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Second-order closure modeling of diffusion in the atmospheric boundary layer

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Abstract

A method for calculating turbulent diffusion in the planetary boundary layer is developed based on Donaldson's second-order closure approach. The resulting partial differential equation for the turbulent mass flux has a hyperbolic character for early times when the plume scale is small compared with the ambient turbulent scale, with a smooth transition to a parabolic, gradient-diffusion-type character when the plume scale is large. Calculations are compared with available estimates from the literature for different values of Rossby number and Richardson number in the ambient atmosphere. Comparison of model predictions with laboratory simulation of diffusion in a free convection, mixed layer is good, with the model able to predict the maximum concentration rising from the ground as observed.

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References

  • Csanady, G. T.: 1973, Turbulent Diffusion in the Environment, Reidel Publishing Co., Boston.

    Google Scholar 

  • Deardorff, J. W.: 1972, Numerical Investigation of Neutral and Unstable Planetary Boundary Layers, J. Atmospheric Sci. 29, 91–115.

    Google Scholar 

  • Deardorff, J. W. and Willis, G. E.: 1974, Physical Modeling of Diffusion in the Mixed Layer, Proc. Symp. Atm.Diffusion Air Pollution, Santa Barbara, Calif., September 1974, American Meteorological Society, Boston, 387–391.

    Google Scholar 

  • Donaldson, C. duP., Sullivan, R. D., and Rosenbaum, H.: 1972, A Theoretical Study of the Generation of Atmospheric Clear-Air Turbulence, AIAA J. 10, 162–170.

    Google Scholar 

  • Donaldson, C. duP.: 1973, Construction of a Dynamic Model of the Production of Atmospheric Turbulence and the Dispersal of Atmospheric Pollutants, in Workshop on Micrometeorology, American Meteorological Society, Boston, pp. 313–392.

    Google Scholar 

  • Lamb, R. G., Chen, W. H., and Seinfeld, J. H.: 1974, Numerico-Empirical Analyses of Atmospheric Diffusion Theories, Proc. Symp. Atm. Diffusion Air Pollution, Santa Barbara, Calif., September 1974, American Meteorological Society, Boston, 317–324.

    Google Scholar 

  • 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.

    Google Scholar 

  • Lewellen, W. S., Teske, M. and Donaldson, C. duP.: 1974a, ‘Turbulence Model of Diurnal Variations in the Planetary Boundary Layer’, Proc. 1974 Heat Transfer and Fluid Mechanics Institute, Stanford University Press, 301–319.

  • Lewellen, W. S., Teske, M., Contiliano, R. M., Hilst, Glenn R., and Donaldson, C. duP.: 1974b, Invariant Modeling of Turbulent Diffusion in the Planetary Boundary Layer, Environmental Protection Agency Report EPA-650J4-74-035.

  • Lewellen, W. S., Teske, M., and Donaldson, C. duP.: 1975, Examples of Variable Density Flows Computed by a Second-Order Closure Description of Turbulence, AIAA Paper No. 75-871 (to be published in the AIAA Journal).

  • Lumley, J. L. and Khajeh-Nouri, B.: 1974, Computational Modeling of Turbulent Transport, Advan. Geophys. 18A, Academic Press, New York, 169–192.

    Google Scholar 

  • Mellor, G. L.: 1973, Analytic Prediction of the Properties of Stratified Planetary Surface Layers, J. Atmospheric Sci. 30, 1061–1069.

    Google Scholar 

  • Mellor, G. L. and Yamada, T.: 1974, A Hierarchy of Turbulence Closure Models for Planetary Boundary Layers, J. Atmospheric Sci. 31, 1791–1806.

    Google Scholar 

  • Naot, D., Sbavit, A., and Wolfshtein, M.: 1973, Two-Point Correlation Model and the Redistribution of Reynolds Stress, Phys. Fluids 16, 738–743.

    Google Scholar 

  • Panofsky, H. A.: 1974, The Atmospheric Boundary Layer Below 150 Meters, Ann. Rev. Fluid Mech. Annual Reviews, Inc. Palo Alto, 147–177.

    Google Scholar 

  • Pasquill, F.: 1974, Atmospheric Diffusion, 2nd edition, John Wiley & Sons, Inc., New York.

    Google Scholar 

  • Wasko, P. E. and Moses, H.: 1959, Atmospheric Diffusion Studies, Argonne National Lab. Report No. 6049.

  • Willis, G. E. and Deardorff, J. W.: 1974, A Laboratory Model of the Unstable Planetary Boundary Layer, J. Atmospheric Sci. 31, 1297–1307.

    Google Scholar 

  • Wyngaard, J. C., Coté, O. R., and Rao, K. S.: 1974, Modeling the Atmospheric Layer, Advan. Geophys. 18A, Academic Press, New York, 193–212.

    Google Scholar 

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Authors and Affiliations

  1. Aeronautical Research Associates of Princeton, Inc., 50 Washington Road, Princeton, N.J., USA

    W. S. Lewellen & M. E. Teske

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  1. W. S. Lewellen
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  2. M. E. Teske
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This project has been funded in part with Federal funds from the Environmental Protection Agency under contract number EPA 68-02-1310.

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Lewellen, W.S., Teske, M.E. Second-order closure modeling of diffusion in the atmospheric boundary layer. Boundary-Layer Meteorol 10, 69–90 (1976). https://doi.org/10.1007/BF00218725

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  • DOI: https://doi.org/10.1007/BF00218725

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