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A simple and unifying physical interpretation of scalar fluctuation measurements from many turbulent shear flows

Published online by Cambridge University Press:  26 April 2006

P. C. Chatwin  and
Paul J. Sullivan
P. C. Chatwin
Affiliation:
Department of Mathematics and Statistics, Brunei University, Uxbridge, UBS 3PH, UK
Paul J. Sullivan
Affiliation:
Department of Applied Mathematics, University of Western Ontario. London, Canada N6A 5B9
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Abstract

It is shown that measurements of the statistical properties of the concentration distributions of dispersing scalars taken from many different turbulent shear flows have a great number of common features. In particular the same simple relationship between the mean concentration and the mean-square fluctuation is shown to hold in all the flows, and this relationship is derived theoretically from well-known results for the unreal case when there is no molecular diffusion by a natural hypothesis about the effects of molecular diffusion. Application of the hypothesis to the higher moments and shape parameters gives results that agree reasonably well with the data (given the unavoidable experimental errors). The hypothesis should be subjected to further experimental analysis, and could simplify the application of turbulence closures and similar models. Extensions of the ideas to the probability density function of the scalar concentration suggest that it becomes self-similar. A final conclusion is that more attention to experimental errors due to instrument smoothing is highly desirable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 533 - 556
Copyright
© 1990 Cambridge University Press

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