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Influence of the sampling time on the kinematics of turbulent diffusion from a continuous source

Published online by Cambridge University Press:  26 April 2006

Richard M. Eckman
Richard M. Eckman
Affiliation:
Atmospheric Turbulence and Diffusion Division, NOAA/ARL, Oak Ridge, TN 37831, USA
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Abstract

A kinematic description is presented of how turbulent diffusion from a continuous source varies with the sampling time in stationary, homogeneous turbulence. Unlike most previous theories, the sampling is assumed to take place at fixed downstream distances from the source. It is shown that the sampling-time effects depend on two-particle velocity statistics. Thus, time-average diffusion at fixed downstream distances is more akin to relative diffusion than to absolute diffusion. Two simple diffusion models are developed from the kinematic equations. These models are in fairly good agreement with diffusion data obtained both in a wind tunnel and in the field. Moreover, these models have significant practical implications. For example, the models indicate that care must be taken when using band-pass spectral filtering as a paradigm for turbulent diffusion. Also, the models show that the mean flow speed U has an important influence on the sampling-time effects. To account for U properly, diffusion measurements with differing sampling times Λ should be compared using the product UΛ, and not just Λ.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 270 , 10 July 1994 , pp. 349 - 375
Copyright
© 1994 Cambridge University Press

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References

Batchelor, G. K. 1950 The application of the similarity theory of turbulence to atmospheric diffusion. Q. J. R. Met. Soc. 76, 133–146.Google Scholar
Batchelor, G. K. 1952 Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345–362.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1964 Diffusion from sources in a turbulent boundary layer. Arch. Mech. Stosowanej 16, 661–670.Google Scholar
Doran, J. C., Horst, T. W. & Nickola, P. W. 1978 Variations in measured values of lateral diffusion parameters. J. Appl. Met. 17, 825–831.Google Scholar
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279–302.Google Scholar
Eckman, R. M. 1989 The influence of the sampling time on diffusion measurements in the atmosphere. PhD dissertation, The Pennsylvania State University, University Park.
Eckman, R. M. & Mikkelsen, T. 1991 Estimation of horizontal diffusion from oblique aerial photographs of smoke clouds. J. Atmos. Oceanic Technol. 8, 873–878.Google Scholar
Gage, K. S. 1979 Evidence for a k5/3 law inertial range in mesoscale two-dimensional turbulence. J. Atmos. Sci. 36, 1950–1954.Google Scholar
Gautschi, W. & Cahill, J. H. 1964 Exponential integral and related functions. In Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (ed. M. Abramowitz & I. Stegun), p. 227. US National Bureau of Standards.
Georgopoulos, P. G. & Seinfeld, J. H. 1988 Estimation of relative dispersion parameters from atmospheric turbulence spectra. Atmos. Environ. 22, 31–41.Google Scholar
Gifford, F. A. 1957 Relative atmospheric diffusion of smoke puffs. J. Met. 14, 410–414.Google Scholar
Gifford, F. A. 1980 Smoke as a quantitative atmospheric diffusion tracer. Atmos. Environ. 14, 1119–1121.Google Scholar
Gifford, F. A. 1988 A similarity theory of the tropospheric turbulence energy spectrum. J. Atmos. Sci. 45, 1370–1379.Google Scholar
Hanna, S. R., Briggs, G. A. & Hosker, R. P. 1982 Handbook on atmospheric diffusion. DOE/TIC-11223, Technical Information Center, US Dept of Energy.
Hay, J. S. & Pasquill, F. 1959 Diffusion from a continuous source in relation to the spectrum and scale of turbulence. Adv. Geophys. 6, 345–365.Google Scholar
Hino, M. 1968 Maximum ground-level concentration and sampling time. Atmos. Environ. 2, 149–165.Google Scholar
Højstrup, J. 1982 Velocity spectra in the unstable boundary layer. J. Atmos. Sci. 39, 2239–2248.Google Scholar
Kristensen, L., Jensen, N. O. & Petersen, E. L. 1981 Lateral dispersion of pollutants in a very stable atmosphere — the effect of meandering. Atmos. Environ. 15, 837–844.Google Scholar
Mikkelsen, T. 1983 The Borris field experiment: observations of smoke diffusion in the surface layer over homogeneous terrain. Risø-R-479, Risø National Laboratory, Denmark.
Mikkelsen, T. & Eckman, R. M. 1985 Instantaneous observations of plume dispersion in the surface layer. In Air Pollution Modeling and It Application IV (ed. C. De Wispelaere), p. 549. Plenum.
Mikkelsen, T., Larsen, S. E. & Pécseli, H. L. 1987 Diffusion of Gaussian puffs. Q. J. R. Met. Soc. 113, 81–105.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1. MIT Press.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press.
Nappo, C. J. 1984 Turbulence and dispersion parameters derived from smoke-plume photoanalysis. Atmos. Environ. 18, 299–306.Google Scholar
Ogura, Y. 1957 The influence of finite observation intervals on the measurement of turbulent diffusion parameters. J. Met. 14, 176–181.Google Scholar
Ogura, Y. 1959 Diffusion from a continuous source in relation to a finite observation interval. Adv. Geophys. 6, 149–159.Google Scholar
Panofsky, H. A. & Dutton, J. A. 1984 Atmospheric Turbulence: Models and Methods for Engineering Applications. John Wiley.
Pasquill, F. & Smith, F. B. 1983 Atmospheric Diffusion. Halsted Press.
Richardson, L. F. 1926 Atmospheric diffusion shown on a distance-neighbor graph. Proc. R. Soc. Lond. 110, 709–737.Google Scholar
Sawford, B. L. 1982 Comparison of some different approximations in the statistical theory of relative dispersion. Q. J. R. Met. Soc. 108, 191–206.Google Scholar
Sheih, C. M. 1980 On lateral dispersion coefficients as functions of averaging time. J. Appl. Met. 19, 557–561.Google Scholar
Shimanuki, A. 1961 Diffusion from the continuous source with finite release time. Sci. Rep. Tôhoku Univ. (5) 12, 184–190.Google Scholar
Smedman-Högström, A. & Högström, U. 1975 Spectral gap in surface-layer measurements. J. Atmos. Sci. 32, 340–350.Google Scholar
Smith, F. B. & Hay, J. S. 1961 The expansion of clusters of particles in the atmosphere. Q. J. R. Met. Soc. 87, 82–101.Google Scholar
Sutton, O. G. 1953 Micrometeorology. McGraw-Hill.
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. (2) 20, 196–212.Google Scholar
Thomson, D. J. 1987 Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech. 180, 529–556.Google Scholar
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.Google Scholar
Wollenweber, G. C. & Panofsky, H. A. 1989 Dependence of velocity variance on sampling time. Boundary-Layer Met. 47, 205–215.Google Scholar