Advertisement

Boundary-Layer Meteorology

, Volume 9, Issue 4, pp 381–390 | Cite as

Three-dimensional air pollutant modeling in the lower atmosphere

  • Gour-Tsyh Yeh
  • Chin-Hua Huang
Article

Abstract

A steady-state, three-dimensional turbulent diffusion equation describing the concentration distribution of an air pollutant from an elevated point source in the lower atmosphere is solved analytically. The same formulation can be used to obtain solutions from line, area or other kinds of sources. The solution is developed for the cases in which the velocity, vertical and lateral diffusivities are given by the power law. The model preserves the beauty of analytical solution without sacrificing much on the accuracy of approximating the velocity and eddy diffusivities. Methods of evaluating the parameters, which are required for the model applications, are discussed. Results indicate that the ratio of the plume width to the plume length increases with decreasing stability and with increasing source height. These consequences are in response to the variations of the size of eddies in the vertical direction.

Keywords

Point Source Vertical Direction Diffusion Equation Concentration Distribution Model Application 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brutsaert, W. and Yeh, G. T.: 1970a, ‘A Power Wind Law for Turbulent Transfer Computations’, Water Resources Res. 6, 1387–1391.Google Scholar
  2. Brutsaert, W. and Yeh, G. T.: 1970b, ‘Implication of a Type of Empirical Evaporation Formula for Lakes and Pans, Water Resources Res. 6, 1202–1208.Google Scholar
  3. 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.Google Scholar
  4. Calder, K. L.: 1949, ‘Eddy Diffusion and Evaporation in Flow Aerodynamically Smooth and Rough Surfaces: A Treatment Based on Laboratory Laws of Turbulent Flow with Special Reference to Conditions in the Lower Atmosphere’, Quart. J. Mech. Appl. Math. 2, 153–176.Google Scholar
  5. Carslaw, H. S. and Jaegar, J. C.: 1959, Conduction of Heat in Solids, Clarendon Press, Oxford.Google Scholar
  6. Davies, D. R.: 1947, ‘Turbulence and Diffusion in the Lower Atmosphere with Particular Reference to the Lateral Effect’, Proc. Roy. Soc. A190, 232–244.Google Scholar
  7. Davies, D. R.: 1950, ‘Three-Dimensional Turbulence and Evaporation in the Lower Atmosphere’, I and II’, Quart. J. Mech. Appl. Math. 3, 51–73.Google Scholar
  8. Dyer, A. J. and Hicks, B. B.: 1970, ‘Flux-Gradient Relationships in the Constant Flux Layer’, Quart. J. Roy. Meteorl. Soc. 96, 715–721.Google Scholar
  9. Ellison, T. H.: 1957, ‘Turbulent Transport of Heat and Momentum from an Infinite Rough Plane’, J. Fluid Mech. 2, 456–466.Google Scholar
  10. Frost, R.: 1946, ‘Turbulence and Diffusion in the Lower Atmosphere’, Proc. Roy. Soc. A186, 20–35.Google Scholar
  11. Gifford,Jr., F. A.: 1961, ‘Use of Routine Meteorological Observations for Estimating Atmospheric Dispersion’, Nuclear Safety 2, 47–51.Google Scholar
  12. Gifford Jr., F. A.: 1968, ‘An Outline of Theories of Diffusion in the Lower Layer of the Atmosphere’, in Meteorology and Atomic Energy - 1968, D. H. Slade (ed.), USAEC Report TID-24190, 65–116, July, 1968.Google Scholar
  13. Hanna, S. R.: 1974, ‘Fog and Drift Deposition from Evaporation Cooling Towers’, Nuclear Safety 15, 190–196.Google Scholar
  14. Kondo, J.: 1962, ‘Observations on Wind and Temperature Profiles near the Ground’, Science Reports, Tohoku University, Ser. 5, Geophys. 14, 41–56.Google Scholar
