Abstract
Eulerian turbulence observations, madein the surface layer under unstable conditions (z/L > 0),by a sonic anemometer were used to estimatethe Lagrangian structure function constant O. Twomethods were considered. The first one makes use of arelationship, widely used in the Lagrangian stochasticdispersion models, relating O to the turbulent kineticenergy dissipation rate ε, wind velocity variance andLagrangian decorrelation time. The second one employsa novel equation, connecting O to the constant of thesecond-order Eulerian structure function. Beforeestimating O, the measurements were processed in orderto discard non-stationary cases at least to a firstapproximation and cases in which local isotropy couldnot be assumed. The dissipation ε was estimated eitherfrom the best fit of the energy spectrum in theinertial subrange or from the best fit of the third-orderlongitudinal Eulerian structure function. Thefirst method was preferred and applied to the subsequentpart of the analysis. Both methods predict thepartitioning of O in different spatial components as aconsequence of the directional dependence of theEulerian correlation functions due to the isotropy.The O values computed by both methods are presented anddiscussed. In conclusion, both methods providerealistic estimates of O that compare well withprevious estimations reported in the literature, evenif a preference is to be attributed to the second method.
Similar content being viewed by others
References
Anand, M. S. and Pope, S. B.: 1985, ‘Diffusion behind a Line Source in a Grid Turbulence’, in L. J. S. Bradbury, F. Durst, B. E. Lauder, F. W. Schmidt, and J. H. Whitelaw (eds.), Turbulent Shear Flows, Vol. 4, Springer-Verlag, Berlin, pp. 46–61.
Angell, J. K., Pack, D. H., Hoecker, W. H., and Delver, N.: 1971, ‘Lagrangian-Eulerian Time-Scale Estimated from Constant Volume Balloon Flights Past a Tall Tower’, Quart. J. Roy. Meteorol. Soc. 97, 87–92.
Cassardo, C., Sacchetti, D., Morselli, M. G., Anfossi, D., Brusasca, G., and Longhetto, A.: 1995, ‘A Study of the Assessment of Air Temperature, and Sensible and Latent Heat Fluxes from Sonic Anemometer Observations’, Nuovo Cimento 18C, 419–440.
Corrsin, S.: 1963, ‘Estimates of the Relations between Eulerian and Lagrangian Scales in Large Reynolds Number Turbulence’, J. Atmos. Sci. 20, 115–119.
Csanady, G. T.: 1973, Turbulent Diffusion in the Environment, Geophysics and Astrophysics Monograps, Reidel, Boston, 248 pp.
Degrazia, G. A. and Anfossi, D.: 1998, ‘Estimation of the Kolmogorov Constant C0 from Classical Statistical Diffusion Theory’, Atmos. Environ. 32, 3611–3614.
Du, S., Sawford, B. L., Wilson, J. D., and Wilson, D. J.: 1995, ‘Estimation of the Kolmogorov Constant for the Lagrangian Structure Function, Using a Second-Order Lagrangian Model of Grid Turbulence’, Phys. Fluids 7, 3083–3090.
Du, S., Wilson, J. D., and Yee, E.: 1994, ‘Probability Density Functions for Velocity in the Convective Boundary Layer and Implied Trajectory Models’, Atmos. Environ. 28, 1211–1217.
Ferrero, E. and Anfossi, D.: 1998a, ‘Sensitivity Analysis of Lagrangian Stochastic Models for CBL with Different PDF's and Turbulence Parameterizations’, in S. E. Gryning and N. Chaumerliac (eds.), Air Pollution Modelling and Its Applications XI, Vol. 22, Plenum Press, New York, pp. 267–273.
Ferrero E. and Anfossi D.: 1998b, ‘Comparison of PDFs, Closures Schemes and Turbulence Parameterizations in Lagrangian Stochastic Models’, Int. J. Environ. Pollut. 9, 384–410.
Flesch, T. K. and Wilson, D. J.: 1992, ‘A Two-Dimensional Trajectory Simulation Model for Non-Gaussian Inhomogeneous Turbulence within Plant Canopies’, Boundary-Layer Meteorol. 61, 349–374.
Frisch, U.: 1995, Turbulence, Cambridge University Press, U.K., 296 pp.
