Skip to main content
Log in

A Lagrangian Solution To The Relationship Between A Distributed Source And Concentration Profile

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

A new solution is presented to the problem ofrelating source strength and concentration profiles within a plant canopy. The solution is based on the Lagrangian dispersion theory developed by G. I. Taylor in 1921. A dispersion matrix is derived that relates the source and concentration profiles based on profiles of the turbulent length and velocity scales. The matrix translates the effects of persistence (a temporal effect) into spatialcoordinates and represents the change from near-field to far-field in acontinuous fashion, successfully accounting for both regimes. A test ofthe new model using wind-tunnel data showed excellent quantitative agreement between model and measurements. A comparison was also made withM. R. Raupach's localized near-field theory, which underestimated the near-field effect in the wind-tunnel data and relative to the new model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Collineau, S. and Brunet, Y.: 1993a, ‘Detection of Turbulent Coherent Motions in a Forest Canopy, Part I: Wavelet Analysis’, Boundary-Layer Meteorol. 65, 357-379.

    Google Scholar 

  • Collineau, S. and Brunet, Y.: 1993b, ‘Detection of Turbulent Coherent Motions in a Forest Canopy Part II: Time-Scales and Conditional Analysis’, Boundary-Layer Meteorol. 66, 49-73.

    Google Scholar 

  • Coppin, P. A., Raupach, M. R., and Legg, B. J.: 1986, ‘Experiments on Scalar Dispersion within a Model Plant Canopy Part II: An Elevated Plane Source’, Boundary-Layer Meteorol. 335, 167-191.

    Google Scholar 

  • Corrsin, S.: 1963, ‘Estimates of the Relations between Eulerian and Lagrangian Scales in Large Reynolds Number Turbulence’, J. Atmos. Sci. 20, 115-119.

    Google Scholar 

  • Csanady, G. T.: 1973, Turbulent Diffusion in the Environment, D. Reidel Publishing Company, Boston, MA, 248 pp.

    Google Scholar 

  • Frenkiel, F. N.: 1953, ‘Turbulent Diffusion: Mean Concentration Distribution in a Flow Field of Homogeneous Turbulence’, Adv. Appl. Mech. 3, 61-107.

    Google Scholar 

  • Kraichnan, R. H.: 1964, ‘Relation between Lagrangian and Eulerian Correlation Times of a Turbulent Velocity Field’, Phys. Fluids 7, 142-143.

    Google Scholar 

  • Leclerc, M. Y. and Thurtell, G. W.: 1990, ‘Footprint Prediction of Scalar Fluxes Using a Markovian Analysis’, Boundary-Layer Meteorol. 52, 247-258.

    Google Scholar 

  • McNaughton, K. G. and Van Den Hurk, B. J. J. M.: 1995, ‘A “Lagrangian” Revision of the Resistors in the Two-Layer Model for Calculating the Energy Budget of a Plant Canopy’, Boundary-Layer Meteorol. 74, 261-288.

    Google Scholar 

  • Novak, M. D., Warland, J. S., Orchansky, A. L., Ketler, R., and Green, S.: 2000, ‘Wind Tunnel and Field Measurements of Turbulent Flow in Forests. Part I: Uniformly Thinned Stands’, Boundary-Layer Meteorol. 95, 457-495.

    Google Scholar 

  • Raupach, M. R.: 1987, ‘A Lagrangian Analysis of Scalar Transfer in Vegetation Canopies’, Quart. J. Roy. Meteorol. Soc. 113, 107-120.

    Google Scholar 

  • Raupach, M. R.: 1989, ‘A Practical Lagrangian Method for Relating Scalar Concentrations to Source Distributions in Vegetation Canopies’, Quart. J. Roy. Meteorol. Soc. 115, 609-632.

    Google Scholar 

  • Raupach, M. R., Coppin, P. A., and Legg, B. J. 1986, ‘Experiments on Scalar Dispersion within a Model Plant Canopy. Part I: The Turbulence Structure’, Boundary-Layer Meteorol. 35, 21-52.

    Google Scholar 

  • Raupach, M. R., Finnigan, J. J., and Brunet, Y.: 1989, ‘Coherent Eddies in Vegetation Canopies’, in Proc. Fourth Australasian Conf. on Heat and Mass Transfer, pp. 75-90.

  • Raupach, M. R., Finnigan, J. J., and Brunet, Y.: 1996, ‘Coherent Eddies and Turbulence in Vegetation Canopies: The Mixing-Layer Analogy’, Boundary-Layer Meteorol. 78, 351-382.

    Google Scholar 

  • Richardson, L. F.: 1920, ‘Some Measurements of Atmospheric Turbulence’, Phil. Trans. Roy. Soc. Lond. A221, 1-28.

    Google Scholar 

  • Rodean, H. C.: 1996, Stochastic Lagrangian Models of Turbulent Diffusion, Meteorological Monographs, Vol. 26, No. 48, American Meteorological Society, Boston, MA, 84 pp.

    Google Scholar 

  • Shaw, R. H., Brunet, Y., Finnigan, J. J., and Raupach, M. R.: 1995, ‘A Wind Tunnel Study of Air Flow in Waving Wheat: Two-Point Velocity Statistics’, Boundary-Layer Meteorol. 76, 349-376.

    Google Scholar 

  • Taylor, G. I.: 1915, ‘Eddy Motions in the Atmosphere’, Phil. Trans. Roy. Soc. Lond. A215, 1-26.

    Google Scholar 

  • Taylor, G. I.: 1921, ‘Diffusion by Continuous Movements’, Proc. Lond. Math. Soc., Ser. 2 20, 196-211.

    Google Scholar 

  • Van Den Hurk, B. J. J. M. and McNaughton, K. G.: 1995, ‘Implementation of Near-Field Dispersion in a Simple Two-Layer Surface Resistance Model’, J. Hydrol. 166, 293-311.

    Google Scholar 

  • Wygnanski, I. and Fiedler, H. E.: 1970, ‘The Two-Dimensional Mixing Region’, J. Fluid Mech. 41, 327-361.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Warland, J.S., Thurtell, G.W. A Lagrangian Solution To The Relationship Between A Distributed Source And Concentration Profile. Boundary-Layer Meteorology 96, 453–471 (2000). https://doi.org/10.1023/A:1002656907873

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1002656907873

Navigation