Fischer, Hugo B. (1966) Longitudinal dispersion in laboratory and natural streams. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechKHR:KHR12

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Abstract
This study concerns the longitudinal dispersion of fluid particles which are initially distributed uniformly over one cross section of a uniform, steady, turbulent open channel flow. The primary focus is on developing a method to predict the rate of dispersion in a natural stream. Taylor's method of determining a dispersion coefficient, previously applied to flow in pipes and twodimensional open channels, is extended to a class of threedimensional flows which have large widthtodepth ratios, and in which the velocity varies continuously with lateral crosssectional position. Most natural streams are included. The dispersion coefficient for a natural stream may be predicted from measurements of the channel crosssectional geometry, the crosssectional distribution of velocity, and the overall channel shear velocity. Tracer experiments are not required. Large values of the dimensionless dispersion coefficient D / rU* are explained by lateral variations in downstream velocity. In effect, the characteristic length of the cross section is shown to be proportional to the width, rather than the hydraulic radius. The dimensionless dispersion coefficient depends approximately on the square of the width to depth ratio. A numerical program is given which is capable of generating the entire dispersion pattern downstream from an instantaneous point or plane source of pollutant. The program is verified by the theory for twodimensional flow, and gives results in good agreement with laboratory and field experiments. Both laboratory and field experiments are described. Twentyone laboratory experiments were conducted: thirteen in twodimensional flows, over both smooth and roughened bottoms; and eight in threedimensional flows, formed by adding extreme side roughness to produce lateral velocity variations. Four field experiments were conducted in the GreenDuwamish River, Washington. Both laboratory and flume experiments prove that in threedimensional flow the dominant mechanism for dispersion is lateral velocity variation. For instance, in one laboratory experiment the dimensionless dispersion coefficient D/rU* (where r is the hydraulic radius and U* the shear velocity) was increased by a factor of ten by roughening the channel banks. In threedimensional laboratory flow, D/rU* varied from 190 to 640, a typical range for natural streams. For each experiment, the measured dispersion coefficient agreed with that predicted by the extension of Taylor's analysis within a maximum error of 15%. For the GreenDuwamish River, the average experimentally measured dispersion coefficient was within 5% of the prediction.
Item Type:  Report or Paper (Technical Report) 

Group:  W. M. Keck Laboratory of Hydraulics and Water Resources 
Record Number:  CaltechKHR:KHR12 
Persistent URL:  http://resolver.caltech.edu/CaltechKHR:KHR12 
Usage Policy:  You are granted permission for individual, educational, research and noncommercial reproduction, distribution, display and performance of this work in any format. 
ID Code:  25984 
Collection:  CaltechKHR 
Deposited By:  Imported from CaltechKHR 
Deposited On:  14 Jun 2004 
Last Modified:  26 Dec 2012 13:50 
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