Garratt, J. R.: 1992, The Atmospheric Boundary Layer, Cambridge University Press, U.K., 316 pp.
Gifford, F. A.: 1955, ‘A Simultaneous Lagrangian-Eulerian Turbulence Experiment’, Mon. Wea. Rev. 83, 293–301.
Hanna, S. R.: 1981, ‘Lagrangian and Eulerian Time-Scale in the Daytime Boundary Layer’, J. Appl. Meteorol. 20, 242–249.
Hay, J. S. and Pasquill, F.: 1959, ‘Diffusion from a Continuous Source in Relation to the Spectrum and Scale of Turbulence’, in F. N. Frenkiel and P. A. Sheppard (eds.), Atmospheric Diffusion and Air Pollution, Advances in Geophysics, Vol. 6, Academic Press, pp. 345–365.
Hinze, J. O.: 1975, Turbulence, McGraw Hill, New York, 790 pp.
Horst, T. W. and Weil, J.: 1992, ‘Footprint Estimation for Scalar Flux Measurements in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 59, 279–296.
Hurley, P. J. and Physick, W.: 1991, ‘A Skewed Homogeneous Lagrangian Particle Model for Convective Conditions, Atmos. Environ. 25A, 1313–1325.
Hurley, P. J. and Physick, W. L.: 1993, ‘A Lagrangian Particle Model of Fumigation by Breakdown of the Nocturnal Inversion’, Atmos. Environ. 27A, 619–642.
Kaimal, J. C. and Finnigan, J. J.: 1994, ‘Atmospheric Boundary Layer Flows’, Oxford University Press, 289 pp.
Kaiser, R. and Fedorovich, E.: 1998, ‘Turbulence Spectra and Dissipation Rates in a Wind Tunnel Model of the Atmospheric Convevtive Boundary Layer’, J. Atmos. Sci. 55, 580–594.
Landau, L. D. and Lifshitz, E. M.: 1987, Fluid Mechanics, Second Edition, Pergamon Press, Oxford, 539 pp.
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, 1191–1924.
McMillen, R. T.: 1988, ‘An Eddy Correlation Technique with Extended Applicability to Non Simple Terrain’, Boundary-Layer Meteorol. 43, 231–245.
Monin, A. S. and Yaglom, A. M.: 1975, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2, MIT Press, 874 pp.
Moore, G. E., Liu, M. K., and Shi, L. H.: 1985, ‘Estimates of Integral Time Scales from a 100-m Meteorological Tower at a Plains Site’, Boundary-Layer Meteorol. 31, 349–368.
Panofsky, H. A. and Dutton, J. A.: 1984, Atmospheric Turbulence —Model and Methods for Engineering Applications, John Wiley and Sons, New York, 397 pp.
Pasquill, F.: 1974, Atmospheric Diffusion, Wiley & Sons, New York, 429 pp.
Physick, W. L., Noonan, J. A., McGregor, J. L., Hurley, P. J., Abbs, D. J., and Manins, P. C.: 1994, ‘LADM: A Lagrangian Atmospheric Dispersion Model’, Technical Report, 24, CSIRO Division of Atmospheric Research, Australia
Rodean, H. C.: 1991, ‘The Universal Constant for the Lagrangian Structure Function’, Phys. Fluids A3, 1479–1480.
Rodean, H. C.: 1994, Notes on the Langevin Model for Turbulent Diffusion of “Marked” Particles, UCRL-ID-115869 Report of Lawrence Livermore National Laboratory, 122 pp.
Rotach, M. W, Gryning, S. E., and Tassone, C.: 1996, ‘A Two-Dimensional Lagrangian Stochastic Dispersion Model for Daytime Conditions’, Quart. J. Roy. Meteorol. Soc. 122, 367–389.
Saffman, P. G.: 1963, ‘An Approximate Calculation of the Lagrangian Autocorrelation Coefficient for Stationary Homogeneous Turbulence’, Appl. Sci. Res. 11, 245.
Sawford, B. L.: 1991, ‘Reynolds Number Effects in Lagrangian Stochastic Models of Turbulent Dispersion’, Phys. Fluids A3, 1577–1566.
Sawford, B. L.: 1993, ‘Recent Developments in the Lagrangian Stochastic Theory of Turbulent Dispersion’, Boundary-Layer Meteorol., 62, 197–215.
