Acta Mechanica Sinica

, Volume 33, Issue 1, pp 10–19 | Cite as

Coherent structures and wavepackets in subsonic transitional turbulent jets

  • Haihua Yang
  • Xingchen Zhang
  • Lingke Ran
  • Dejun Sun
  • Zhenhua Wan
Research Paper


A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of \(Re=10^5\), which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous experimental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent structures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The \(m=0,1\) modes have high coherence of near-field pressure for both jets, while the coherence of \(m=0\) modes is enhanced greatly by heating. Based on the coherent structures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heating would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.


Wavepacket Noise Coherent structure Turbulent jet 



The project was supported by the National Natural Science Foundation of China (Grants 11232011, 11402262, 11572314, 11621202) and the Fundamental Research Funds for the Central Universities.


  1. 1.
    Lighthill, M.J.: On sound generated aerodynamically. I. General theory. Proc. R. Soc. Lond. A 211, 564–587 (1952)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Lau, J.C., Morris, P.J., Fisher, M.J.: Measurements in subsonic and supersonic free jets using a laser velocimeter. J. Fluid Mech. 93, 1–27 (1979)CrossRefGoogle Scholar
  3. 3.
    Tam, C.K.W., Golebiowski, M., Seiner, J.M.: On the Two Components of Turbulent Mixing Noise from Supersonic Jets. American Institute of Aeronautics and Astronautics, Orlando (1996)CrossRefGoogle Scholar
  4. 4.
    Viswanathan, K.: Aeroacoustics of hot jets. J. Fluid Mech. 516, 39–82 (2004)CrossRefMATHGoogle Scholar
  5. 5.
    Tam, C.K.W.: Supersonic jet noise. Annu. Rev. Fluid Mech. 27, 17–43 (1995)CrossRefGoogle Scholar
  6. 6.
    Tam, C.K.W., Viswanathan, K., Ahuja, K.K., et al.: The sources of jet noise: experimental evidence. J. Fluid Mech. 615, 253–292 (2008)CrossRefMATHGoogle Scholar
  7. 7.
    Colonius, T., Lele, S.K.: Computational aeroacoustics: progress on nonlinear problems of sound generation. Prog. Aerosp. Sci. 40, 345–416 (2004)CrossRefGoogle Scholar
  8. 8.
    Jordan, P., Colonius, T.: Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195 (2013)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Papamoschou, D.: Wavepacket modeling of the jet noise source. AIAA Paper, 2011–2835 (2011)Google Scholar
  10. 10.
    Crow, S.C., Champagne, F.H.: Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591 (1971)CrossRefGoogle Scholar
  11. 11.
    Brown, G.L., Roshko, A.: On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816 (1974)CrossRefGoogle Scholar
  12. 12.
    Moore, C.J.: The role of shear-layer instability waves in jet exhaust noise. J. Fluid Mech. 80, 321–367 (1977)CrossRefGoogle Scholar
  13. 13.
    Suzuki, T., Colonius, T.: Instability waves in a subsonic round jet detected using a near-field phased microphone array. J. Fluid Mech. 565, 197–226 (2006)CrossRefMATHGoogle Scholar
  14. 14.
    Tam, C.K.W., Burton, D.E.: Sound generated by instability waves of supersonic flows. Part 2. Axisymmetric jets. J. Fluid Mech. 138, 273–295 (1984)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Cheung, L.C., Lele, S.K.: Linear and nonlinear processes in two-dimensional mixing layer dynamics and sound radiation. J. Fluid Mech. 625, 321 (2009)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Gudmundsson, K., Colonius, T.: Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97–128 (2011)CrossRefMATHGoogle Scholar
  17. 17.
