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Disagreements between gradient-diffusion and Lagrangian stochastic dispersion models, even for sources near the ground

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Abstract

It is well known that if turbulent mass convection is modelled as diffusion, errors result unless trajectories from the source (ath) to the point of observation (z p ) comprise many statistically-independent segments (Taylor, 1921). We show that this is not guaranteed merely by the Lagrangian timescale (τ) at the source being small (e.g., source at ground), but that a better criterion ist≫max[τ(h), τ(z p )], wheret is a typical travel time toz p .

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References

  • Abramowitz, M. and Stegun, I. A.: 1970,Handbook of Mathematical Functions, Dover.

  • Barad, M. L.: 1958, ‘Project Prairie Grass, a Field Program in Diffusion (Vol. II)’,Geophysical Research Papers No. 59, Air Force Cambridge Research Center TR-58-235(II). National Technical Information Service NTIS AD-152573.

  • Durbin, P. A.: 1983, ‘Stochastic Differential Equations and Turbulent Dispersion’, NASA reference publication 1103.

  • Gradshteyn, I. S. and Ryzhik, I. M.: 1980,Table of Integrals, Series, and Products, Academic Press.

  • Raupach, M. R. and Legg, B. J.: 1983, ‘Turbulent Dispersion from an Elevated Line Source: Measurements of Wind-Concentration Moments and Budgets’,J. Fluid Mech. 136, 111–137.

    Google Scholar 

  • Sullivan, P. J. and Yip, H.: 1989, ‘Near Source Dispersion of Contaminant from an Elevated Line-Source’,J. Appl. Math. Phys (ZAMP) 40, 297–299.

    Google Scholar 

  • Taylor, G. I.: 1921, ‘Diffusion by Continuous Movements’,Proc. London Math. Soc. Series 2,20, 196–212.

    Google Scholar 

  • Thomson, D. J.: 1987, ‘Criteria for the Selection of Stochastic Models of Particle Trajectories in Turbulent Flows’,J. Fluid Mech. 180, 529–556.

    Google Scholar 

  • Wilson, J. D.: 1982, ‘An Approximate Analytical Solution to the Diffusion Equation for Short Range Dispersion from a Continuous Ground-Level Source’,Boundary-Layer Meteorol. 23, 85–103.

    Google Scholar 

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Authors and Affiliations

  1. University of Alberta, T6G 2H4, Edmonton, Alberta, Canada

    C. J. Mooney & J. D. Wilson

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  1. C. J. Mooney
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  2. J. D. Wilson
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Mooney, C.J., Wilson, J.D. Disagreements between gradient-diffusion and Lagrangian stochastic dispersion models, even for sources near the ground. Boundary-Layer Meteorol 64, 291–296 (1993). https://doi.org/10.1007/BF00708967

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  • DOI: https://doi.org/10.1007/BF00708967

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