Some Issues in Geophysical Turbulence and the Need for Accurate High Reynolds Number Measurements

  • Jackson R. Herring


We review here some issues related to geophysical flows, which have been investigated numerically, but for which new high-precision experiments would play a vital role in discriminating between competing theories and ideas. The selection of these topics is very much determined by the author’s own research, and those of several members of the geophysical turbulence group at NCAR. They are (1) the collective self-organization of large-scale convective patterns in the atmospheric mesoscale, (2) the dispersal of particles released in the fluid under conditions of stable stratification, and (3) the degree to which the transfer of energy to small scale is local in wave-number space. In our discussion, we bring into focus information gleaned from both simple scaling ideas (and sometimes the underlying statistical theory), and numerical simulations, at, perforce, small Rλ.


Rayleigh Number Planetary Boundary Layer Isotropic Turbulence Inertial Range Stable Stratification 
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]
    Monin, A.S., and Obukhov, A.M., 1958. Small scale oscillations of the atmosphere and adaption of meteorological fields. Izv. Akad. Naut USSR, Ser Geofiz. 11, 1360–1373.Google Scholar
  2. [2]
    Monin, A.S., 1990: Theoretical Geophysical Fluid Dynamics. Dordrecht, pp. 399.Google Scholar
  3. [3]
    Azad, R., 1993: The Atmospheric Boundary Layer for Engineers. Dordrecht, Boston, London. 565pp.CrossRefGoogle Scholar
  4. [4]
    Priestley, C. H. B., 1960. Temperature fluctuations in the atmospheric boundary layer. J. Fluid Mech. 7, 375–438.ADSMATHCrossRefGoogle Scholar
  5. [5]
    Heslot, F., Castaing, B. Libchaber, A., 1987. Transition to turbulence in helium gas. Phys. Rev. A36, 5870–5873.ADSGoogle Scholar
  6. [6]
    Shraiman, B. I., and Siggia, E., 1991. Heat Transport in High Rayleigh Number Convection. Phys. Rev. A 42, 3650–3653.ADSCrossRefGoogle Scholar
  7. [7]
    Kerr, R. M., 1996. Rayleigh number scaling in numerical convection. J. Fluid Mech. 310, 139–179.ADSMATHCrossRefGoogle Scholar
  8. [8]
    Krishnamurti, R., 1994. Low Frequency Oscillations in Turbulent Rayleigh-Bénard Convection. PreprintGoogle Scholar
  9. [9]
    Kerr, R.M, Herring, J. R. and Brandenburg, A. 1994. Large-scale structure in Rayleigh-Bénard convection with impenetrable side-walls. Chaos, Solitons, and Fractals 5, No. 10, 2047–2053.ADSCrossRefGoogle Scholar
  10. [10]
    Moeng, C.-H., and Sullivan, P. P., 1994. A Comparison of Shear-and Buoyancy-Driven Planetary Boundary Layer Flows. J. Atmos. Sci. 51, 999–1022.ADSCrossRefGoogle Scholar
  11. [11]
    Yaglom, A.M., 1993. Fluctuation spectra and variance in a convective atmospheric surface layer: a reevaluation of old models. Phys. Fluids, A6, 962–972.MathSciNetADSGoogle Scholar
  12. [12]
    Zilitinkevich, S., 1993. A Generalized Scaling for Convective Shear Flows. Boundary-Layer Meteorology. 49, 1–4.ADSCrossRefGoogle Scholar
  13. [13]
    Riley, J.J., Metcalfe, R.W., and Weissman, M.A., 1982. Direct numerical simulations of homogeneous turbulence in density stratified fluids. Proc. AIP Conf. on Nonlinear Properties of Internal Waves., p. 679–712.Google Scholar
  14. [14]
    Métais, O. and Herring, J. R., 1989. Numerical studies of freely decaying homogeneous stratified turbulence. J. Fluid Mech. 202, 117–148.ADSCrossRefGoogle Scholar
  15. [15]
    Herring, J. R. and Métais, O. 1989. Numerical experiments in forced stably stratified turbulence. J. Fluid Mech. 202, 97–115.ADSCrossRefGoogle Scholar
  16. [16]
    Britter, R. E., Hunt, J.C.R.G.L., Marsh, G. L. and Snyder, W. H. 1993. The effects of stable stratification on the turbulent diffusion and the decay of grid turbulence. J. Fluid Mech. 127, 27–44.ADSCrossRefGoogle Scholar
  17. [17]
    Csanady, G.T, 1964. Turbulent Diffusion in a Stratified Fluid. J. Atmos. Sci. 21, 439–447.MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    Kraichnan, R. H., 1976. Eddy viscosity in two- and three-dimensional turbulence. J. Atmos. Sci. 33, 1521–1536.ADSCrossRefGoogle Scholar
  19. [19]
    Kimura, Y. and Herring, J. R., 1996. Diffusion in stably stratified turbulence, to appear in, J. Fluid Mech. Google Scholar
  20. [20]
    Lesieur, M., and Schertzer, D., 1978. Amortissement auto similarité d’une turbulence á grand nombre de Reynolds. J. de Mécanique 17, 609–646.MathSciNetADSMATHGoogle Scholar
  21. [21]
    Smith, M. R., Donnelly, R. J., Goldenfeld, N., and Vinen, W. F., 1993. Decay of Homogeneous Turbulence in Superfluid Helium. Phys. Rev. Let 71, 2583.ADSCrossRefGoogle Scholar
  22. [22]
    Gage, K.S., 1979. Evidence for a k −5/3 law inertial range in mesoscale two-dimensional turbulence. J. Atmos. Sci. 36, 1950–1954ADSCrossRefGoogle Scholar
  23. [23]
    Kraichnan, R. H., 1971. Inertial-range transfer in two and three dimensional turbulence. J. Fluid Mech. 47, 525–535.ADSMATHCrossRefGoogle Scholar
  24. [24]
    Lilly, D.K., 1971. Numerical simulation of developing and decaying two-dimensional turbulence. J. Fluid Mech. 45, 395–415ADSMATHCrossRefGoogle Scholar
  25. [25]
    Van Atta, C., 1979. Inertial range bispectra in turbulence. Phys. Fluids 22, 1440–1442.ADSCrossRefGoogle Scholar
  26. [26]
    Helland, K. N., Lii, K. S., and Rosenblatt, M., 1978. Bispectra of atmospheric and wind tunnel turbulence. In Applications of Statistics. (P. R. Krishnaih, ed.) pp. 223–248. North Holland publishing company.Google Scholar
  27. [27]
    Herring, J. R., and Métais, O. 1992. Spectral Transfer and Bispectra for Turbulence with Passive Scalars. J. Fluid Mech. 235, 103–121.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1998

Authors and Affiliations

  • Jackson R. Herring
    • 1
  1. 1.N.C.A.R.BoulderUSA

Personalised recommendations