Abstract
A new approach for calculating the concentration distribution in inhomogeneous turbulence is suggested. The model is a 3-D model, constrained to describe incompressible flow. The model requires a knowledge of the covariance matrix of the Eulerian velocities and the two-point third moments. The model is applied for three types of turbulent field: homogeneous isotropic turbulence, constant flux neutral boundary layer and free convective turbulence. The required Eulerian moments are calculated using the ‘eddy model’ of the turbulent field. Concentration moments are calculated and results are compared to experimental data. Other model predictions which have no experimental support can be compared to measurements when available.
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References
Batchelor, G.K. (1952).Diffusion in a field of homogeneous turbulence II:The relative motion of particles. Proc. Camb. Phil. Soc.48, 345–362.
Batchelor, G.K. (1956).The theory of homogeneous turbulence. Cambridge University Press.
Batchelor, G. K. (1964).Diffusion from sources in a turbulent boundary layer. Archiv. Mechaniki Stoswanej.,3, 661.
Bernstein J. H., Berkowicz R. (1984),Monte-Carlo simulation of plume dispersion in the convective boundary layer., Atmos. Environ.,18, 701–712.
Corrsin, S. (1952).Heat transfer in isotropic turbulence. J. Appl. Phys. 23,1, 113–117.
Deardorff J. W. Willis G. E. (1985),Further results from a laboratory model of the convective planetary boundary layer, Bound. Lay. Met.,32, 205–236.
Deardorff J. W. Willis G. E. (1988),Concentration fluctuations within laboratory convectively mixed layer, in “Lectures on Air Pollution Modeling” ed. by A. Venkatram and J. C. Wyngaard AMS Boston, 366–370.
De Baas A. F., Van-Dop H., Nieuwstadt F. T. M. (1986),An application of the Langevin equation for inhomogeneous conditions to dispersion in the convective boundary layer. Atmos. Environ.,18, 701–712.
Dinar N., Kaplan H. and Kleiman M. (1988),Characterization of concentration fluctuations of a surface plume in a neutral boundary layer Bound. Lay. Met.45, 157–175.
Durbin, P.A. (1980).A Stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech.100, 279–302.
Egbert, G.D. and Baker, M.B. (1984).Comments on the effect of Gaussian particle-pair distribution functions in the statistical theory of concentration fluctuations in homogeneous turbulence. B.L. Sawford 1983, 339–353. Q.J.R. Met. Soc.110, 1195–1199.
Fackrell, J.E. and Robins, A.G. (1982).Concentration fluctuations and fluxes in plumes from point source in a turbulent boundary layer. J. Fluid Mech.117, 1–26.
Grant, H.L. (1958).The large eddies of turbulent motion. J. Fluid Mech.4, 149–190.
Gifford, F.A. (1982).Horizontal diffusion in the atmosphere: A Lagrangian dynamical theory. Atmos. Environ.,16, 505–512.
Hanna, S.R. (1981).Turbulent energy and Lagrangian time scale in the planetary boundary layer. A.M.S. 5th Symp. on turbulence diffusion and air pollution, Atlanta,Ga, 61–62
Hanna, S. R. (1984).The exponential probability density function and concentration fluctuations in smoke plumes Bound. Lay. Met.29, 361–375
Horst, T. W., (1979).Lagrangian similarity modelling of vertical diffusion from a ground level source. J. App. Met.,18, 733–740.
Hunt J. C. R., Kaimal J. C., Gaynor J. E. (1988)Eddy structure in the convective boundary layernew measurements and new concepts., Q. J. R. Met. Soc.,114, 827–858.
Kaimal, J.S., Wyngaard, J.C., Hangen, D.A., Cotè, O.R., Izumi, Y., Caughey, J.J. Reading, C.J. (1976).Turbulent structure in the convective boundary layer. J. Atm. Sci.33, 2152–2169.
Kaplan, H. and Dinar, N. (1988a).A stochastic model for dispersion and concentration distribution in homogeneous turbulence. J. Fluid. Mech.190, 121–140
Kaplan, H. and Dinar, N., (1988b).A three dimensional stochastic model for concentration fluctuation statistics in isotropic homogeneous turbulence. Journal of Computational Physics,79, No.2, 317–335.
