Results of Jet Instability Theory

  • Alfons Michalke
Conference paper


Theoretical results concerning the instability of axisymmetric jets are reviewed. For inviscid parallel jet flow the various parameters affecting jet instability as shear layer thickness, Mach number, temperature ratio, and external flow velocity are discussed. Furthermore, viscous and nonlinear effects are considered. Finally, the influences of flow divergence and of nozzle-jet interaction are discussed.


Mach Number Shear Layer Strouhal Number Vortex Sheet Shear Layer Thickness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Batchelor, G. K. and Gill, E. A. “Analysis of the Stability of Axisymmetric Jets,” J. Fluid Mech. 14 (1962), 529–551.MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    Bechert, D. “Excited Waves in Shear Layers.” Deutsche Luft- und Raumfahrt, DLR-FB 82–83, 1982.Google Scholar
  3. [3]
    A Model of the Excitation of Large Scale Fluctuations in a Shear Layer. AIAA Paper 83–0724, 1983.Google Scholar
  4. [4]
    Bechert, D. and Michel, U. “The Control of a Thin Free Shear Layer With and Without a Semi-Infinite Plate by a Pulsating Flow Field.” Acoustica 33 (1975), 287–307.ADSMATHGoogle Scholar
  5. [5]
    Blumen, W., Drazin, P. G., and Billings, D. F. “Shear Layer Instability of an Inviscid Compressible Fluid, Part 2.” J. Fluid Mech. 71 (1975), 305–316.ADSMATHCrossRefGoogle Scholar
  6. [6]
    Chan, Y. Y. “Spatial Waves in Turbulent Jets.” Physics of Fluids, 17 (1974), 46–53.ADSCrossRefGoogle Scholar
  7. [7]
    Chan, Y. Y. and Leong, R. K. “Discrete Acoustic Radiation Generated by Jet Instability.” Canadian Acoustics and Space Institute Trans. 6 (1973), 65–72.Google Scholar
  8. [8]
    Crighton, D. G. “Acoustics as a Branch of Fluid Mechanics.” J. Fluid Mech. 106 (1981), 261–298.ADSMATHCrossRefGoogle Scholar
  9. [9]
    Crighton, D. G. and Gaster, M. “Stability of Slowly Diverging Jet Flow.” J. Fluid Mech. 77 (1976), 397–413.ADSMATHCrossRefGoogle Scholar
  10. [10]
    Crow, S. C. and Champagne, F. H. “Orderly Structure in Jet Turbulence.” J. Fluid Mech. 48 (1971), 547–591.ADSCrossRefGoogle Scholar
  11. [11]
    Gaster, M. “A Note on the Relation Between Temporally-Increasing and Spatially-Increasing Disturbances in Hydrodynamic Stability.” Fluid Mech. 14 (1962), 222–24.MathSciNetADSMATHCrossRefGoogle Scholar
  12. [12]
    Gill, A. E. “Instabilities of ’Top-Hat’ Jets and Wakes in Compressible Fluid.” Physics of Fluid. 8 (1965), 1428–30.CrossRefGoogle Scholar
  13. [13]
    Gill, A. E. and Drazin, P. G. “Note on Instability of Compressible Jets and Wakes to Long-Wave Disturbances.” J. Fluid Mech. 22 (1965), 415.MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    Gropengießer, H. “Beitrag zur Stabilität freier Grenzschichten in kompressiblen Medien.” Deutsche Luft- und Raumfahrt, DLR-FB 69–25, 1969.Google Scholar
  15. [15]
    Haertig, J. “Theoretical and Experimental Study of Wavelike Disturbances in a Round Jet With Emphasis Being Placed on Orderly Structures.” In Mechanics of Sound Generation in Flows. Ed. E. A. Müller, New York: Springer Verlag, 1979, pp. 167–173.Google Scholar
