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Lagrangian similarity hypothesis applied to diffusion in turbulent shear flow

Published online by Cambridge University Press:  28 March 2006

J. E. Cermak
J. E. Cermak
Affiliation:
College of Engineering, Colorado State University
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Abstract

The concept suggested by Batchelor that motion of a marked particle in turbulent shear flow may be similar at stations downstream from the point of release is applied to a variety of diffusion data obtained in the laboratory and in the surface layer of the atmosphere. Two types of shear flow parallel to a plane solid boundary are considered. In the first case mean velocity is a linear function of log z (neutral boundary layer) and in the second case the mean velocity is slightly perturbed from the logarithmic relationship by temperature variation in the z-direction (diabatic boundary layer). Besides the parameters introduced in previous applications of the Lagrangian similarity hypothesis to turbulent diffusion, the ratio of source height to roughness length h/z0 is shown to be of major importance. Predictions of the variation of maximum ground-level concentration for continuous point and line sources and the variation of plume width for a continuous point source with distance downstream from the source agree with the assorted data remarkably well for a range of length scales extending over three orders-of-magnitude. It is concluded that results from application of the Lagrangian similarity hypothesis are significant for the laboratory modelling of diffusion in the atmospheric surface layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 15 , Issue 1 , January 1963 , pp. 49 - 64
Copyright
© 1963 Cambridge University Press

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