Kaplan, H. and Dinar, N. (1988c).Comments on the paper: On the relative dispersion of two particles in homogeneous stationary turbulence and the implication for the size of concentration fluctuations at large time. By D.J. Thompson (1986), Q.J.R. Met. Soc. 12, 890–894. Q.J.R. Met. Soc.114, 545–550.
Kaplan, H. and Dinar, N. (1989a).The interference of two passive scalars in a homogeneous isotropic turbulent field. J. Fluid. Mech.203, 273–287.
Kaplan H., Dinar N. (1989b).Diffusion of an instantaneous cluster of particles in homogeneous turbulence. Atmos. Envi.,23, 1459–1463.
Lee, J. T. and Stone, G. L. (1983).The use of Eulerian initial conditions in a Lagrangian model of turbulent diffusion. Atmos. Environ.,17, 2477–2481.
Lenschow, D. H., Wyngaard, J. C., Pennel, W. T. (1980)Mean field and second moment budgets in a baroclinic, convective boundary layer., J. Atmos. Sci.,37, 1313–1326.
Luhar A. K. and Britter R. E. (1989),A random walk model for dispersion in inhomogeneous turbulence in a convective boundary layer., Atmos. Environ.,23, No. 9, 1911–1924.
Misra P. K. (1982).Dispersion of non-buoyant particles inside a convective boundary layer. J. Atmos. Sci.,41, 3162–3169.
Novikov, E. A. (1963).Random force method in turbulence theory. Soviet Physics JEPT,17, 1449–1454.
Pasquill, F. and Smith, F. B. (1983).Atmospheric Diffusion, third edition, Ellis Horwood Chichester.
Pope, S.B. (1985).P df methods for turbulent reactive flows. Prog. Energy Combust. Sci.11, 119–192.
Sawford, B.L. (1982).Lagrangian Monte-Carlo simulation of a turbulent motion of a pair of particles. Q.J.R. Met. Soc.108, 207–213.
Sawford, B. L., Frost C. C. and Allen T. C. (1985)Atmospheric boundary layer measurements of concentration statistics from isolated and multiple sources Bound. Lay. Met.31, 249–268.
Sawford B. L., Guest F. M., (1987),Lagrangian stochastic analysis of flux gradient relationship in the convective boundary layer. J. Atmos. Sci.,44, No. 8, 1952–1165.
Sutton, O. G. (1953).Micrometeorology, McGraw-Hill, New-York.
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.
Thomson, D.J. (1986).On the relative dispersion of two particles in homogeneous stationary turbulence and the implication for the size of concentration fluctuations a large times. Q.J.R. Met. Soc.12, 890–894.
Thomson, D.J. (1987).Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech.180, 529–556.
Thomson, D.J. (1990).A stochastic model for the motion of particle pairs in isotropic high Reynold number turbulence, and its application to the problem of concentration variance. J. Fluid Mech.210, 113–153
Townsend, A.A. (1956).The structure of turbulent shear flow. Cambridge Univ. Press.
van Ulden, A. P. (1978).Simple estimates for vertical diffusion from sources near the ground. Atmos. Environ.12, 2125–2129.
Venkatram A. (1983).On dispersion in the convective boundary layer, Atmos. Environ.,17, 529–533.
Warhaft, Z. (1984)The interference of thermal fields for line sources in grid turbulence J. Fluid. Mech.144 363–381.
Willis G. E. Deardorff J. W. (1976),A laboratory study of diffusion into the convective planetary boundary layer, Q. J. R. Met. Soc.,102, 427–445.
Willis G. E. Deardorff J. W. (1978),A laboratory study of dispersion from an elevated source within a modeled convective planetary boundary layer. Atmos. Environ.,12, 1305–1311.
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Kaplan, H., Dinar, N. A three-dimensional model for calculating the concentration distribution in inhomogeneous turbulence. Boundary-Layer Meteorol 62, 217–245 (1993). https://doi.org/10.1007/BF00705556
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DOI: https://doi.org/10.1007/BF00705556