    Cavalieri, A.V.G., Rodríguez, D., Jordan, P., et al.: Wavepackets in the velocity field of turbulent jets. J. Fluid Mech. 730, 559–592 (2013)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Sinha, A., Rodríguez, D., Brès, G.A., et al.: Wavepacket models for supersonic jet noise. J. Fluid Mech. 742, 71–95 (2014)CrossRefGoogle Scholar
  19. 19.
    Suzuki, T.: Coherent noise sources of a subsonic round jet investigated using hydrodynamic and acoustic phased-microphone arrays. J. Fluid Mech. 730, 659–698 (2013)CrossRefMATHGoogle Scholar
  20. 20.
    Breakey D.E.S., Jordan P., Cavalieri A.V.G. et al.: Near-field wavepackets and the far-field sound of a subsonic jet. In: 19th AIAA/CEAS Aeroacoustics Conference, AIAA Paper, 2013–2083 (2013)Google Scholar
  21. 21.
    Bodony, D.J., Lele, S.K.: On using large eddy simulation for the prediction of noise from cold and heated turbulent jets. Phys. Fluids 17, 085103 (2005)CrossRefMATHGoogle Scholar
  22. 22.
    Wan, Z.H., Zhou, L., Yang, H.H., et al.: Large eddy simulation of flow development and noise generation of free and swirling jets. Phys. Fluids 25, 126103 (2013)CrossRefGoogle Scholar
  23. 23.
    Guo, L., Zhang, X., He, G.W.: Large-eddy simulation of circular cylinder flow at subcritical Reynolds number: turbulent wake and sound radiation. Acta Mech. Sin. 32, 1–11 (2016)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Sirovich, L.: Turbulence and the dynamics of coherent structures. Part I: Coherent structures. Quart. Appl. Math. 45, 561–571 (1987)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Wan, Z.H., Yang, H.H., Zhang, X.C., et al.: Instability waves and aerodynamic noise in a subsonic transitional turbulent jet. Eur. J. Mech. B 57, 192–203 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Giles, M.B.: Nonreflecting boundary conditions for euler equation calculations. AIAA J. 28, 2050–2058 (1990)CrossRefGoogle Scholar
  27. 27.
    Tanna, H.K.: An experimental study of jet noise part I: turbulent mixing noise. J. Sound Vib. 50, 405–428 (1977)CrossRefGoogle Scholar
  28. 28.
    Lush, P.A.: Measurements of subsonic jet noise and comparison with theory. J. Fluid Mech. 46, 477–500 (1971)CrossRefGoogle Scholar
  29. 29.
    Stromberg, J.L., McLaughlin, D.K., Troutt, T.R.: Flow field and acoustic properties of a mach number 0.9 jet at a low Reynolds number. J. Sound Vib. 72, 159–176 (1980)CrossRefGoogle Scholar
  30. 30.
    Mollo-Christensen, E., Kolpin, M.A., Martuccelli, J.R.: Experiments on jet flows and jet noise far-field spectra and directivity patterns. J. Fulid Mech. 18, 285–301 (1964)CrossRefMATHGoogle Scholar
  31. 31.
    Bogey, C., Barré, S., Fleury, V., et al.: Experimental study of the spectral properties of near-field and far-field jet noise. Int. J. Aeroacoustics 6, 73–92 (2007)Google Scholar
  32. 32.
    Freund, J.B., Colonius, T.: Turbulence and sound-field pod analysis of a turbulent jet. Int. J. Aeroacoustics 8, 337–354 (2009)CrossRefGoogle Scholar
  33. 33.
    Wan, Z.H., Zhou, L., Wang, B.F., et al.: Dynamic mode decomposition of forced spatially developed transitional jets. Eur. J. Mech. B 51, 16–26 (2015)CrossRefGoogle Scholar
  34. 34.
    Cavalieri, A.V.G., Jordan, P., Agarwal, A., et al.: Jittering wave-packet models for subsonic jet noise. J. Sound Vib. 330, 4474–4492 (2011)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Haihua Yang
    • 1
  • Xingchen Zhang
    • 1
  • Lingke Ran
    • 1
  • Dejun Sun
    • 1
  • Zhenhua Wan
    • 1
  1. 1.Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiChina

Personalised recommendations