Boundary-Layer Meteorology

, Volume 16, Issue 3, pp 395–408 | Cite as

A Similarity Model for Maximum Ground-Level Concentration in a Freely Convective Atmospheric Boundary Layer

  • Bryan R. Kerman


A model of buoyancy- and momentum-driven industrial plumes in a freely convective boundary layer is proposed. The development combines the Lagrangian similarity models of Yaglom for non-buoyant releases in the convective surface layer with the Scorer similarity model for industrial plumes. Constraints on the validity of the extension of Yaglom’s model to the entire convective planetary boundary layer, arrived at by consideration of Batchelor’s formulation for diffusion in an inertial subrange, are often met in practice.

The resulting formulation applies to an interval of time in which the entrainment of the atmosphere by the plume is balanced by the entrainment of the plume by the atmosphere. It is argued that during this interval, both maximum plume rise and ground contact are achieved. Further examination of the physical interrelationship with the Csanady-Briggs formulation serves to consolidate the model hypotheses, as well as to simplify the derivation of maximum ground-level concentrations. Experimental evidence is presented for the validity of the model, based on Moore’s published data.


Surface Heat Flux Convective Boundary Layer Ambient Turbulence Entrainment Rate Inertial Subrange 
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  1. Batchelor, G. K.: 1950, ‘The Application of the Similarity Theory of Turbulence to Atmospheric Diffusion’, Quart. J. Roy. Meteorol. Soc. 76, 133–146.CrossRefGoogle Scholar
  2. Briggs, G. A.: 1972, ‘Diffusion of Chimney Plumes in Neutral and Stable Surroundings’, Atmos. Environ. 6, 507–510.CrossRefGoogle Scholar
  3. Briggs, G. A.: 1975, ‘Plume Rise Predictions’. In: Lectures on Air Pollution and Environmental Impact Analysis, (Ed. D. A. Haugen), American Meteorological Scoeity), Boston, Mass.Google Scholar
  4. Csanady, G. T.: 1965, ‘The Buoyant Motion Within a Hot Gas Plume in a Horizontal Wind’, J. Fluid Mech. 22, 225–239.CrossRefGoogle Scholar
  5. Deardorff, J. W. and G. E. Willis: 1975, ‘A Parameterization of Diffusion Into the Mixed Layer’, J. Appl. Meteorol. 14, 1451–1458.CrossRefGoogle Scholar
  6. Hanna, S. R., G. A. Briggs, J. W. Deardorff, B. A. Egan, F. A. Gifford, and F. Pasquill: 1977, ‘AMS Workshop on Stability Classification Schemes and Sigma Curves — Summary and Recommendations’, Bull. Am. Meteorol. Soc. 58, 1305–1309.Google Scholar
  7. Kaimal, J. C., J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, S. J. Caughey, and C. J. Readings: 1976, ‘Turbulence Structure in the Convective Boundary Layer’, J. Atmos. Sci. 33, 2152–2169.CrossRefGoogle Scholar
  8. Kerman, B. R.: 1978, ‘A Proposed Method for Estimating Diffusion in a Freely Convective Boundary Layer by Acoustic Sounding’, Atmos. Environ. 12, 1827–1838.CrossRefGoogle Scholar
  9. Monin, A. S.: 1959, ‘Smoke Propagation in the Surface Layer of the Atmosphere’, Adv. Geophys. 6, 331–341.CrossRefGoogle Scholar
  10. Moore, D. J.: 1969, ‘The Distribution of Surface Concentrations of Sulphur Dioxide emitted from Tall Chimneys’, Phil. Trans. Roy. Soc., Lond. 265, 245–259.CrossRefGoogle Scholar
  11. Moore, D. J.: 1974, ‘Observed and Calculated Magnitudes and Distances of Maximum Ground Level Concentrations of Gaseous Effluent Material Downwind of Tall Stack’, Adv. Geophys. 18, 201–221.CrossRefGoogle Scholar
  12. Panofsky, H. A., H. Tennekes, D. H. Lenschow, and J. C. Wyngaard: 1977, ‘The Characteristics of Turbulent Velocity Components in the Surface Layer Under Convective Conditions’, Boundary-Layer Meteorol. 11, 355–361.CrossRefGoogle Scholar
  13. Pasquill, F.: 1976, ‘Atmospheric Dispersion Parameters in Gaussian Plume Modelling. Part II. Possible Requirements for Change in the Turner Workbook Values’, Environmental Protection Agency Report EPA-600/4-76-030b.Google Scholar
  14. Scorer, R. S.: 1959, ‘The Behaviour of Chimney Plumes’, Int. J. Air Pollut. 1, 198–220.Google Scholar
  15. Tennekes, H.: 1973, ‘Similarity Laws and Scale Relations in Planetary Boundary Layers’. Workshop on Micrometeorology, D. A. Haugen, Ed., Boston, Mass., Amer. Meteorol. Soc.Google Scholar
  16. Turner, D. B.: 1970, Workbook of Atmospheric Dispersion Estimates, Environmental Protection Agency (U.S.A.).Google Scholar
  17. Weil, J.: 1977, ‘Evaluation of the Gaussian Plume Model at Maryland Power Plants’. Paper presented at AMS-APCS Joint Conference on Applications of Air Pollution Meteorology, Salt Lake City, Utah.Google Scholar
  18. Yaglom, A. M.: 1972, ‘Turbulent Diffusion in the Surface Layer of the Atmosphere’, Atmos. and Oceanic Phys. 8, 333–340.Google Scholar
  19. Zeman, O. and H. Tennekes: 1977, ‘Parameterization of the Turbulent Energy Budget at the Top of the Daytime Atmospheric Boundary Layer’, J. Atmos. Sci. 34, 111–123.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1979

Authors and Affiliations

  • Bryan R. Kerman
    • 1
  1. 1.Atmospheric Environment ServiceDownsviewCanada

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