Abstract
This paper presents a new model of concentration fluctuations for neutrally buoyant gas clouds dispersing in a wind tunnel. It is derived from a series of exact results, which apply in the hypothetical case when there is no molecular diffusion, coupled with a probability density function model previously used to describe steady releases of contaminant. A simple self-similar relationship between the evolution of the concentration intensity and mean is established. As a first step the time independent variant of the model, applicable to a continuous plume, is tested against some previously published experimental data for steady wind-tunnel releases. Comparisons of experimental results and model predictions at different downwind positions, heights and source geometry are presented. Then, the results for the time dependent model, applicable to instantaneous releases, are discussed. The experimental evidence presented here supports the self-similar relationship established earlier. The implications for modelling higher moments of concentration and the fixed point probability density function are investigated.
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Batchelor, G. K.: 1952a, ‘The Effect of Homogeneous Turbulence on Material Lines and Surfaces’, Proc. Roy. Soc. A213, 349–366.
Batchelor, G. K.: 1952b, ‘Diffusion in a Field of Homogeneous Turbulence II. The Relative Motion of Particles’, Proc. Camb. Philo. Soc. 48, 345–362.
Batchelor, G. K.: 1959, ‘Small-Scale Variation of Convected Quantities Like Temperature in Turbulent Fluid. Part 1. General Discussion and the Case of Small Conductivity’, J. Fluid Mech. 5, 113–133.
Borgas, M. S. and Sawford, B. L.: 1996, ‘Molecular Diffusion and Viscous Effects on Concentration Statistics in Grid Turbulence’, J. Fluid Mech. 324, 25–54.
Carn, K. K. and Chatwin, P. C.: 1985, ‘Variability and Heavy Gas Dispersion’, J. Hazardous Materials 11, 281–300.
Chatwin, P. C. and Robinson, C.: 1997, ‘The Moments of the PDF of Concentration for Gas Clouds in the Presence of Fences’, Il Nuovo Cimento 20, 361–383.
Chatwin, P. C. and Sullivan, P. J.: 1990, ‘A Simple and Unifying Physical Interpretation of Scalar Fluctuation Measurements from Many Turbulent Shear Flows’, J. Fluid Mech. 212, 533–556.
Chatwin, P. C., Lewis, D. M., and Sullivan, P. J.: 1995, ‘Turbulent Dispersion and the Beta Distribution’, Environmetrics 6, 395–402.
Deardorff, J. W. and Willis, G. E.: 1984, ‘Groundlevel Concentration Fluctuations from Buoyant and a Non-Buoyant Source within a Laboratory Convectively Mixed Layer’, Atmos. Environ. 18, 1297–1309.
Durbin, P. A.: 1980, ‘A Stochastic Model of Two-Particle Dispersion and Concentration Fluctuations in Homogenous Turbulence’, J. Fluid Mech. 100, 279–302.
Fackrell, J. E.: 1980, ‘A Flame Ionization Detector for Measuring Fluctuating Concentration’, J. Phys. E, Sci. Instrum. 13, 888–893.
Fackrell, J. E. and Robins, A. G.: 1982, ‘Concentration Fluctuations and Fluxes in Plumes from Point Sources in a Turbulent Boundary-Layer’, J. Fluid Mech. 117, 1–26.
Hall, D. J., Waters, R. A., Marsland, G.W., Upton, S. L., and Emmott, M. A.: 1991, ‘Repeat Variability in Instantaneously Released Heavy Gas Clouds — Some Wind Tunnel Experiments’, Technical Report LR 804(PA), Warren Spring Laboratory, Dept. of Trade and Industry, U.K.
Hanna, S. R.: 1984, ‘The Exponential pdf and Concentration Fluctuations in Smoke Plumes’, Boundary-Layer Meteorol. 29, 361–375.
Hanna, S. R.: 1986, ‘Spectra of Concentration Fluctuations: The Two Time Scales of a Meandering Plume’, Atmos. Environ. 20, 1131–1137.
Lewellen, W. S. and Sykes, R. I.: 1986, ‘Analysis of Concentration Fluctuations from Lidar Observations of Atmospheric Plumes’, J. Climate Appl. Meteorol. 25, 1145–1154.
Lewis, D. M. and Chatwin, P. C.: 1995a, ‘A New Model pdf for Contaminants Dispersing in the Atmosphere’, Environmetrics 6, 583–593.
Lewis, D. M. and Chatwin, P. C.: 1995b, ‘The Treatment of Atmospheric Dispersion Data in the Presence of Noise and Baseline Drift’, Boundary-Layer Meteorol. 72, 53–85.
Lewis, D. M. and Chatwin, P. C.: 1997, ‘A Three Parameter pdf for the Concentration of an Atmospheric Pollutant’, J. Appl. Meteorol. 36, 1064–1075.
