Advertisement

Boundary-Layer Meteorology

, Volume 4, Issue 1–4, pp 289–309 | Cite as

Turbulenece spectra, length scales and structure parameters in the stable surface layer

  • J. C. Kaimal
Article

Abstract

The paper describes the basic similarity in the spectral forms for velocity and temperature, and the cospectral forms for stress and heat flux in a stably stratified surface layer. A practical scheme is developed for estimating these spectra and cospectra using only height and Richardson number. From this development emerges certain simple relationships between Richardson number, turbulent dissipation rates, characteristic length scales and structure parameters. The paper also presents evidence for isotropy in the surface layer, and the dependence of the limiting wavelength for the 4/3 ratio between transverse and longitudinal velocity components on height and stability.

Keywords

Heat Flux Surface Layer Velocity Component Isotropy Dissipation Rate 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boundary Layer Branch: 1967, ‘Wind and Temperature Profiles from Project Windy Acres’, Special Report No. 65, AFCRL-67-0339.Google Scholar
  2. Busch, N. E. and Panofsky, H. A.: 1968, ‘Recent Spectra of Atmospheric Turbulence’,Quart. J. Roy. Meteorol. Soc. 94, 132–148.Google Scholar
  3. Comte-Bellot, G. and Corrsin, S.: 1972, ‘Simple Eulerian Time Correlation of Full and Narrow Band Velocity Signals in Grid Generated ‘Isotropic’ Turbulence’,J. Fluid Mech. 48, 273–337.Google Scholar
  4. Corrsin, S.: 1951, ‘On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence’,J. Appl. Phys. 22, 469–473.Google Scholar
  5. Gisina, F. A. and Ponomareva, S. M.: 1971, ‘Evaluation of the Integral Scales of Velocity and Temperature Fluctuations in the Ground Layer’,Izv. Acad. Sci., U.S.S.R., Phys. Atmos. Ocean,7, 658–661.Google Scholar
  6. Haugen, D. A., Kaimal, J. C., and Bradley, E. F.: 1971, ‘An Experimental Study of Reynolds Stress and Heat Flux in the Atmospheric Surface Layer’,Quart. J. Roy. Meteorol. Soc. 97, 168–180.Google Scholar
  7. Kaimal, J. C., Borkowski, J., Panchev, S., Gjessing, D. T., and Hasse, L.: 1969, ‘Anisotropy of the Fine Structure’,Radio Sci. 4, 1369–1370.Google Scholar
  8. Kaimal, J. C., Wyngaard, J. C., and Haugen, D. A.: 1968, ‘Deriving Power Spectra from a Three-Component Sonic Anemometer’,J. Appl. Meteorol. 7, 827–837.Google Scholar
  9. Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Coté, O. R.: 1972, ‘Spectral Characteristics of Surface Layer Turbulence’,Quart. J. Roy. Meteorol. Soc. 98, 563–589.Google Scholar
  10. Lin, C. C.: 1953, ‘On Taylor's Hypothesis and the Acceleration Terms in the Navier-Stoke's Equation’,Quart. Appl. Math. 10, 295–306.Google Scholar
  11. Lumley, J. L.: 1965, ‘Interpretation of Time Spectra Measured in High Intensity Shear Flows’,Phys. Fluids 8, 1056–1062.Google Scholar
  12. Lumley, J. L. and Panofsky, H. A.: 1964,The Structure of Atmospheric Turbulence, Interscience, NewYork.Google Scholar
  13. Okamoto, M. and Webb, E. K.: 1970, ‘The Temperature Fluctuations in Stable Stratifications’,Quart. J. Roy. Meteorol. Soc. 97, 591–600.Google Scholar
  14. Panofsky, H. A.: 1968, ‘The Structure Constant for the Index of Refraction in Relation to the Gradient of Index of Refraction in the Surface Layer’,J. Geophys. Res. 73, 6047–6049.Google Scholar
  15. Panofsky, H. A., Cramer, H. E., and Rao, V. R. K.: 1968, ‘The Relation Between Eulerian Time and Space Spectra’,Quart. J. Roy. Meteorol. Soc. 84, 270–273.Google Scholar
  16. Stewart, R. W.: 1969, ‘Turbulence and Waves in a Stratified Atmosphere’,Radio Sci. 4, 1269–1278.Google Scholar
  17. Tatarski, V. I.: 1961,Wave Propagation in a Turbulent Medium (translated by R. A. Silverman), McGraw Hill, New York.Google Scholar
  18. Taylor, G. I.: 1938, ‘The Spectrum of Turbulence’,Proc. Roy. Soc. A164, 476–490.Google Scholar
  19. Tennekes, H. and Lumley, J. L.: 1972,A First Course in Turbulence, The MIT Press, Cambridge, Mass.Google Scholar
  20. Tsvang, L. R.: 1969, ‘Microstructure of Temperature Fields in the Free Atmosphere’,Radio Sci. 4, 1175–1177.Google Scholar
  21. Webb, E. K.: 1955, ‘Autocorrelations and Energy Spectra of Atmospheric Turbulence’,Tech. Paper, No. 5, Div. of Meteor. Phys., CSIRO, Melbourne.Google Scholar
  22. Wyngaard, J. C. and Coté, O. R.: 1971, ‘The Budgets of Turbulent Kinetic Energy and Temperature Variance in the Atmospheric Surface Layer’,J. Atmospheric Sci. 28, 190–201.Google Scholar
  23. Wyngaard, J. C. and Coté, O. R.: 1972, ‘Cospectral Similarity in the Atmospheric Surface Layer’,Quart. J. Roy. Meteorol. Soc. 98. 590–603.Google Scholar
  24. Wyngaard, J. C., Izumi, Y., and Collins, S. A.: 1971, ‘Behavior of the Refractive Index Structure Parameter Near the Ground’,J. Opt. Soc. Amer. 61, 1646–1650.Google Scholar

Copyright information

© D. Reidel Publishing Company 1973

Authors and Affiliations

  • J. C. Kaimal
    • 1
  1. 1.Air Force Cambridge Research LaboratoriesBedfordUSA

Personalised recommendations