# Dispersion of a Passive Scalar Fluctuating Plume in a Turbulent Boundary Layer. Part I: Velocity and Concentration Measurements

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## Abstract

The prediction of the probability density function (PDF) of a pollutant concentration within atmospheric flows is of primary importance in estimating the hazard related to accidental releases of toxic or flammable substances and their effects on human health. This need motivates studies devoted to the characterization of concentration statistics of pollutants dispersion in the lower atmosphere, and their dependence on the parameters controlling their emissions. As is known from previous experimental results, concentration fluctuations are significantly influenced by the diameter of the source and its elevation. In this study, we aim to further investigate the dependence of the dispersion process on the source configuration, including source size, elevation and emission velocity. To that end we study experimentally the influence of these parameters on the statistics of the concentration of a passive scalar, measured at several distances downwind of the source. We analyze the spatial distribution of the first four moments of the concentration PDFs, with a focus on the variance, its dissipation and production and its spectral density. The information provided by the dataset, completed by estimates of the intermittency factors, allow us to discuss the role of the main mechanisms controlling the scalar dispersion and their link to the form of the PDF. The latter is shown to be very well approximated by a Gamma distribution, irrespective of the emission conditions and the distance from the source. Concentration measurements are complemented by a detailed description of the velocity statistics, including direct estimates of the Eulerian integral length scales from two-point correlations, a measurement that has been rarely presented to date.

## Keywords

Atmospheric turbulence Eulerian integral length scale Gamma distribution Intermittency Pollutant dispersion Wind-tunnel experiments## Notes

### Acknowledgments

The authors would like to express their gratitude to D. Cane for his support in artworks and to O. Marsden for carefully reading the manuscript and providing a critical review of its content.