  15. Laikhtman, D. L. and Panomareva, S. M.: 1969, ‘On the Ratio of the Turbulent Transfer Coefficients for Heat and Momentum in the Surface Layer of the Atmosphere’, Izv. Atmos. Ocean Phys. 5, 1245–1250.Google Scholar
  16. Morse, P. M. and Feshbach, H.: 1953, Methods of Theoretical Physics, Part I, McGraw-Hill Book Company, Inc., New York, N.Y.Google Scholar
  17. Panofsky, H. A.: 1961, ‘An Alternative Derivation of the Diabatic Wind Profile’, Quart. J. Roy. Meteorol. Soc. 87, 109–110.Google Scholar
  18. Pruitt, W. O., Morgan, D. L., and Lourence, F. V.: 1973, ‘Momentum and Mass Transfer in the Surface Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 99, 370–386.Google Scholar
  19. Ragland, K. W. and Peirce, J. J.: 1975, ‘Boundary Layer Model for Air Pollutant Concentrations Due to Highway Traffic, J. Air Poll. Control Assoc. 25, 48–51.Google Scholar
  20. Smith, F. B.: 1957, ‘The Diffusion of Smoke from a Continuous Elevated Point Source into a Turbulent Atmosphere’, J. Fluid Mech. 2, 49–76.Google Scholar
  21. Sutton, O. G.: 1934, ‘Wind Structure and Evaporation in a Turbulent Medium’, Proc. Roy. Soc. A149, 701–702.Google Scholar
  22. Sutton, O. G.: 1953, Micrometeorology, McGraw-Hill, New York, 333 pp.Google Scholar
  23. Sutton, W. G. L.: 1943, ‘On the Equation of Diffusion in a Turbulent Medium’, Proc. Roy. Soc. A182, 48–75.Google Scholar
  24. Swinbank, W. C.: 1964, ‘The Exponential Wind Profile’, Quart. J. Roy. Meteorol. Soc. 90, 119–135.Google Scholar
  25. Swinbank, W. C.: 1968, ‘A Comparison Between Predictions of Dimensional Analysis for the Constant Flux Layer and Observations in Unstable Conditions’, Quart. J. Roy. Meteorol. Soc. 94, 460–467.Google Scholar
  26. Watson, G. N.: 1966, A Treatise on the Theory of Bessel Functions, Cambridge at the University Press, Cambridge, Great Britain.Google Scholar
  27. Webb, E. K.: 1970, ‘Profile Relationships: The Log-Linear Range and Extension to Strong Stability’, Quart. J. Roy. Meteorol. Soc. 96, 67–90.Google Scholar
  28. Yamamoto, G.: 1959, ‘Theory of Turbulent Transfer in Non-Neutral Conditions’, J. Meteorol. Soc. Japan, Ser. 2, 37, 60–70.Google Scholar
  29. Yamamoto, G. and Shimanuki, A.: 1960, ‘Numerical Solution of the Equation of Atmospheric Turbulent Diffusion, Science Reports, Tohoku University, Ser. 5, Geophys. 12, 24–35.Google Scholar
  30. Yeh, G. T. and Brutsaert, W.: 1970, ‘Perturbation Solution of an Equation of Atmospheric Turbulent Diffusion’, J. Geophys. Res. 75, 5173–5178.Google Scholar
  31. Yeh, G. T. and Brutsaert, W.: 1971, ‘A Solution for Simultaneous Turbulent Heat and Vapor Transfer Between a Water Body and the Atmosphere’, Boundary-Layer Meteorol. 2, 64–68.Google Scholar
  32. Yeh, G. T.: 1975, ‘Green's Functions of a Diffusion Equation’, J. Geophys. Res. Letters 2, 293–296.Google Scholar
  33. Yih, C. S.: 1952a, ‘On a Differential Equational on Atmospheric Diffusion’, Trans. Amer. Geophys. Union 33, 8–12.Google Scholar
  34. Yih, C. S.: 1952b, ‘Similarity Solution of a Specialized Diffusion Equation’, Trans. Amer. Geophys. Union 33, 356–360.Google Scholar

Copyright information

© D. Reidel Publishing Company 1975

Authors and Affiliations

  • Gour-Tsyh Yeh
    • 1
  • Chin-Hua Huang
    • 1
  1. 1.Stone and Webster Engineering CorporationBostonUSA

Personalised recommendations