Sawford, B. L. and Borgas, M. S.: 1994, ‘On the continuity of Stochastic Models for the Lagrangian Velocity in Turbulence’, Physica D 76, 297–311.
Sawford, B. L. and Guest, F. M.: 1988, ‘Uniqueness and Universality of Lagrangian Stochastic Models of Turbulent Dispersion’, in 8th Symposium on Turbulence and Diffusion, Amer. Meteorol. Soc., San Diego, CA, pp. 96–99.
Sawford, B. L. and Tivendale, C. M.: 1992, ‘Measurements of Concentrations Statistics Downstream of a Line Source in Grid Turbulence’, in Proceedings of the 11th Australasian Fluid Mechanics Conference, University of Tasmania, pp. 945–948.
Slade, D. H.: 1968, Meteorology and Atomic Energy 1968, USAEC, Division of Technical Information Extension, Oak Ridge, U.S.A., 445 pp.
Smith, F. B.: 1967, ‘Eulerian and Lagrangian Time-Scale Relationship in One-Dimensional Turbulence’, in USAEC Meteorological Information Meeting, Chalk River, Canada (AECL-2787), pp. 476–483.
Sorbjan, Z.: 1989, Structure of the Atmospheric Boundary Layer, Prentice Hall, New Jersey, 317 pp.
Tassone, C., Gryning, S. E., and Rotach, M.: 1994, ‘A Random Walk Model for Atmospheric Dispersion in the Daytime Boundary Layer’, in S. E. Gryning and M. Millan (eds.), Air Pollution Modeling and Its Application X, Plenum Press, pp. 243–251.
Tennekes, H.: 1982, ‘Similarity Relations, Scaling Laws and Spectral Dynamics’, in F. T. M. Nieuwstadt and H. van Dop (eds.), Atmospheric Turbulence and Air Pollution Modelling, Reidel, Dordrecht, pp. 37–68.
Thomsen, A., Barring, L., Gryning, S. E., Sogaard, H., and Thorgeirsson, H.: 1994, Data Report for the NOPEX Tisby Site —Concentrated Field Effort #1, May 27–June 23, 1994.
Thomson, D. J.: 1987, ‘Criteria for the Selection of Stochastic Models of Particle Trajectories in Turbulent Flows’, J. Fluid Mech. 180, 529–556.
Van Dop, H., Nieuwstadt, F. T. M., and Hunt, J. C. R.: 1985, ‘Random Walk Models for Particle Displacements in Inhomogeneous Unsteady Turbulent Flows’, Phys. Fluids 28, 1639–1653.
Wandel, C. F. and Kofoed-Hansen, O.: 1962, ‘On the Eulerian-Lagrangian Transform in the Statistical Theory of Turbulence’, J. Geophys. Res. 76, 3089–3093.
Weil, J. C.: 1990, ‘A Diagnosis of the Asymmetry in Top-Down and Bottom-Up Diffusion Using a Lagrangian Stochastic Model’, J. Atmos. Sci. 47, 501–515.
Wilson, J. D. and Flesch, T. K.: 1993, ‘Flow Boundaries in Random-Flight Dispersion Models: Enforcing the Well-Mixed Condition’, J. Appl. Meteorol. 32, 1695–1707.
Wilson, J. D. and Sawford, B. L.: 1996, ‘Review of Lagrangian Stochastic Models for Trajectories in the Turbulent Atmosphere’, Boundary-Layer Meteorol. 78, 191–210.
Wilson, J. D., Legg, B. J., and Thomson, D. J.: 1983, ‘Calculation of Particle Trajectories in the Presence of a Gradient in Turbulent-Velocity Variance’, Boundary-Layer Meteorol. 27, 163–169.
Zannetti, P.: 1990, Air Pollution Modelling, Computational Mechanics Publications, 444 pp.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Anfossi, D., Degrazia, G., Ferrero, E. et al. Estimation Of The Lagrangian Structure Function Constant C0 From Surface-Layer Wind Data. Boundary-Layer Meteorology 95, 249–270 (2000). https://doi.org/10.1023/A:1002697221093
Issue Date:
DOI: https://doi.org/10.1023/A:1002697221093