Lewis, D. M., Chatwin, P. C., and Mole, N.: 1997, ‘Investigation of the Collapse of the Skewness and Kurtosis Exhibited in Atmospheric Dispersion Data’, Il Nuovo Cimento 20, 385–398.
McQuaid, J.: 1985, ‘Design of the Thorney Island Continuous Release Trials’, J. Hazardous Materials 16, 1–8.
Mole, N. and Jones, C. D.: 1994, ‘Concentration Fluctuation Data from Dispersion Experiments Carried out in Stable and Unstable Conditions’, Boundary-Layer Meteorol. 67, 41–74.
Mole, N. and Clarke, E. D.: 1995, ‘Relationships between Higher Moments of Concentration and of Dose in Turbulent Dispersion’, Boundary-Layer Meteorol. 73, 35–52.
Monin, A. S. and Yaglom, A. M.: 1971, in J. L. Lumley (ed.), Statistical Fluid Mechanics, Vol. 1, MIT Press, MA, 769 pp.
Mylne, K. R. and Mason, P. J.: 1991, ‘Concentration Fluctuation Measurements in a Dispersing Plume at a Range of up to 1000 m’, Quart. J. Roy. Meteorol. Soc. 117, 177–206.
Nielsen, M., Bengtsson, R., Jones, C. D., Nyrén, K., Ott, S., and Ride, D. J.: 1994, Design of the FLADIS Field Experiments with Dispersion of Liquefied Ammonia, Risø-R-755 (EN), 35 pp. (Available from the Risø National Laboratory, Roskilde, Denmark.)
Richardson, L. F.: 1926, ‘Atmospheric Diffusion Shown on a Distance-Neighbour Graph’, Proc. Roy. Soc. A 110, 709–737.
Robinson, C.: 1996, ‘An Overview of Gas Dispersion with Fences’, Report No. TR/01/96, School of Mathematics and Statistics, University of Sheffield.
Sawford, B. L. and Hunt, J. C. R.: 1986, ‘Effects of Turbulence Structure, Molecular Diffusion and Source Size on Scalar Fluctuations in Homogenous Turbulence’, J. Fluid Mech. 165, 373–400.
Sullivan, P. J.: 1990, ‘The Modelling of Contaminant Diffusion’, Environmetrics 1, 163–177.
Sykes, R. I., Lewellen, W. S., and Parker, S. F.: 1984, ‘A Turbulent-Transport Model for Concentration Fluctuations and Fluxes’, J. Fluid Mech. 139, 193–218.
Sykes, R. I., Parker, S. F., Henn, D. S., and Lewellen, W. S.: 1993, ‘Numerical Simulation of ANATEX Tracer Data Using a Turbulence Closure Model for Long-Range Dispersion’, J. Appl. Meteorol. 32, 929–949.
Thomson, D. J.: 1990, ‘A Stochastic Model for the Motion of Particle Pairs in Isotropic High Reynolds Number Turbulence, and its Application to the Problem of Concentration Variance’, J. Fluid Mech. 210, 113–153.
Wilson, D. J. and Netterville, D. D. J.: 1981, ‘A Fast Response Heated-Element Concentration Detector for Wind Tunnel Applications’, J. Wind Engineer. Indust. Aerodyn. 7, 55–64.
Ye, H.: 1995, A New Statistic for the Contaminant Dilution Process in Turbulent Flows, PhD Thesis, University of Western Ontario, London, Canada.
Yee, E., Kosteniuk, P. R., Chandler, G.M., Biltoft, C. A., and Bowers, J. F.: 1993, ‘Statistical Characteristics of Concentration Fluctuations in Dispersing Plumes in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 65, 69–109.
Yee, E., Chan, R., Kosteniuk, P. R., Chandler, G. M., Biltoft, C. A., and Bowers, J. F.: 1994, ‘Experimental Measurements of Concentration Fluctuations and Scales in a Dispersing Plume in the Atmospheric Surface Layer Obtained Using a Very Fast Response Concentration Detector’, J. Appl. Meteorol. 33, 996–1016.
Yee, E. and Chan, R.: 1997, ‘A Simple Model for the Probability Density Function of Concentration Fluctuations in Atmospheric Plumes’, Atmos. Environ. 31, 991–1002.
Zimmerman, W. B. and Chatwin, P. C.: 1995, ‘Fluctuations in Dense Gas Concentrations Measured in a Wind-Tunnel’, Boundary-Layer Meteorol. 75, 321–352.
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Lewis, D.M. A Simple Model of Concentration Fluctuations in Neutrally Buoyant Clouds. Boundary-Layer Meteorology 90, 117–153 (1999). https://doi.org/10.1023/A:1001791306018
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DOI: https://doi.org/10.1023/A:1001791306018