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Relative dispersion of a scalar plume in a turbulent boundary layer

Published online by Cambridge University Press:  02 August 2010

Q. LIAO  and
E. A. COWEN
Q. LIAO*
Affiliation:
Department of Civil Engineering and Mechanics, University of Wisconsin–Milwaukee, Milwaukee, WI 53211, USA
E. A. COWEN
Affiliation:
DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14850, USA
*
†Email address for correspondence: liao@uwm.edu
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Abstract

The relative dispersion of a scalar plume is examined experimentally. A passive fluorescent tracer is continuously released from a flush-bed mounted source into the turbulent boundary layer of a laboratory-generated open channel flow. A two-dimensional particle image velocimetry–laser-induced florescence (PIV–LIF) technique is applied to measure the instantaneous horizontal velocity and concentration fields. Measured results are used to investigate the relationship between the boundary-layer turbulence and the evolution of the distance-neighbour function, namely the probability density distribution of the separation distance between two marked fluid particles within a cloud of particles. Special attention is paid to the hypothesis that a diffusion equation can describe the evolution of the distance-neighbour function. The diffusion coefficient in such an equation, termed the ‘relative diffusivity’, is directly calculated based on the concentration distribution. The results indicate that the relative diffusivity statistically depends on particle separation lengths instead of the overall size of the plume. Measurements at all stages of the dispersing plume collapse onto a single curve and follow a 4/3 power law in the inertial subrange. The Richardson–Obukhov constant is estimated from the presented dataset. The relationship between the one-dimensional (1D) representation of the distance-neighbour function and its three-dimensional (3D) representation is discussed. An extended model for relative diffusivity beyond the inertial subrange is proposed based on the structure of the turbulent velocity field, and it agrees well with measurements. The experimental evidence implies that, while the diffusion of the distance-neighbour function is completely determined by the underlying turbulence, the overall growth rate of the plume is affected by both the turbulent flow and its actual concentration distribution.

JFM classification

Turbulent Flows: Turbulent boundary layers Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 661 , 25 October 2010 , pp. 412 - 445
Copyright
Copyright © Cambridge University Press 2010

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