Abstract
The knowledge of the concentration probability density function (pdf) is of importance in a number of practical applications, and a Lagrangian stochastic (LS) pdf model has been developed to predict statistics and concentration pdf generated by continuous releases of non-reactive and reactive substances in canopy generated turbulence. Turbulent dispersion is modelled using a LS model including the effects of wind shear and along-wind turbulence. The dissipation of concentration fluctuations associated with turbulence and molecular diffusivity is simulated by an Interaction by Exchange with the Conditional Mean (IECM) micromixing model. A general procedure to obtain the micromixing time scale needed in the IECM model useful in non-homogeneous conditions and for single and multiple scalar sources has been developed. An efficient algorithm based on a nested grid approach with particle splitting, merging techniques and time averaging has been used, thus allowing the calculation for cases of practical interest. The model has been tested against wind-tunnel experiments of single line and multiple line releases in a canopy layer. The approach accounted for chemical reactions in a straightforward manner with no closure assumptions, but here the validation is limited to non-reacting scalars.
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References
Baldocchi D (1992) A Lagrangian random walk model for simulating water vapour, CO2 and sensible heat flux densities and scalar profile over and within a soybean canopy. Boundary-Layer Meteorol 61:113–144
Brown RJ, Bilger RW (1998a) Experiments on reacting plume-1. Conventional concentration statistics. Atmos Environ 32(4):611–628
Brown RJ, Bilger RW (1998b) Experiments on reacting plume-2. Conditional concentration statistics. Atmos Environ 32(4):629–646
Brown RJ, Woodfield PL (2004) Prediction of short-range maximum NO 2 concentrations using scalars pdfs. Atmos Environ 38(4):1379–1386
Brunet Y, Finnigan JJ, Raupach MR (1994) A wind tunnel study of air flow in waving wheat: single point velocity statistics. Boundary-Layer Meteorol 70:95–132
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 to neutral boundary layer. Atmos Environ 39(8):1457–1469
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(8):1471–1479
Cassiani M, Radicchi A, Giostra U (2005c) Probability density function modelling of concentration fluctuation in and above a canopy. layer Agric For Meteorol 133:153–165
Cassiani M, Radicchi A, Albertson JD, Giostra U (2006) An efficient algorithm for scalar pdf modelling in incompressible turbulent flow; numerical analysis with evaluation of IEM and IECM micromixing models. J Comput Phys, in press
Coppin PA, Raupach MR, Legg BJ (1986) Experiments on scalar dispersion within a model plant canopy. Part II: an elevated plane source. Boundary-Layer Meteorol 35:167–191
Dopazo C, O’Brien EE (1974) An approach to the auto ignition of a turbulent mixture. Acta Astronaut 1:1239–1266
Dopazo C, Valino L, Fuego F (1997) Statistical description of the turbulent mixing of scalar fields. Int J Mod Phys B 11(25):2975–3014
Du SM, Sawford BL, Wilson JD, Wilson DJ (1995) Estimation of the Kolmogorov constant (C-0) for the Lagrangian Structure Function, using 2nd-order Lagrangian model of grid turbulence. Phys. Fluids 7(12):3083–3090
Du S (1997) Universality of the Lagrangian structure function constant (C 0) across different kinds of turbulence. Boundary-Layer Meteorol 83:207–219
Fackrell JE, Robins AG (1982) Concentration fluctuations and fluxes in plumes from point sources in turbulent boundary layer. J Fluid Mech 117:1–26
Franzese P (2003) Lagrangian stochastic modelling of a fluctuating plume in the convective boundary layer. Atmos Environ 37:1691–1701
Franzese P, Cassiani M (2006) A statistical Theory of turbulent relative dispersion. J Fluid Mech In Press
Flesch TK, Wilson JD (1992) A two dimensional trajectory simulation model for non Gaussian inhomogeneous turbulence within plant canopies. Boundary-Layer Meteorol 61:349–374
Fox RO (1996) On velocity conditioned scalar mixing in homogeneous turbulence. Phys Fluids 8:2678–2691
Fox RO (2003) Computational models for turbulent reacting flows. Cambridge University Press, Cambridge, 419 pp
Gardiner CW (1983) Handbook of stochastic methods for physics chemistry and the natural sciences. Springer-Verlag, Berlin 442 pp
Garmory A, Richardson ES, Mastorakos E (2006) Micromixing effects in a reacting plume by the stochastic fields method. Atmos Environ 40:1078–1091
Gifford FA (1977) Tropospheric relative diffusion observations. J Appl Meteorol 16:311–313
Griffith RF, Megson LC (1984) The effect of uncertainties in human toxic response on hazard range estimation for ammonia and chlorine. Atmos Environ 18:1195–1206
Heinz S (2003) Statistical mechanics of turbulent flows. Springer Verlag, Berlin Heidelberg, 214 pp
