Buoyancy effects on the large scale structure of free turbulent shear flows

  • E.J. Hopfinger
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 75)


The stratified turbulent shear flow established by a cold wall jet issuing into an ambiant heated stream has been investigated experimentally. Conditions were such that buoyancy remained negligible in the jet establishment zone but became important further downstream. It was found previously that entrainment ceases when the “difference” Richardson number Ri, based on the scales of the free mixing zone of the wall jet, increased to a value of 1/3 and the same value has also been reported for the stop of the growth of a mixing layer. Flow visualisations carried out in a mixing layer with a Reynolds number close to that of the jet (≈103) _showed that it is the pairing process which is inhibited when Ri ≽ 1/3. From the results obtained in the jet it is inferred that a pairing process is also fundamental to the jet growth, even though no two-dimensional spanwise rolls exist in the jet and the spanwise temperature variation seems to indicate streamwise rolls. The turbulence becomes increasingly more anisotropic with increasing Ti and the vertical heat flux decreases relative to the longitudinal heat flux or the vertical momentum flux. These variations are explained using time scale arguments. When entrainment ceases the turbulence intensity was found to be still high and the Reynolds stress still appreciable, a result which is somewhat unexpected.


Reynolds Stress Richardson Number Splitter Plate Small Scale Eddy Vertical Heat Flux 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Townsend, A.A: Turbulent flow in a stably stratified atmosphere. J. Fluid Mech. 3 (1957) 361–372.Google Scholar
  2. 2.
    Thorpe, S.A.: Experiments on the instability of stratified shear flows. J. Fluid Mech. 46 (1971) 299–319.Google Scholar
  3. 3.
    Hopfinger, E.J.: Development of a stratified turbulent shear flow. Proc. Int. Symp. on Stratified Flows (1972) A.S.C.E. Publ., New York 553–565.Google Scholar
  4. 4.
    Winant,C.D.: Experimental comparison of the non-linear behaviour of stratified and unstratified shear layers. Proc. Int. Symp. on Stratified Flows (1972), A.S.C.E. Publ. New York 707–714.Google Scholar
  5. 5.
    Turner, J.S.: Buoyancy effects in fluids. Cambridge University Press 1973, (P. 151).Google Scholar
  6. 6.
    Corcos, G.M. and Sherman, F.S.: Vorticity and the dynamics of unstable free shear layers. J. Fluid Mech. 73 (1976) 241–264.Google Scholar
  7. 7.
    Nichol, C.I.H.: Some dynamical effects of heat on a turbulent boundary layer. J. Fluid Mech. 40 (1970) 361–384.Google Scholar
  8. 8.
    Schlichting, H. Turbulenz bei Wärmeschichtung. Z. angew. Math. Mech. 15 (1935) 313–338.Google Scholar
  9. 9.
    Townsend, A.A.: The mechanism of entrainment in free turbulent flows. J. Fluid Mech. 26 (1966) 689–715.Google Scholar
  10. 10.
    Kruka, V. and Eskinazi, S.: The wall jet in a moving stream J. Fluid Mech. 20 (1964) 555–579.Google Scholar
  11. 11.
    Corcos, G.M. and Hopfinger E.J.: L'instabilité motrice de la turbulence en écoulements libres. J. de Physique tome 37 (1976) 95–99.Google Scholar
  12. 12.
    Davies, A.E., Keffer J.F. and Baines, W.D.: Spread of a heated plane turbulent jet. Phys. Fluids 18 (1975) 770–775.CrossRefGoogle Scholar
  13. 13.
    Avsec, D.: Tourbillons thermoconvectifs dans l'air, application à la météorologie. Thèse d'état, Université de Paris 1939.Google Scholar
  14. 14.
    Brown, G. L. and Roshko, A.: On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (1974) 775–816.Google Scholar
  15. 15.
    Launder, B.E.: On the effects of a gravitational field on the turbulent transport of heat and momentum. J. Fluid Mech. 67 (1975) 569–581.Google Scholar
  16. 16.
    Moreau, R. and Alemany, A.: Experimental results on MHD homogeneous turbulence. Symposium on Turbulence, Berlin 1977.Google Scholar
  17. 17.
    Webster, C.A.G.: An experimental study of turbulence in a density stratified shear flow. J. Fluid Mech. 19 (1964) 221–245.Google Scholar
  18. 18.
    Turner, J.S.: The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33 (1968) 639–656.Google Scholar
  19. 19.
    Hopfinger, E. J. and Toly, J.A.: Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78 (1976) 155–175.Google Scholar
  20. 20.
    Linden, P.F. and Turner J.S.: Small scale mixing in stably stratified fluids: a report on Euremech 51 (communication by E.J. Hopfinger). J.Fluid Mech. 67 (1975) 1–16.MathSciNetGoogle Scholar
  21. 21.
    Winant, C.D. and Browand, F.K.: Vortex pairing:the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63 (1974) 237–255.Google Scholar
  22. 22.
    Koop, C.G.: Instability and Turbulence in a stratified shear layer. Ph.D. thesis (1976) Dep. of Aerespace Eng. U.S.C.Google Scholar
  23. 23.
    Chandrsuda, C., Mehta, R.B., Weir, A.D., Bradshaw, P.: Effect of free-stream turbulence on orderly structure in mixing layers. J. Fluid Mech. (submitted 1976).Google Scholar
  24. 24.
    Kolpin, M.C. The flow in the mixing region of a jet. J. Fluid Mech. 18 (1964) 529–548.Google Scholar
  25. 25.
    Patnaik, C.P.: Sherman, F.S., Corcos, G.M.: A numerical simulation of Kelvin-Helmholtz waves of finite amplitude. J. Fluid Mech. 73 (1976) 215–240.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • E.J. Hopfinger
    • 1
  1. 1.Institut de Mécanique (associé au C.N.R.S.)Université de GrenobleFrance

Personalised recommendations