Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Inertial range behaviour of the longitudinal heat flux cospectrum


Hot and cold wire measurements in the atmospheric surface layer support a -5/3 intertial range behaviour for the longitudinal and heat flux cospectrum. A narrow -5/3 region, which precedes a -7/3 region, can be observed in existing atmospheric data for momentum and heat flux cospectra.

This is a preview of subscription content, log in to check access.


  1. Antonia, R. A., and Raupach, M. R.: 1993, ‘Spectral Scaling in a High Reynolds Number Laboratory Boundary Layer’,Boundary-Layer Meteorol. 65, 289–306.

  2. Bradley, E. F., Antonia, R. A., and Chambers, A. J.: 1981, ‘Turbulence Reynolds Number and the Turbulent Kinetic Energy Balance in the Atmospheric Surface Layer’,Boundary-Layer Meteorol. 21, 183–197.

  3. Bradshaw, P.: 1967, ‘Conditions for the Existence of an Inertial Subrange in Turbulent Flow’,ARC R & M No. 3603.

  4. Caughey, S. J.: 1977, ‘Boundary-Layer Turbulence Spectra in Stable Conditions’,Boundary-Layer Meteorol. 11, 3–24.

  5. Caughey, S. J., Wyngaard, J. C., and Kaimal, J. C.: 1979, ‘Turbulence in the Evolving Stable Boundary Layer’,J. Atmos. Sci. 36, 1041–1052.

  6. Champagne, F. H., Friehe, C. A., LaRue, J. C., and Wyngaard, J.: 1977, ‘Flux Measurements, Flux Estimation Techniques, and Fine-Scale Turbulence Measurements in the Unstable Surface Layer Over Land’,J. Atmos. Sci. 34, 515–530.

  7. Corrsin, S.: 1951, ‘On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence’,J. Appl. Phys. 22, 469–473.

  8. Corrsin, S.: 1957, ‘Some Current Problems in Turbulent Shear Flows’,Naval Hydrodynamics, Publication 515, National Academy of Sciences — National Research Council, U.S.A., 373–400.

  9. Kader, B. A. and Yaglom, A. M.: 1991, ‘Spectra and Correlation Functions of Surface Layer Atmospheric Turbulence in Unstable Thermal Stratification’, in O. Metais and M. Lesieur (eds.),Turbulence and Coherent Structures, Dordrecht, Kluwer, pp. 387–412.

  10. Kaimal, J. C.: 1973, ‘Turbulence Spectra, Length Scales and Structure Parameters in the Stable Surface Layer’,Boundary-Layer Meteorol. 4, 289–309.

  11. Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Coté, O. R.: 1972, ‘Spectral Characteristics of Surface-Layer Turbulence’,Quart. J. R. Meteorol. Soc. 98, 563–589.

  12. Kolmogorov, A. N.: 1941 ‘Energy Dissipation in Locally Isotropic Turbulence’,Dokl. AN SSSR,32, 19–21.

  13. Lumley, J. L.: 1964, ‘The Spectrum of Nearly Inertial Turbulence in a Stably Stratified Fluid’,J. Atmos. Sci. 21, 99–102.

  14. Lumley, J. L.: 1967, ‘Similarity and the Turbulent Energy Spectrum’,Phys. Fluids 10, 855–858.

  15. Marusic, I.: 1991,The Structure of Zero- and Adverse-Pressure-Gradient Turbulent Boundary Layers, Ph.D. Thesis, University of Melbourne, Australia.

  16. Mestayer, P.: 1982, ‘Local Isotropy and Anisotropy in a High-Reynolds-Number Turbulent Boundary Layer’,J. Fluid Mech. 125, 475–503.

  17. Monin, A. S., and Yaglom, A. M.: 1975,Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2, Cambridge, Mass., MIT Press.

  18. Obukhov, A. M.: 1949, ‘Structure of the Temperature Field in a Turbulent Flow’,Izv. Akad. Nauk. SSSR, Ser. Geogr. i Geofiz. 13, 58.

  19. Park, J. T. and Van Atta, C. W.: 1980, ‘Hot- and Cold-Wire Sensitivity Corrections for Moments of the Fine Scale Turbulence in Heated Flows’,Phys. Fluids 23, 701–705.

  20. Pond, S., Phelps, G. T., Paquin, J. E., McBean, G., and Stewart, R. W.: 1971, ‘Measurements of the Turbulent Fluxes of Momentum, Moisture and Sensible Heat Over the Ocean’,J. Atmos. Sci. 28, 901–917.

  21. Saddoughi, S. G. and Veeravalli, S. V.: 1993, ‘Local Isotropy in Turbulent Boundary Layers at High Reynolds Number’,CTR Manuscript 142, Stanford University/NASA-Ames Research Center.

  22. Tchen, C-M: 1954, ‘Transport Processes as Foundations of the Heisenberg and Obukhoff Theories of Turbulence’,Phys. Rev. 93, 4–14.

  23. Van Atta, C. W. and Wyngaard, J. C.: 1975, ‘On Higher-Order Spectra of Turbulence’,J. Fluid Mech. 72, 673–694.

  24. Wyngaard, J. C. and Coté, O. R.: 1972, ‘Cospectral Similarity in the Atmospheric Surface Layer’,Quart. J. R. Meteorol. Soc. 98, 590–603.

  25. Wyngaard, J. C., Pennell, W. T., Lenschow, D. H., and LeMone, M. A.: 1978, ‘The Temperature-Humidity Covariance Budget in the Convective Boundary Layer’,J. Atmos. Sci. 35, 47–58.

  26. Wyngaard, J. C. and Sundarajan, A.: 1979, ‘The Temperature Skewness Budget in the Lower Atmosphere and its Implications for Turbulence Modeling’, in F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw (eds.),Turbulent Shear Flows I, Berlin, Springer, pp. 319–326.

  27. Yaglom, A. M.: 1981, ‘Laws of Small-Scale Turbulence in Atmosphere and Ocean (In Commemoration of the 40th Anniversary of the Theory of Locally Isotropic Turbulence)’,Izv. Atmos. Oceanic Phys. 17, 919–935.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Antonia, R.A., Zhu, Y. Inertial range behaviour of the longitudinal heat flux cospectrum. Boundary-Layer Meteorol 70, 429–434 (1994). https://doi.org/10.1007/BF00713779

Download citation


  • Heat Flux
  • Surface Layer
  • Atmospheric Surface Layer
  • Inertial Range
  • Atmospheric Data