  16. [16]
    Une Solution Analytique du Problème de l’instabilité d’un Jet Libre Rond Compressible. Institut Franco-Allemand de Recherche de Saint-Louis, ISL-R 119/81, 1981.Google Scholar
  17. [17]
    Ho, C. M. and Huang, L. S. “Subharmonics and Vortex Merging in Mixing Layers.” J. Fluid Mech. 119 (1982), 443–473.ADSCrossRefGoogle Scholar
  18. [18]
    Kambe, T. “The Stability of an Axisymmetric Jet With Parabolic Profile. J. Phys. Soc. Japan 26 (1969), 566–575.ADSCrossRefGoogle Scholar
  19. [19]
    Kapur, S. S. and Morris, P. J. “A Model for the Orderly Structure of Turbulence in a Two-Dimensional Shear Layer.” In The Generation and Radiation of Supersonic Jet Noise. Ed. H. E. Plumblee. Marietta, Georgia: Lockheed-Georgia, 1974, I-76-I-83.Google Scholar
  20. [20]
    Kelly, R. E. “On the Instability of an Inviscid Shear Layer Which is Periodic in Space and Time.” J. Fluid Mech. 27 (1967), 657–689.ADSMATHCrossRefGoogle Scholar
  21. [21]
    Leconte, J. “On the Influence of Musical Sounds on the Flame of a Jet of Coal-Gas. Phil. Mag. 15 (1858), 235–239.Google Scholar
  22. [22]
    Lessen, M., Fox, J. A., and Zien, H. M. “The Instability of Inviscid Jets and Wakes in Compressible Fluid.” J. Fluid Mech. 21 (1965), 129–143.MathSciNetADSMATHCrossRefGoogle Scholar
  23. [23]
    Lessen, M. and Singh, P. J. “The Stability of Axisymmetric Free Shear Layers.” J. Fluid Mech. 60 (1973), 443–457.ADSGoogle Scholar
  24. [24]
    Maestrello, L. and Bayliss, A. “Flowfield and Far Field Acoustic Amplification Properties of Heated and Unheated Jets.” AIAA Journal, 20 (1982), 1539–46.ADSCrossRefGoogle Scholar
  25. [25]
    Maslowe, S. A. and Kelly, R. E. “Inviscid Instability of an Unbounded Heterogeneous Shear Layer.” J. Fluid Mech. 48 (1971), 405–415ADSMATHCrossRefGoogle Scholar
  26. [26]
    Mattingly, G. E. and Chang, C. C. “Unstable Wave on an Axisymmetric Jet Column.” J. Fluid Mech. 65 (1974), 541–560.ADSMATHCrossRefGoogle Scholar
  27. [27]
    Michalke, A. “On Spatially Growing Disturbances in an Inviscid Shear Layer.” J. Fluid Mech. 28 (1965), 521–544.MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    “A Note on the Spatial Jet-Instability of the Compressible Cylindrical Vortex Sheet.” Deutsche Luftund Raumfahrt, DLR-FB 70–51, 1970.Google Scholar
  29. [29]
    “Instabilität eines kompressiblen runden Freistrahls unter Berücksichtigung des Einflusses der Strahlgrenzschichtdicke.” Z. Flugwiss. 19 (1971), 319–328. English translation NASA Tech. Memo. 75190, 1977.Google Scholar
  30. [30]
    “The Instability of Free Shear Layers—A Survey on the State of the Art.” Progr. Aerospace Sei. 12, 1972. Ed. D. Küchemann, New York: Pergamon Press, 213–239.Google Scholar
  31. [31]
    Michalke, A. and Freymuth, P. “The Instability and the Formation of Vortices in a Free Boundary Layer.” AGARD Conference Proc. No. 4, Separated Flows, Part II, 1966, 575–595.Google Scholar
  32. [32]
    Michalke, A. and Hermann, G. “On the Inviscid Instability of a Circular Jet With External Flow.” J. Fluid Mech. 114 (1982), 343–359.ADSMATHCrossRefGoogle Scholar
  33. [33]
