Abstract
Methods are studied which permit one to evaluate turbulent fluxes from the results of spectral measurements in turbulent laboratory flows and an unstable atmospheric surface layer. The well known dissipation method of flux measurements, which uses spectral data related to the inertial range, is reanalyzed. New theoretical ideas and the latest experimental data are used to specify this method in cases of moderately and very strongly unstable thermal stratifications.
Moreover, it is also explained how to estimate momentum and heat fluxes from data in the low frequency parts of the velocity and temperature spectra in the low frequency ranges beyond the lower limit of the inertial range. This permits one to estimate fluxes using rather simple and cheap instruments (e.g., Pilot-tubes and thermocouples in laboratory flows or cup anemometers and crude resistance thermometers in meteorological studies). The equations for flux determination are based in such cases on the recent models by Kader (1987, 1988) and Kader and Yaglom (1990, 1991) of spectral shapes at mesoscale wave numbers; these models agree quite satisfactorily with many (though not all) data of direct spectral measurements. It is shown that estimated momentum and heat fluxes in the laboratory and in an unstably stratified atmospheric surface layer obtained by the method suggested in this paper agree satisfactorily with direct flux measurements.
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Betchov, R., and Yaglom, A. M.: 1971, ‘Comments on the Theory of Similarity as Applied to Turbulence in an Unstably Stratified Fluid’, Izv. Akad. nauk SSSR. Ser. Fiz. Atmosf. i Okeana 7, 1270–1279 (829–832 in the Engl. transl. of the journal).
Bradley, E. F., Antonia, R. A. and Chambers, A. J.: 1981a, ‘Temperature Structure in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 20, 275–292.
Bradley, E. F., Antonia, R. A. and Chambers, A. J.: 1981b, ‘Turbulence Reynolds Number and the Turbulent Kinetic Energy Balance in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 21, 183–197.
Bradley, E. F., Antonia, R. A., Chambers, A. J.: 1982, ‘Streamwise Heat Flux Budget in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 23, 3–15.
Businger, J. A., Wyngaard, J. C., Izumi, Y. and Bradley, F. F.: 1971, ‘Flux-Profile Relationships in the Atmospheric Surface Layer’, J. Atmos. Sci. 28, 181–189.
Champagne, F. H., Friehe, C. A. and LaRue, J. C.: 1977, ‘Flux Measurements, Flux Estimations Techniques, and Fine-Scale Turbulence Measurements in the Unstable Surface Layer over Land’, J. Atmos. Sci. 34, 515–530.
Chiba, O.: 1978, ‘Stability Dependence of the Vertical Wind Velocity Skewness in the Atmospheric Surface Layer’, J. Meteorol. Soc. Japan 56, 140–142.
Coantic, M.: 1966, ‘Contribution à l'étude de la Structure de la Turbulence dans une Conduite de Section Circulaire’, Thèse de Doctorat des Sciences Physiques. Université d'Aix, Marseille.
Fairall, C. W. and Larsen, S. E.: 1986, ‘Inertial-Dissipation Methods and Turbulent Fluxes at the Air-Ocean Interface’, Boundary-Layer Meteorol. 34, 287–301.
Fulachier, L.: 1972, ‘Contribution à l'étude des Analogies des Champs Dynamique et Thermique dans une Couche Limite Turbulente. Effet de l'Aspiration’, Thèse de Doctorat d'Elat. Université de Provence. Marseille.
Högström, U.: 1990, ‘Analysis of Turbulence Structure in the Surface Layer with a Modified Similarity Formulation for near Neutral Conditions’, J. Atm. Sci. 46, 1949–1972.
Kader, B. A.: 1984, ‘Structure of Anisotropic Velocity and Temperature Fluctuations in a Developed Turbulent Boundary Layer’, Izv. Akad. nauk SSSR. Ser. Mech. Zhidk. i Gasa. 4, 47–56.
Kader, B. A.: 1987. ‘Anisotropic Wind Velocity and Temperature Fluctuations in a Neutrally Stratified Atmospheric Surface Layer’, in L. R. Tsvang and B. A. Kader (eds.). Meteorological Researches 28, 26–35. Akad. Sci. USSR. Soviet Geophys. Committee (Transl. Fluid Mech.-Sov. Res. 19. No. 4, 104–114. 1990).
