Abstract
The atmospheric surface layer model of Lewellen and Teske (1973) is extended. Obvious discrepancies between model results and empirical data suggest the use of improved closure schemes for the non-diffusive parts of the pressure-velocity correlations in the Reynolds stress equations. Subsequently a time scale for the surface layer, which is based on vertical velocity fluctuations, is tested by means of the extended model. Finally the extended model is optimized by variation of the diffusion parameters, and an additional equation is introduced for the dissipation rate of Reynolds stresses. Investigations show that the normalized mean velocity and temperature gradients are verified by all model versions favorably, whereas the other turbulence variables % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaanaaabaGaam% yDaGqaciaa-DcacaWFGaGaamyDaiaa-DcaaaGaaiilaiaabccadaqd% aaqaaiabew8a1jaa-DcacaWFGaGaeqyXduNaa83jaaaacaqGSaGaae% iiamaanaaabaGaae4Daiaa-DcajaaqcaWFGaGccaqG3bGaa83jaaaa% caqGSaGaaeiiamaanaaabaGaamyDaiaa-DcajaaqcaWFGaGccaWFub% Gaa83jaaaaaaa!4DB4!\[\overline {u' u'} ,{\rm{ }}\overline {\upsilon ' \upsilon '} {\rm{, }}\overline {{\rm{w}}' {\rm{w}}'} {\rm{, }}\overline {u' T'} \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-rfaca% WFNaqcaaKaa8hiaOGaa8hvaiaa-Dcaaaa!3BB8!\[T' T'\] cannot be simulated so easily. Complications especially arise in unstable temperature stratification.
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References
McBean, G. A.: 1971, ‘The Variations of the Statistics of Wind, Temperature and Humidity Fluctuations with Stability’, Boundary-Layer Meteorol. 1, 438–457.
Blackadar, A. K.: 1974, ‘Experiments With Simplified Second-Moment Approximations for Use in Regional Scale Models’, Second Annual Progress Report, Select Research Group in Air Pollution Meteorology 1, 234–271; Environmental Protection Agency EPA-650/4–74–045-a.
Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux-Profile Relationships in the Atmospheric Surface Layer’, J. Atmos. Sci. 28, 181–189.
Donaldson, Coleman duP.: 1973, ‘Construction of A Dynamic Model of the Production of Atmospheric Turbulence and the Dispersal of Atmospheric Pollutants’, Workshop on Micrometeorology, Chapter 8, D. Haugen, (ed), American Meteorological Society, 313–392.
Hasse, L.: 1978, ‘Parameterization of the Dissipation Term in Second Order Closure Modelling of the Planetary Boundary Layer Under Conditions of Forced Convection’, Beiträge zur Physik der Atmosphäre 51, 166–173.
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.
Launder, B. E., Reece, G. J., and Rodi, W.: 1975, ‘Progress in the Development of a Reynolds-Stress Turbulence Closure’, J. Fluid Mech. 68, part 3, 537–566.
Lewellen, W. S. and Teske, M.: 1973, ‘Prediction of the Monin-Obukhov Similarity Functions from an Invariant Model of Turbulence’, J. Atmos. Sci. 30, 1340–1345.
Lumley, J. L. and Khajeh-Nouri, B.: 1974, ‘Computational modeling of turbulent transport’, Adv. Geophys., Academic Press, New York, 18A, 169–192.
Mellor, G. L.: 1973, ‘Analytic Prediction of the Properties of Stratified Planetary Surface Layers’, J. Atmos. Sci. 30, 1061–1069.
Monin, A. S. and Yaglom, A. M.: 1971, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 1, MIT Press, Cambridge, Mass, and London, England, 517–526 pp.
Panofsky, H. A., Tennekes, H., Lenschow, D. H. and Wyngaard, J. C.: 1977, ‘Characteristics of Turbulent Velocity Components in the Surface Layer Under Convective Conditions’, Boundary-Layer Meteorol. 11, 355–361.
Prenosil, T.: 1978, ‘Untersuchungen zur Bestimmung der universellen Funktionen der Monin-Obuchow Theorie aus einem Second-Order-Closure-Modell für die Prandtl-Schicht’, Diss. thesis, Universität Frankfurt/Main.
Rotta, J.: 1951, ‘Statistische Theorie nichthomogener Turbulenz, 1. Mitteilung’, Zeitschrift für Physik 129, 547–572.
Wesely, M. L.: 1974, ‘Magnitudes of Turbulent Fluctuations in the Atmospheric Surface Layer’, Proceedings of the Symposium on Atmos. Diffusion and Air Pollution, Santa Barbara/Cal., American Meteorological Society.
Wyngaard, J. C., Coté, O. R., and Izumi, Y.: 1971, ‘Local Free Convection, Similarity, and the Budgets of Shear Stress and Heat Flux’, J. Atmos. Sci. 28, 1171–1182.
Wyngaard, J. C., Coté O., R., and Rao, K. S.: 1974, ‘Modelling the Atmospheric Boundary Layer’, Adv. Geophys., Academic Press, New York, 18A, 193–211.
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Prenosil, T. Prediction of the Monin-Obukhov similarity functions from a second-order-closure model. Boundary-Layer Meteorol 17, 495–516 (1979). https://doi.org/10.1007/BF00118613
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DOI: https://doi.org/10.1007/BF00118613