## References

- Amicarelli A, Salizzoni P, Leuzzi G, Monti P, Soulhac L, Cierco FX, Leboeuf F (2012) Sensitivity analysis of a concentration fluctuation model to dissipation rate estimates. Int J Environ Pollut 48:164–173CrossRefGoogle Scholar
- Andronopoulos S, Grigoriadis D, Robins A, Venetsanos A, Rafailidis S, Bartzis J (2002) Three-dimensional modeling of concentration fluctuations in complicated geometry. Environ Fluid Mech 1:415–440CrossRefGoogle Scholar
- Arya PS (1999) Air pollution meteorology and dispersion. Oxford University Press, UK, 310 ppGoogle Scholar
- Bergametti G, Dutot AL, Buat-Ménard P, Losno R, Remoudaki E (1989) Seasonal variability of the elemental composition of atmospheric aerosol particles over the northwestern Mediterranean. Tellus 41B:353–361CrossRefGoogle Scholar
- Bewley GP, Chang K, Bodenschatz E (2012) On integral length scales in anisotropic turbulence. Phys Fluids 24:061702CrossRefGoogle Scholar
- Carlotti P, Drobinski P (2004) Length scales in wall-bounded high-Reynolds-number turbulence. J Fluid Mech 516:239–264CrossRefGoogle Scholar
- Cassiani M, Franzese P, Giostra U (2005a) A PDF micromixing model of dispersion for atmospheric flow. Part I: development of the model, application to homogeneous turbulence and neutral boundary layer. Atmos Environ 39:1457–1469CrossRefGoogle Scholar
- Cassiani M, Franzese P, Giostra U (2005b) A PDF micromixing model of dispersion for atmospheric flow. Part II: application to convective boundary layer. Atmos Environ 39:1471–1479CrossRefGoogle Scholar
- Chatwin PC, Sullivan PJ (1990) A simple and unifying physical interpretation of scalar fluctuations measurements from many turbulent shear flows. J Fluid Mech 212:533–556CrossRefGoogle Scholar
- Du S, Sawford BL, Wilson JD (1995) Estimation of the Kolmogorov constant for the Lagrangian structure function, using a second order Lagrangian model of grid turbulence. Phys Fluids 7:3083–3090CrossRefGoogle Scholar
- Duplat J, Villermaux E (2008) Mixing by random stirring in confined mixtures. J Fluid Mech 617:51–86CrossRefGoogle Scholar
- Durbin PA (1980) A stochastic model of two-particles dispersion and concentration fluctuations in homogeneous turbulence. J Fluid Mech 100:279–302CrossRefGoogle Scholar
- Fackrell JE (1980) A flame ionisation detector for measuring fluctuating concentration. J Phys E Sci Instrum 13:888–893CrossRefGoogle Scholar
- Fackrell JE, Robins AG (1982a) Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer. J Fluid Mech 117:1–26CrossRefGoogle Scholar
- Fackrell JE, Robins AG (1982b) The effects of source size on concentration fluctuations in plumes. Boundary-Layer Meteorol 22:335–350CrossRefGoogle Scholar
- Franzese P (2003) Lagrangian stochastic modeling of a fluctuating plume in the convective boundary layer. Atmos Environ 37:1691–1701CrossRefGoogle Scholar
- Frisch U (1995) Turbulence. Cambridge University Press, UK, 296 ppGoogle Scholar
- Gifford F (1959) Statistical properties of a fluctuating plume dispersion model. Adv Geophys 6:117–137CrossRefGoogle Scholar
- Hall DJ, Emmott MA (1991) Avoiding aerosol sampling problems in fast response flame ionisation detectors. Exp Fluids 10:237–240CrossRefGoogle Scholar
- Hilderman T, Wilson DJ (2007) Predicting plume meandering and averaging time effects on mean an fluctuating concentrations in atmospheric dispersion simulated in a water channel. Boundary-Layer Meteorol 122:535–575CrossRefGoogle Scholar
- Hinze JO (1975) Turbulence. McGraw-Hill, New York, 790 ppGoogle Scholar
- Jackson PS (1981) On the displacement height in the logarithmic velocity profile. J Fluid Mech 111:15–25CrossRefGoogle Scholar
- Jiménez J (2004) Turbulent flows over rough walls. Annu Rev Fluid Mech 36:173–196CrossRefGoogle Scholar
- Jorgensen FE (2002) How to measure turbulence with hot-wire anemometers—a practical guide. Technical report, Dantec DynamicsGoogle Scholar
- Kaimal JC, Wyngaard JC, Izumi J, Coté OR (1972) Spectral characteristics of surface-layer turbulence. Q J R Meteorol Soc 98:563–589CrossRefGoogle Scholar
- Klein PM, Young DT (2011) Concentration fluctuations in a downtown urban area. Part I: analysis of Joint Urban 2003 full-scale fast-response measurements. Environ Fluid Mech 11:23–42CrossRefGoogle Scholar
- Klein PM, Leitl B, Schatzmann M (2011) Concentration fluctuations in a downtown urban area. Part II: analysis of Joint Urban 2003 wind tunnel measurements. Environ Fluid Mech 11:43–60CrossRefGoogle Scholar
- Krogstad PA, Antonia RA (1994) Structure of turbulent boundary layers on smooth and rough walls. J Fluid Mech 277:1–21CrossRefGoogle Scholar
- Leuzzi G, Amicarelli A, Monti P, Thomson DJ (2012) A 3D Lagrangian micromixing dispersion model LAGFLUM and its validation with a wind tunnel experiment. Atmos Environ 54:117–126CrossRefGoogle Scholar
- Lewis DM, Chatwin PC, Mole N (1997) Investigation of the collapse of the skewness and kurtosis exhibited in atmospheric dispersion data. Il Nuovo Cimento 20 C:385–398Google Scholar
- Lien R, D’Asaro EA (2002) The Kolmogorov constant for the Lagrangian velocity spectrum structure function. Phys Fluids 14:4456–4459CrossRefGoogle Scholar
- Luhar AK, Hibberd MF, Borgas MS (2000) A skewed meandering plume model for concentration statistics in the convective boundary layer. Atmos Environ 34:3599–3616CrossRefGoogle Scholar
