Abstract
The extension of Lagrangian similarity theory of diffusion to stratified flow is examined, to improve its prediction of the vertical spread of a passive substance. In the basic equation,\(d\bar Z/dt = bu_* \phi (\bar Z/L)\) where\(\bar Z\) is the average height of a cluster of particles,u * is the friction velocity andL is Monin-Obukhov length. It is shown theoretically, under the assumption of an equivalence between the diffusivities of heat and matter, that the unspecified function φ is the reciprocal of a more familiar meteorological parameter φ n , the dimensionless temperature gradient. The universal constantb is found to be approximately equal to von Karman's constant κ for various stability conditions. The predicted effect of stability on vertical spread shows excellent agreement with that of the published data from the O'Neill experiments.
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References
Batchelor, G. K.: 1959, ‘Note on Diffusion from Sources in a Turbulent Boundary Layer’, Unpublished.
Batchelor, G. K.: 1964, ‘Diffusion from Sources in a Turbulent Boundary Layer’,Arch. Mech. Stosowanej 3, 661–670.
Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux-Profile Relationships in the Atmospheric Surface Layer’,J. Atmospheric Sci. 28, 181–189.
Cermak, J. E.: 1963, ‘Lagrangian Similarity Hypothesis Applied to Diffusion in Turbulent Shear Flow’,J. Fluid Mech. 15, 49–64.
Chatwin, P. C.: 1968, ‘The Dispersion of a Puff of Passive Substance in the Constant Stress Region’,Quart. J. Roy. Meterol. Soc. 94, 401–411.
Elliot, W. P.: 1961, ‘The Vertical Diffusion of Gas from a Continuous Source’,Int. J. Air Water Poll. 4, 33.
Gifford, F. A.: 1962, ‘Diffusion in a Diabatic Surface Layer’,J. Geophys. Res. 67, 3207–3212.
Kazanski, A. B. and Monin, A. S.: 1957, ‘The Form of Smoke Jets’,Izv. Akad. Nauk S.S.S.R., Ser. Geofiz. 8, 1020–1033.
Klug, W.: 1968, ‘Diffusion in Atmospheric Surface Layer: Comparison of Similarity Theory with Observation’,Quart. J. Roy. Meteorol. Soc. 94, 555–562.
Monin, A. S.: 1959, ‘Smoke Propagation in Surface Layer of Atmosphere’,Adv. Geophys. 6, 331–343.
Monin, A. S. and Obukhov, A. M.: 1954, ‘Basic Relationships for Turbulent Mixing in the Atmospheric Ground Layer’,Trud. Geofiz. Inst. Akad. Nauk S.S.S.R. 151, 163–187.
Monin, A. S. and Yaglom, A. M.: 1965,Statistical Hydromechanics, Nauka Press, Moscow.
Panofsky, H. A. and Prasad, B.: 1965, ‘Similarity Theory and Diffusion’,Int. J. Air Water Poll. 9, 419–430.
Pasquill, F.: 1966, ‘Lagrangian Similarity and Vertical Diffusion from a Source at Ground Level’,Quart. J. Roy. Meteorol. Soc. 92, 185–195.
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Chaudhry, F.H., Meroney, R.N. Similarity theory of diffusion and the observed vertical spread in the diabatic surface layer. Boundary-Layer Meteorol 3, 405–415 (1973). https://doi.org/10.1007/BF01034984
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DOI: https://doi.org/10.1007/BF01034984