Experiments in Fluids

, 60:22 | Cite as

Screech-tone prediction using upstream-travelling jet modes

  • Matteo MancinelliEmail author
  • Vincent Jaunet
  • Peter Jordan
  • Aaron Towne
Research Article


The purpose of this paper is to characterise and model the A1 and A2 screech modes in supersonic jets operating at off-design conditions. The usual screech-modelling scenario involves a feedback loop between a downstream-travelling Kelvin–Helmholtz instability wave and an upstream-travelling acoustic wave. We review state-of-the-art screech-frequency prediction models and associated limitations. Following the work of Edgington-Mitchell et al. (J Fluid Mech 855, 2018), a new prediction approach is proposed where the feedback loop is closed by the upstream-travelling jet modes first discussed in Tam and Hu (J Fluid Mech 201:447–483, 1989) in lieu of the free-stream sound waves. The Kelvin–Helmholtz and upstream-travelling jet modes are obtained using a cylindrical vortex-sheet model. The predictions provide a better agreement with experimental observations than does the classical screech-prediction approach. Screech dynamics associated with the staging process is explored through a wavelet analysis, highlighting that staging involves mutually exclusive switching that is underpinned by non-linear interactions.

Graphical abstract



M. M. acknowledges the support of Centre National d’Études Spatiales (CNES) under a post-doctoral grant.


  1. Bogey C, Gojon R (2017) Feedback loop and upwind-propagating waves in ideally expanded supersonic impinging round jets. J Fluid Mech 823:562–591MathSciNetCrossRefGoogle Scholar
  2. Edgington-Mitchell D, Jaunet V, Jordan P, Towne A, Soria J, Honnery D (2018) Upstream-travelling acoustic jet modes as a closure mechanism for screech. J Fluid Mech. CrossRefzbMATHGoogle Scholar
  3. Farge M (1992) Wavelet transforms and their applications to turbulence. Annu Rev Fluid Mech 24(1):395–458MathSciNetCrossRefGoogle Scholar
  4. Gao J, Li X (2010) A multi-mode screech frequency prediction formula for circular supersonic jets. J Acoust Soc Am 127(3):1251–1257CrossRefGoogle Scholar
  5. Gojon R, Bogey C, Mihaescu M (2018) Oscillation modes in screeching jets. AIAA J 56(7):1–7CrossRefGoogle Scholar
  6. Harper-Bourne M (1974) The noise from shock waves in supersonic jets-noise mechanism. Agard Cp-131 11:1–13Google Scholar
  7. Jiang Q, Suter BW (2017) Instantaneous frequency estimation based on synchrosqueezing wavelet transform. Signal Process 138:167–181CrossRefGoogle Scholar
  8. Jordan P, Jaunet V, Towne A, Cavalieri AVG, Colonius T, Schmidt O, Agarwal A (2018) Jet-flap interaction tones. J Fluid Mech 853:333–358MathSciNetCrossRefGoogle Scholar
  9. Landau LD, Lifshitz EM (2013) Course of theoretical physics. Elsevier, AmsterdamGoogle Scholar
  10. Lessen M, Fox JA, Zien HM (1965) On the inviscid stability of the laminar mixing of two parallel streams of a compressible fluid. J Fluid Mech 23(2):355–367CrossRefGoogle Scholar
  11. Mancinelli M, Di Marco A, Camussi R (2017a) Multivariate and conditioned statistics of velocity and wall pressure fluctuations induced by a jet interacting with a flat plate. J Fluid Mech 823:134–165CrossRefGoogle Scholar
  12. Mancinelli M, Pagliaroli T, Di Marco A, Camussi R, Castelain T (2017b) Wavelet decomposition of hydrodynamic and acoustic pressures in the near field of the jet. J Fluid Mech 813:716–749MathSciNetCrossRefGoogle Scholar
  13. Meneveau C (1991) Analysis of turbulence in the orthonormal wavelet representation. J Fluid Mech 232:469–520MathSciNetCrossRefGoogle Scholar
  14. Mercier B, Castelain T, Bailly C (2017) Experimental characterisation of the screech feedback loop in underexpanded round jets. J Fluid Mech 824:202–229CrossRefGoogle Scholar
  15. Merle M (1957) Nouvelles recherches sur les fréquences ultrasonores émises par les jets d’air. In: Ann. Télécommun, vol 12. Springer, pp 424–426Google Scholar
  16. Michalke A (1970) A note on the spatial jet-lnstability of the compressible cylindrical vortex sheet. Technical report, DLRGoogle Scholar
  17. Michalke A (1984) Survey on jet instability theory. Prog Aerosp Sci 21:159–199CrossRefGoogle Scholar
  18. Pack DC (1950) A note on prandtl’s formula for the wave-length of a supersonic gas jet. Q J Mech Appl Math 3(2):173–181MathSciNetCrossRefGoogle Scholar
  19. Panda J (1999) An experimental investigation of screech noise generation. J Fluid Mech 378:71–96CrossRefGoogle Scholar
  20. Pierce AD, Beyer RT (1990) Acoustics: an introduction to its physical principles and applications, 1989 edn. Acoustical Society of America, New YorkGoogle Scholar
  21. Powell A (1953) On the mechanism of choked jet noise. Proc Phys Soc Lond Sect B 66:1039CrossRefGoogle Scholar
  22. Powell A, Umeda Y, Ishii R (1992) Observations of the oscillation modes of choked circular jets. J Acoust Soc Am 92(5):2823–2836CrossRefGoogle Scholar
  23. Raman G (1999) Supersonic jet screech: half-century from powell to the present. J Sound Vib 225(3):543–571CrossRefGoogle Scholar
  24. Shen H, Tam CKW (2002) Three-dimensional numerical simulation of the jet screech phenomenon. AIAA J 40(1):33–41CrossRefGoogle Scholar
  25. Tam CKW (1995) Supersonic jet noise. Annu Rev Fluid Mech 27(1):17–43CrossRefGoogle Scholar
  26. Tam CKW, Ahuja KK (1990) Theoretical model of discrete tone generation by impinging jets. J Fluid Mech 214:67–87MathSciNetCrossRefGoogle Scholar
  27. Tam CKW, Hu FQ (1989) On the three families of instability waves of high-speed jets. J Fluid Mech 201:447–483MathSciNetCrossRefGoogle Scholar
  28. Tam CKW, Seiner JM, Yu JC (1986) Proposed relationship between broadband shock associated noise and screech tones. J Sound Vib 110(2):309–321CrossRefGoogle Scholar
  29. Towne A, Cavalieri AVG, Jordan P, Colonius T, Schmidt O, Jaunet V, Brès GA (2017) Acoustic resonance in the potential core of subsonic jets. J Fluid Mech 825:1113–1152CrossRefGoogle Scholar
  30. Walker SH, Thomas FO (1997) Experiments characterizing nonlinear shear layer dynamics in a supersonic rectangular jet undergoing screech. Phys Fluids 9(9):2562–2579CrossRefGoogle Scholar
  31. Walker SH, Gordeyev SV, Thomas FO (1997) A wavelet transform analysis applied to unsteady aspects of supersonic jet screech resonance. Exp Fluids 22(3):229–238CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Département Fluides Thermique et CombustionInstitut Pprime-CNRS-Université de Poitiers-ENSMAChasseneuil-du-Poitou, PoitiersFrance
  2. 2.Direction des LanceursCNESParisFrance
  3. 3.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA

Personalised recommendations