- Marro M, Nironi C, Salizzoni P, Soulhac L (2015) Dispersion of a passive scalar from a point source in a turbulent boundary layer. Part II: analytical modelling. Boundary-Layer Meteorol. doi: 10.1007/s10546-015-0041-9
- Milliez M, Carissimo B (2008) Computational fluid dynamical modelling of concentration fluctuations in an idealized urban area. Boundary-Layer Meteorol 127(2):241–259CrossRefGoogle Scholar
- Mole N, Clarke E (1995) Relationships between higher moments of concentration and of dose in turbulent dispersion. Boundary-Layer Meteorol 73:35–52CrossRefGoogle Scholar
- Nironi C (2013) Concentration fluctuations of a passive scalar in a turbulent boundary layer. PhD Thesis, Ecole Centrale de LyonGoogle Scholar
- Philips DA, Rossi R, Iaccarino G (2013) Large-eddy simulation of passive scalar dispersion in an urban-like canopy. J Fluid Mech 723:404–428CrossRefGoogle Scholar
- Pope SB (2000) Turbulent flows. Cambridge University Press, UK, 771 ppGoogle Scholar
- Postma JV, Wilson DJ, Yee E (2011) Comparing two implementations of a micromixing model. Part I: wall shear-layer flows. Boundary-Layer Meteorol 140:207–224CrossRefGoogle Scholar
- Raupach M, Coppin P (1983) Turbulent dispersion from an elevated line source: measurements of wind concentration moments and budgets. J Fluid Mech 136:111–137CrossRefGoogle Scholar
- Raupach MR, Thom AS, Edwards I (1980) A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces. Boundary-Layer Meteorol 18:373–397CrossRefGoogle Scholar
- Rizza U, Mangia C, Carvalho JC, Anfossi D (2006) Estimation of the Lagrangian velocity structure function constant \(C_0\) by large-eddy simulation. Boundary-Layer Meteorol 120:25–37CrossRefGoogle Scholar
- Salizzoni P, Soulhac L, Mejean P, Perkins R (2008) Influence of a two scale surface roughness on a turbulent boundary layer. Boundary-Layer Meterorol 127(1):97–110CrossRefGoogle Scholar
- Sawford B (2004) Micro-mixing modelling of scalar fluctuations for plumes in homogeneous turbulence. Flow Turbul Combust 72:133–160CrossRefGoogle Scholar
- Sawford B, Hunt JCR (1986) Effects of turbulence structure, molecular diffusion and source size on scalar fluctuations in homogeneous turbulence. J Fluid Mech 165:373–400CrossRefGoogle Scholar
- Sawford B, Stapountzis H (1986) Concentration fluctuations according to fluctuating plume models in one and two dimensions. Boundary-Layer Meteorol 37:89–105CrossRefGoogle Scholar
- Schopflocher TP, Sullivan PJ (2005) The relationship between skewness and kurtosis of a diffusing scalar. Boundary-Layer Meteorol 115:341–358CrossRefGoogle Scholar
- Sykes RI, Lewellen WS, Parker SF (1984) A turbulent-transport model for concentration fluctuations and fluxes. J Fluid Mech 139:193–218CrossRefGoogle Scholar
- Takimoto H, Inagaki A, Kanda M, Sato A, Michioka T (2013) Length-scale similarity of turbulent organised structures over surfaces with different roughness types. Boundary-Layer Meteorol 147:217–236CrossRefGoogle Scholar
- Taylor G (1921) Diffusion by continuous movements. Proc Lond Math Soc 20:196–211Google Scholar
- Tennekes H (1982) Similarity relations, scaling laws and spectral dynamics. In: Niewstadt F, Van Dop H (eds) Atmospheric turbulence and air pollution modelling. D. Reidel Publishing Company, Dordrecht, pp 37–68Google Scholar
- Tennekes H, Lumley JL (1972) A first course in turbulence. MIT Press, Cambridge, MA, 300 ppGoogle Scholar
- Thom AS (1971) Momentum absorption by vegetation. Q J R Meteorol Soc 97:414–428CrossRefGoogle Scholar
- Tritton DJ (1988) Physical fluid dynamics. Oxford Science Publications, UK, 519 ppGoogle Scholar
- Villermaux E, Duplat J (2003) Mixing as an aggregation process. Phys Rev Lett 91:184501CrossRefGoogle Scholar
- Vinkovic I, Aguirre C, Simoëns S (2006) Large-eddy simulation and Lagrangian stochastic modeling of passive scalar dispersion in a turbulent boundary layer. J Turbul 7:1–14CrossRefGoogle Scholar
- Xie Z, Hayden P, Voke P, Robins A (2004) Large-eddy simulation of dispersion: comparison between elevated and ground-level sources. J Turbul 5:1–16CrossRefGoogle Scholar
- Yee E (2009) Probability law of concentration in plumes dispersing in an urban area. Environ Fluid Mech 9:389–407CrossRefGoogle Scholar
- Yee E, Biltof CA (2004) Concentration fluctuation measurements in a plume dispersing through a regular array of obstacles. Boundary-Layer Meteorol 111:363–415CrossRefGoogle Scholar
- Yee E, Chan R (1997) A simple model for the probability density function of concentration fluctuations in atmospheric plumes. Atmos Environ 31:991–1002CrossRefGoogle Scholar
- Yee E, Skvortsov A (2011) Scalar fluctuations from a point source in a turbulent boundary layer. Phys Rev E 84:036306CrossRefGoogle Scholar
- Yee E, Wilson DJ (2000) A comparison of the detailed structure in dispersing tracer plumes measured in grid-generated turbulence with a meandering plume model incorporating internal fluctuations. Boundary-Layer Meteorol 94:253–296CrossRefGoogle Scholar
- Yee E, Chan R, Kosteniuk PR, Chandler GM, Biltoft CA, Bowers JF (1994) Incorporation of internal fluctuations in a meandering plume model of concentration fluctuations. Boundary-Layer Meteorol 67:11–39CrossRefGoogle Scholar