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Crane, G., H.A. Panofsky, and O. Zeman, 1977: A model for dispersion from area sources in convective turbulence. Atmos. Environ., 11, 893-900, doi:10.1016/0004-6981(77)90018-X.
Vertical mixing coefficients have been computed by integrating vertically changes of concentrations of nonreactive pollutants along horizontal trajectories, during convective conditions.
Mixing coefficients are obtained for three separate periods, and analyzed according to the hypothesis of convective similarity. It was found that normalized mixing coefficients could be represented as "universal" functions of the ratio of the height to the mixing depth. These functions were small at small z and large z and reach a maximum at about half the mixing depth. In fact, the K-coefficients are so large in the middle of the boundary layer, that the concentrations there are effectively independent of height.
In the surface layer, the mixing coefficients agree with the hypothesis that mixing coefficients for contaminants equal mixing coefficients for momentum (eddy viscosity). The observed universal functions also agreed fairly well with predictions made by Lumley and Zeman from second-order closure theory. However, laboratory measurements indicate larger mixing coefficients. It is suggested that K-values estimated both from second-order closure theory and from Los Angeles measurements are systematically underestimated. Nevertheless, it seems likely that K-theory is useful for determining pollutant concentrations from large, continuous area sources at the ground, under convective conditions.
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