    Michalke, A. and Schade, H. “Zur Stabilität von freien Grenzschichten.” Ing. Arch. 33 (1963), 1–23.MATHCrossRefGoogle Scholar
  34. [34]
    Michel, U. and Michalke, A. “Prediction of Fly-Over Jet Noise Spectra.” ALAA Paper No. 81–2025, 1981.Google Scholar
  35. [35]
    Mollendorf, J. C. and Gebhart, B. “An Experimental and Numerical Study of the Viscous Stability of a Round Laminar Jet With and Without Thermal Bouyancy for Symmetric and Asymmetric Disturbances.” J. Fluid Mech. 61 (1973), 367–399.ADSMATHCrossRefGoogle Scholar
  36. [36]
    Morris, P. J. “The Spatial Viscous Instability of Axisymmetric Jets.” J. Fluid Mech. 77 (1976), 511–529.ADSMATHCrossRefGoogle Scholar
  37. [37]
    “Viscous Stability of Compressible Axisymmetric Jets.” AIAA Journal 21 (1983), 481–482.Google Scholar
  38. [38]
    Morris, P. J. and Tarn, C. K. “On the Radiation of Sound by Instability Waves of a Compressible Axisymmetric Jet.” In Mechanics of Sound Generation in Flows. Ed. E. A. Müller. New York: Springer Verlag, 1979, 55–61.Google Scholar
  39. [39]
    Neuwerth, G. “Theorie der Ausbreitung wellenförmiger Störungen entgegen der Strömungsrichtung in einem Unterschall-Freistrahl.” Deutsche Luft und Raumfahrt, DLR-FB 74–20, 1974.Google Scholar
  40. [40]
    Petersen, R. A. “Influence of Wave Dispersion on Vortex Pairing in a Jet.” J. Fluid Mech. 89 (1978), 469–495.ADSCrossRefGoogle Scholar
  41. [41]
    Plaschko, P. “Helical Instabilities of Slowly Diverging Jets.” J. Fluid Mech. 92 (1979), 209–215.ADSMATHCrossRefGoogle Scholar
  42. [42]
    “Axial Coherence Functions of Circular Turbulent Jets Based on Inviscidly Calculated Damped Modes.” Submitted to Physics of Fluid, 1983.Google Scholar
  43. [43]
    Rayleigh, Lord. “On the Instability of Jets.” Proc. London Math. Soc. 10 (1879), 4–13.MATHCrossRefGoogle Scholar
  44. [44]
    Schade, H. “Zur Stabilitätstheorie axialsymmetrischer Parallelströmungen.” Ing. Arch. 31 (1962), 301–316.MathSciNetMATHCrossRefGoogle Scholar
  45. [45]
    Tarn, C.K.W. “Supersonic Jet Noise Generated by Large Scale Disturbances.” J. Sound Vibr. 38 (1975), 51–79.ADSCrossRefGoogle Scholar
  46. [46]
    Tyndall, J. “On the Action of Sonorous Vibrations on Gaseous and Liquid Jets.” Phil. Mag. 33 (1867), 375–391.Google Scholar
  47. [47]
    Watson, J. “On Spatially-Growing Finite Disturbances in a Plane Poiseuille Flow.” Fluid Mech. 14 (1962), 211–221.MathSciNetADSMATHCrossRefGoogle Scholar
  48. [48]
    Wille, R. “Beiträge zur Phänomenologie der Freistrahlen.” Z. Flugwiss. 11 (1963), 222–233.Google Scholar
  49. [49]
    Woolley, J. P. and Karamcheti, K. A Study of Narrow Band Noise Generation by Flow Over Ventilated Walls in Transonic Wind Tunnels• Wright-Patterson Air Force Base, Ohio: Air Force Office of Scientific Research, AFOSR-TR-730503, 1973.Google Scholar
  50. [50]
    “Role of Jet Stability in Edgetone Generation.” AIAA Journal 12 (1974), 1457–58.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Alfons Michalke
    • 1
  1. 1.Hermann-Föttinger-Institut für Thermo- und FluiddynamikTechnische Universität BerlinGermany

Personalised recommendations