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.
Similar content being viewed by others
References
Boundary Layer Branch: 1967, ‘Wind and Temperature Profiles from Project Windy Acres’, Special Report No. 65, AFCRL-67-0339.
Busch, N. E. and Panofsky, H. A.: 1968, ‘Recent Spectra of Atmospheric Turbulence’,Quart. J. Roy. Meteorol. Soc. 94, 132–148.
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.
Corrsin, S.: 1951, ‘On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence’,J. Appl. Phys. 22, 469–473.
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.
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.
Kaimal, J. C., Borkowski, J., Panchev, S., Gjessing, D. T., and Hasse, L.: 1969, ‘Anisotropy of the Fine Structure’,Radio Sci. 4, 1369–1370.
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.
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.
Lin, C. C.: 1953, ‘On Taylor's Hypothesis and the Acceleration Terms in the Navier-Stoke's Equation’,Quart. Appl. Math. 10, 295–306.
Lumley, J. L.: 1965, ‘Interpretation of Time Spectra Measured in High Intensity Shear Flows’,Phys. Fluids 8, 1056–1062.
Lumley, J. L. and Panofsky, H. A.: 1964,The Structure of Atmospheric Turbulence, Interscience, NewYork.
Okamoto, M. and Webb, E. K.: 1970, ‘The Temperature Fluctuations in Stable Stratifications’,Quart. J. Roy. Meteorol. Soc. 97, 591–600.
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.
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.
Stewart, R. W.: 1969, ‘Turbulence and Waves in a Stratified Atmosphere’,Radio Sci. 4, 1269–1278.
Tatarski, V. I.: 1961,Wave Propagation in a Turbulent Medium (translated by R. A. Silverman), McGraw Hill, New York.
Taylor, G. I.: 1938, ‘The Spectrum of Turbulence’,Proc. Roy. Soc. A164, 476–490.
Tennekes, H. and Lumley, J. L.: 1972,A First Course in Turbulence, The MIT Press, Cambridge, Mass.
Tsvang, L. R.: 1969, ‘Microstructure of Temperature Fields in the Free Atmosphere’,Radio Sci. 4, 1175–1177.
Webb, E. K.: 1955, ‘Autocorrelations and Energy Spectra of Atmospheric Turbulence’,Tech. Paper, No. 5, Div. of Meteor. Phys., CSIRO, Melbourne.
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.
Wyngaard, J. C. and Coté, O. R.: 1972, ‘Cospectral Similarity in the Atmospheric Surface Layer’,Quart. J. Roy. Meteorol. Soc. 98. 590–603.
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.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kaimal, J.C. Turbulenece spectra, length scales and structure parameters in the stable surface layer. Boundary-Layer Meteorol 4, 289–309 (1973). https://doi.org/10.1007/BF02265239
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02265239