Journal of Atmospheric Chemistry

, Volume 16, Issue 2, pp 145–155 | Cite as

Second-order closure study of the covariance between chemically reactive species in the surface layer

  • Jordi Vilà-Guerau de Arellano
  • Peter G. Duynkerke


A second-order modelling technique is used to investigate the influence of turbulence on chemical reactions. The covariance and variance equations for the NO-O3-NO2 system are developed as a function of the ratio of the timescale of turbulence (τ t ) and the timescale of chemistry (τCh): the first Damköhler number (τ t Ch). Special attention is given to the calculation of the covariance between NO and O3 normalized by the product of their means, the so-called intensity of segregation (I S ). This parameter quantifies the state of mixing of two chemical species.

The intensity of segregation is calculated as a function of the flux of NO and the first Damköhler number. The model results presented illustrate the importance of taking the effect of turbulence on chemical reactions into account for higher values of the NO flux, for values of the ratio O3/NO larger than 12.5 and for values of the ratio τ t CH larger than 0.1. For such cases, the effective reaction rates are slower than if the chemical species are assumed to be uniformly mixed.

Key words

Second-order modelling technique turbulence pollutants 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bilger, R. W., 1989, Turbulent diffusion flames,Ann. Rev. Fluid Mech. 21, 101–135.Google Scholar
  2. Builtjes, P. J. H. and Talmon, A. M., 1987, Macro- and micro-scale mixing in chemical reactive plumes,Boundary-Layer Meteorol. 41, 417–426.Google Scholar
  3. Caughey, S. J., Wyngaard, J. C., and Kaimal, J. C., 1979, Turbulence in the evolving stable boundary layer,J. Atmos. Sci. 6, 1041–1052.Google Scholar
  4. Csanady, G. T., 1973,Turbulent Diffusion in the Environment, D. Reidel, Dordrecht, The Netherlands.Google Scholar
  5. Danckwerts, P. V., 1952, The definition and measurement of some characteristics of mixtures,Appl. Sci. Res. A3, 279–296.Google Scholar
  6. Donaldson, C. du P. and Hilst, G. R., 1972, Effect of inhomogeneous mixing on atmospheric photochemical reactions,Environ. Sci. Technol. 6, 812–816.Google Scholar
  7. Fitzjarrald, D. R. and Lenschow, D. H., 1983, Mean concentration and flux profiles for chemically reactive species in the atmospheric surface layer,Atmos. Environ. 17, 2505–2512.Google Scholar
  8. Georgopoulos, P. G. and Seinfeld, J. H., 1986, Mathematical modeling of turbulent reacting plumes. I General theory and model formulation,Atmos. Environ. 20, 1791–1807.Google Scholar
  9. Gao, W., Wesley, M. L., and Lee, I. Y., 1991, A numerical study of the effect of air chemistry on fluxes of NO, NO2 and O3 near the surface,J. Geophys. Res. 96, 18,761–18,769.Google Scholar
  10. Hong, M. S. and Carmichael, G. R., 1983, An investigation of sulfate production in clouds using a flow-through chemical reactor model approach,J. Geophys. Res. 88, 10,733–10,743.Google Scholar
  11. Ibrahim, S. S., Bilger, R. W., and Mudford, N. R., 1987, Turbulence effects on chemical reactions in smog chamber flows,Atmos. Environ. 21, 2609–2621.Google Scholar
  12. Janssen, L. H. J. M., Nieuwstadt, F. T. M., and Donze, M., 1990, Time scales of physical and chemical processes in chemically reactive plumes,Atmos. Environ. 24A, 2861–2874.Google Scholar
  13. Komori, S., Hunt, J. C. H., Kanzaki, T., and Murakami, Y., 1991, The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows,J. Fluid Mech. 228, 629–659.Google Scholar
  14. Nieuwstadt, F. T. M., 1984, The turbulent structure of the stable, nocturnal boundary layer,J. Atmos. Sci. 41, 2202–2216.Google Scholar
  15. Panofsky, H. A. and Dutton, J. A., 1984,Atmospheric Turbulence, Wiley, New York.Google Scholar
  16. Schumann, U., 1989, Large-eddy simulation of turbulent diffusion with chemical reactions in the convective boundary layer,Atmos. Environ. 23, 1713–1727.Google Scholar
  17. Vilà-Guerau de Arellano, J. and Duynkerke, P. G., 1992, The influence of chemistry on the flux-gradient relationships in the NO-O3-NO2 system,Boundary-Layer Meteorol. (in press).Google Scholar
  18. Vilà-Guerau de Arellano, J., Duynkerke, P. G., Jonker, P. J., and Builtjes, P. J. H., 1992a, An observational study on the effects of time and space averaging in photochemical models,Atmos. Environ. (in press).Google Scholar
  19. Vilà-Guerau de Arellano, J., Duynkerke, P. G., and Builtjes, P. J. H., 1992b, The divergence of the turbulent diffusion flux due to chemical reactions in the surface layer,Tellus B (in press).Google Scholar
  20. Vilà-Guerau de Arellano, J., Talmon, A., and Builtjes, P. J. H., 1990, A chemically reactive plume model for the No-NO2-O3 system,Atmos. Environ. 24A, 2237–2246.Google Scholar
  21. Wyngaard, J. C., 1982, Boundary-layer modeling, in F. T. M. Nieuwstadt and H. van Dop (eds.),Atmospheric Turbulence and Air Pollution Modelling, D. Reidel, Dordrecht, The Netherlands.Google Scholar
  22. Wyngaard, J. C., Coté, O. R., and Rao, S. R., 1974, Modeling the atmospheric boundary layer,Adv. Geophys. 18A, 193–212.Google Scholar
  23. Wyngaard, J. C. and Coté, O. R., 1971, The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer,Boundary-Layer Meteorol. 9, 441–460.Google Scholar
  24. Zeman, O., 1981, Progress in the modeling of planetary boundary layers,Ann. Rev. Fluid. Mech. 13, 253–272.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Jordi Vilà-Guerau de Arellano
    • 1
  • Peter G. Duynkerke
    • 1
  1. 1.Institute for Marine and Atmospheric ResearchUtrecht UniversityThe Netherlands

Personalised recommendations