Hilderman TL, Hrudey SE, Wilson DJ (1999) A model for effective toxic load from fluctuating gas concentrations. J Hazard Mater A 64:115–134
Jenny P, Pope SB, Muradoglu M, Caughey DA (2001) A hybrid algorithm for the joint pdf equation of turbulent reactive flows. J Comput Phys 166:218–252
Legg BJ, Raupach MR, Coppin PA (1986) Experiments on scalar dispersion within a model plant canopy. Part III: an elevated line source. Boundary-Layer Meteorol 35:277–302
Li G, Modest MF (2001) An effective particle tracking scheme on structured/unstructured grids in hybrid finite volume/pdf Monte Carlo methods. J Comput Phys 173:187–201
Lien RC, D’Asaro E (2002) The Kolmogorov constant for the Lagrangian velocity spectrum and structure function. Phys Fluids 14:4456–4459
Lowe R, Tomlin A (2000) Low-dimensional manifolds and reduced chemical models for tropospheric chemistry simulations. Atmos Environ 34:2425–2436
Luhar AK, Sawford BL (2005a) Micromixing modelling of concentration fluctuations in inhomogeneous turbulence in the convective boundary layer. Boundary-Layer Meteorol 114:1–30
Luhar AK, Sawford BL (2005b) Micromixing modelling of mean and fluctuating scalar fields in the convective boundary layer. Atmos Environ 39:6673–6685
Monin AS, Yaglom AM (1975) Statistical fluid mechanics, Vol 2. MIT Press, Cambridge, MA, 874 pp
Meeder JP, Nieuwstadt FTM (2000) Large eddy simulation of the turbulent dispersion of a reactive plume from point source into a neutral atmospheric boundary layer. Atmos Environ 34:3563–3573
Patton EG, Kenneth JD, Barth MC, Sullivan PP (2001) Decaying scalar emitted by a forest canopy: a numerical study. Boundary-Layer Meteorol 100:91–129
Poggi D, Katul G, Albertson J (2006) Scalar dispersion within model canopy: measurement and three-dimensional Lagrangian models. Adv Water Resour 29:326–335
Pope SB (1985) Pdf methods for turbulent reactive flows. Prog Energy Combust Sci 11:119–192
Pope SB (1994) Lagrangian pdf methods for turbulent flows. Annu Rev Fluid Mech 26:23–63
Pope SB (1998) The vanishing effect of molecular diffusivity on turbulent dispersion: implications for turbulent mixing and the scalar flux. J Fluid Mech 359:299–312
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge, 806 pp
Raupach MR, Coppin PA, Legg BJ (1986) Experiments on scalar dispersion within a model plant canopy. Part I: the turbulence structure. Boundary-Layer Meteorol 35:21–52
Raupach MR, Coppin PA, Legg BJ (1987) Erratum to Raupach MR, Coppin PA, Legg BJ, 1986. Experiments on scalar dispersion within a model plant canopy. Part I: the turbulence structure. Boundary-Layer Meteorol 35:21–52. Boundary-Layer Meteorol 39:423–424
Raupach MR, Finnigan JJ, Brunet Y (1996) Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Boundary-Layer Meteorol 78:351–382
Reynolds AM (1998) Comments on the ‘Universality of the Lagrangian velocity structure function constant (C-0) across different kinds of turbulence’. Boundary-Layer Meteorol 89:161–170
Rodean HC (1996) Stochastic Lagrangian models of turbulent diffusion. Am Meteorol Soc, Met. Monogr 26(48):82 pp
Sawford BL (1999) Rotation of trajectories in Lagrangian stochastic models of turbulent dispersion. Boundary-Layer Meteorol 93:411–424
Sawford BL (2004) Micro-mixing modelling of scalar fluctuations for plumes in homogeneous turbulence. Flow Turb Combust 72:133–160
Sawford BL (2006) Lagrangian stochastic modelling of chemical reaction in a scalar mixing layer. Boundary-Layer Meteorol 118:1–23
Subramaniam S, Pope SB (1998) A mixing model for turbulent reactive flows based on Euclidean minimum spanning trees. Combust Flame 115:487–514
Thomson DJ (1987) Criteria for the selection of the stochastic models of particle trajectories in turbulent flows. J Fluid Mech 180:529–556
Thomson DJ (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
Vickers NJ, Christensen TA, Baker TC, Hildebrand JG (2001) Odour-plume dynamics influence the brain’s olfactory code. Nature 410:466–470
Vilà-Guerau de Arellano J, Dosio A, Vinuesa J-F, Holtslag AAM, Galmarini S (2004) The dispersion of chemically reactive species in the atmospheric boundary layer. Meteorol Atmos Phys 87:23–38
Wilson DJ (1995) Concentration fluctuations and averaging time in vapor clouds. Center for Chemical Process Safety, American Institute of Chemical Engineers, New York, 181 pp
Wilson JD, Flesch TK (1997) Trajectory curvature as a selection criterion for valid Lagrangian stochastic dispersions models. Boundary-Layer Meteorol 84:411–426
Yee E (2001) An analytical model for threshold crossing tares of concentration fluctuations in dispersing plumes. Boundary-Layer Meteorol 98:517–527
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Cassiani, M., Radicchi, A. & Albertson, J.D. Modelling of concentration fluctuations in canopy turbulence. Boundary-Layer Meteorol 122, 655–681 (2007). https://doi.org/10.1007/s10546-006-9122-0
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DOI: https://doi.org/10.1007/s10546-006-9122-0