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Incorporation of internal fluctuations in a meandering plume model of concentration fluctuations

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Abstract

A meandering plume model that explicitly incorporates the effects of small-scale structure in the instantaneous plume has been formulated. The model requires the specification of two physically based input parameters; namely, the meander ratio,M, which is dependent on the ratio of the meandering plume dispersion to the instantaneous relative plume dispersion and, a relative in-plume fluctuation measure,k, that is related inversely to the fluctuation intensity in relative coordinates. Simple analytical expressions for crosswind profiles of the higher moments (including the important shape parameters such as fluctuation intensity, skewness, and kurtosis) and for the concentration pdf have been derived from the model. The model has been tested against some field data sets, indicating that it can reproduce many key aspects of the observed behavior of concentration fluctuations, particularly with respect to modeling the change in shape of the concentration pdf in the crosswind direction.

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Abbreviations

C :

Mean concentration in absolute coordinates

C r :

Mean concentration in relative coordinates

C0 :

Centerline mean concentration in absolute coordinates

C r,0 :

Centerline mean concentration in relative coordinates

f :

Probability density function of concentration in absolute coordinates

f c :

Probability density function of plume centroid position

f r :

Probability density function of concentration in relative coordinates

i :

Absolute concentration fluctuation intensity (standard deviation to mean ratio)

i r :

Relative concentration fluctuation intensity (standard deviation to mean ratio)

k :

Relative in-plume fluctuation measure:k=1/i 2r

K :

Concentration fluctuation kurtosis

M :

Meander ratio of meandering plume variance to relative plume variance

S :

Concentration fluctuation skewness

x :

Downwind distance from source

y :

Crosswind distance from mean-plume centerline

z :

Vertical distance above ground

Θ:

Instantaneous (random) concentration

Θ:

Crosswind dispersion ofnth concentration moment about zero

σ ny :

Mean-plume crosswind (absolute) dispersion

σ y :

Plume centroid (meandering) dispersion in crosswind direction

σ y,c :

Instantaneous plume crosswind (relative) dispersion

ϕ:

Normalized mean concentration in absolute coordinates:C/C 0

χ:

Particular value taken on by instantaneous concentration, Θ

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Authors and Affiliations

  1. Defence Research Establishment Suffield, Medicine Hat, Box 4000, T1A 8K6, Alberta, Canada

    Eugene Yee

  2. Kosteniuk Consulting Ltd., 1301 Cumberland Ave. S., S7H 2L9, Saskatoon, Saskatchewan, Canada

    R. Chan & P. R. Kosteniuk

  3. S & J Engineering, Inc., 3447 Kennedy Rd., Suite 6, M1V 3S1, Scarborough, Ontario, Canada

    G. M. Chandler

  4. Meteorology Division, Material Test Directorate, U.S. Army Dugway Proving Ground, 84022-5000, Dugway, Utah, USA

    C. A. Biltoft & J. F. Bowers

Authors
  1. Eugene Yee
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  2. R. Chan
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  3. P. R. Kosteniuk
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  4. G. M. Chandler
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  5. C. A. Biltoft
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  6. J. F. Bowers
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Yee, E., Chan, R., Kosteniuk, P.R. et al. Incorporation of internal fluctuations in a meandering plume model of concentration fluctuations. Boundary-Layer Meteorol 67, 11–39 (1994). https://doi.org/10.1007/BF00705506

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  • DOI: https://doi.org/10.1007/BF00705506

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