Kader, B. A.: 1988, ‘Three Layer Structures of an Unstably Stratified Atmospheric Surface Layer’, Izv. nauk SSSR, Ser. Fiz. Atmosf. i Okeana 24, 1235–1250.
Kader, B. A. and Perepelkin, V. G.: 1989, ‘Effect of Unstable Stratification on Wind and Temperature Profiles in the Surface Layer’, Izv. Akad. nauk SSSR, Ser. Fiz. Atmosf. i Okeana 25, 787–795.
Kader, B. A. and Perpelkin, V. G.: 1991, ‘Momentum and Heat Flux Estimation Via low Frequency Spectra Measurements’, Izv. Akad. nauk SSSR, Ser. Fiz. Atmosf. i Okeana 27, 1272–1276.
Kader, B. A. and Yaglom, A. M.: 1990, ‘Mean Fields and Fluctuations Moments in Unstably Stratified Turbulent Boundary Layers’, J. Fluid Mech. 212, 637–662.
Kader, B. A. and Yaglom, A. M.: 1991, ‘Spectra and Correlation Functions of Surface Layer Atmospheric Turbulence in Unstable Thermal Stratification’, in O. Métais and M. Lesieur (eds.). Turbulence and Coherent Structures, pp. 387–412, Kluwer Academic Publ., Dordrecht.
Khalsa, S. J. S. and Businger, J. A.: 1977, ‘The Drag Coefficient as Determined by the Dissipation Method and its Relation to Intermittent Convection in the Surface Layer’, Boundary-Layer Meteorol. 12, 273–297.
Monin, A. S. and Yaglom, A. M.: 1975, in J. L. Lumley (ed.). Statistical Fluid Mechanics, Vol 2, MIT Press. Cambridge, Mass.
Monji, N.: 1973, ‘Budgets of Turbulent Energy and Temperature Variance in the Transition Zone from Forced to Free Convection’, J. Meteorol. Soc. Japan II 15, 133–145.
Monji, N.: 1975, ‘Characteristics of the Horizontal Wind Fluctuations in the Surface Layer under Strong Convective Conditions’, J. Meteorol. Soc. Japan 53, 99–102.
Rayment, R. and Caughey, S. J.: 1977, ‘An Investigation of the Turbulence Equations in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 11, 15–26.
Schachter, G. E., Davidson, K. L. and Houlihan, T., Fairall, C. W.: 1981, ‘Measurements of the Rate of the Dissipation of Turbulent Kinetic Energy, ε. over the Ocean’, Boundary-Layer Meteorol. 20, 321–330.
Tsvang, L. R.: 1982, ‘Joint Field Experiment 1981 at Tsimlyansk. U.S.S.R.’, Boundary-Layer Meteorol. 22, 393–394.
Tsvang, L. R., Zubkovskii, S. L., Kader, B. A., Kallistratova, M. A., Foken, T., Gerstmann, V., Przadka, A., Pretel, Ya., Zeleny, Ya., Keder, J.: 1985, ‘International Turbulence Comparison Experiment (ITCE-81)’, Boundary-Layer Meteorol. 31, 325–348.
Wyngaard, J. C. and Coté, O. R.: 1971, ‘The Budget of Turbulent Kinetic Energy and Temperature Variance in the Atmospheric Surface Layer’, J. Atmos. Sci. 28, 190–201.
Yaglom, A. M.: 1981, ‘Laws of Small-Scale Turbulence in Atmosphere and Oceans’, Izv. Akad. nauk SSSR. Ser. Fiz. Atmosf. i Okeana 24, 1235–1250.
Zilitinkevich, S. S.: 1971, ‘On the Turbulence and Diffusion under Free Convection Conditions’, Izv. Akad. nauk SSSR. Ser. Fiz. Atmosf. i Okeana 7, 1263–1269.
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Kader, B.A. Determination of turbulent momentum and heat fluxes by spectral methods. Boundary-Layer Meteorol 61, 323–347 (1992). https://doi.org/10.1007/BF00119096
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DOI: https://doi.org/10.1007/BF00119096