vortices. J. Fluid Mech. 143, 253–276.CrossRefGoogle Scholar
Nichols, J. W. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.CrossRefGoogle Scholar
Nogueira, P. A. S., Cavalieri, A. V. G., Jordan, P. & Jaunet, V. 2019 Large-scale, streaky structures in turbulent jets. J. Fluid Mech. 873, 211–237.CrossRefGoogle Scholar
Paschereit, C. O., Oster, D., Long, T. A., Fiedler, H. E. & Wygnanski, I. 1992 Flow visualization of interactions among large coherent structures in an axisymmetric jet. Exp. Fluids 12 (3), 189–199.CrossRefGoogle Scholar
Pickering, E., Rigas, G., Sipp, D., Schmidt, O. T. & Colonius, T. 2019 Eddy viscosity for resolvent-based jet noise models. In 25th AIAA/CEAS Aeroacoustics Conference, p. 2454.Google Scholar
Pierrehumbert, R. T. & Widnall, S. E. 1982 The two-and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 59–82.CrossRefGoogle Scholar
Qadri, U. A. & Schmid, P. J. 2017 Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity. Phys. Rev. F 2, 013902.Google Scholar
Rigas, G., Pickering, E., Schmidt, O. T., Nogueira, P. A., Cavalieri, A. V., Brès, G. A. & Colonius, T. 2019 Streaks and coherent structures in jets from round and serrated nozzles. In 25th AIAA/CEAS Aeroacoustics Conference, p. 2597.Google Scholar
Rodríguez, D., Cavalieri, A. V. G., Colonius, T. & Jordan, P. 2015 A study of linear wavepacket models for subsonic turbulent jets using local eigenmode decomposition of PIV data. Eur. J. Mech. (B/Fluids) 49, 308–321.CrossRefGoogle Scholar
Rogers, M. M. & Moser, R. D. 1992 The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup. J. Fluid Mech. 243, 183–226.CrossRefGoogle Scholar
Saiyed, N. H., Mikkelsen, K. L. & Bridges, J. E. 2003 Acoustics and thrust of quiet separate-flow high-bypass-ratio nozzles. AIAA J. 41 (3), 372–378.CrossRefGoogle Scholar
Samimy, M., Zaman, K. & Reeder, M. F. 1993 Effect of tabs on the flow and noise field of an axisymmetric jet. AIAA J. 31 (4), 609–619.CrossRefGoogle Scholar
Schmidt, O. T., Towne, A., Rigas, G., Colonius, T. & Brès, G. A. 2018 Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953–982.CrossRefGoogle Scholar
Semeraro, O., Lesshafft, L., Jaunet, V. & Jordan, P. 2016 Modeling of coherent structures in a turbulent jet as global linear instability wavepackets: theory and experiment. Intl J. Heat Fluid Flow 62, 24–32.CrossRefGoogle Scholar
Sinha, A., Rajagopalan, A. & Singla, S. 2016 Linear stability implications of chevron geometry modifications for turbulent jets. In 22nd AIAA/CEAS Aeroacoustics Conference, p. 3053.Google Scholar
Sipp, D. & Marquet, O. 2013 Characterization of noise amplifiers with global singular modes: the case of the leading-edge flat-plate boundary layer. Theor. Comput. Fluid Dyn. 27 (5), 617–635.CrossRefGoogle Scholar
Swearingen, J. D. & Blackwelder, R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255–290.CrossRefGoogle Scholar
Tam, C. K. W. & Hu, F. Q. 1989 On the three families of instability waves of high-speed jets. J. Fluid Mech. 201, 447–483.CrossRefGoogle Scholar
Tissot, G., Lajús, F. C. Jr, Cavalieri, A. V. G. & Jordan, P. 2017a Wave packets and Orr mechanism in turbulent jets. Phys. Rev. F 2 (9), 093901.Google Scholar
Tissot, G., Zhang, M., Lajús, F. C., Cavalieri, A. V. G. & Jordan, P. 2017b Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer. J. Fluid Mech. 811, 95–137.CrossRefGoogle Scholar
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, 821–867.CrossRefGoogle Scholar
Violato, D. & Scarano, F. 2011 Three-dimensional evolution of flow structures in transitional circular and chevron jets. Phys. Fluids 23 (12), 124104.CrossRefGoogle Scholar
Widnall, S. E., Bliss, D. B. & Tsai, C.-Y. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66 (1), 35–47.CrossRefGoogle Scholar
Yang, H., Zhou, Y., So, R. M. C. & Liu, Y. 2016 Turbulent jet manipulation using two unsteady azimuthally separated radial minijets. Proc. R. Soc. Lond. A 472 (2191), 20160417.CrossRefGoogle ScholarPubMed
Yule, A. J. 1978 Large-scale structure in the mixing layer of a round jet. J. Fluid Mech. 89 (3), 413–432.CrossRefGoogle Scholar
Zaman, K. 1999 Spreading characteristics of compressible jets from nozzles of various geometries. J. Fluid Mech. 383, 197–228.CrossRefGoogle Scholar
Zaman, K., Reeder, M. F. & Samimy, M. 1994 Control of an axisymmetric jet using vortex generators. Phys. Fluids 6 (2), 778–793.CrossRefGoogle Scholar