Brock, Richard R. (1967) Development of roll waves in open channels. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechKHR:KHR16

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Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This study is concerned with some of the properties of roll waves that develop naturally from a turbulent uniform flow in a wide rectangular channel on a constant steep slope. The wave properties considered were depth at the wave crest, depth at the wave trough, wave period, and wave velocity. The primary focus was on the mean values and standard deviations of the crest depths and wave periods at a given station and how these quantities varied with distance along the channel. The wave properties were measured in a laboratory channel in which roll waves developed naturally from a uniform flow. The Froude number F (F = u /sqrt(gh[sub n]), u[sub n] = normal velocity, h[sub n] = normal depth, g = acceleration of gravity) ranged from 3.4 to 6.0 for channel slopes S[sub 0] of .05 and . 12 respectively. In the initial phase of their development the roll waves appeared as small amplitude waves with a continuous water surface profile. These small amplitude waves subsequently developed into large amplitude shock waves. Shock waves were found to overtake and combine with other shock waves with the result that the crest depth of the combined wave was larger than the crest depths before the overtake. Once roll waves began to develop, the mean value of the crest depths h[sub max] increased with distance. Once the shock waves began to overtake, the mean wave period T[sub av] increased approximately linearly with distance. For a given Froude number and channel slope the observed quantities hbar[sub max] /h[sub n], T' (T' = S[sub 0] T[sub av] sqrt(gh[sub n])), and the standard deviations of hbar[sub max] /h[sub n] and T', could be expressed as unique functions of l /h[sub n] (l = distance from beginning of channel) for the twofold change in h[sub n] occurring in the observed flows. A given value of hbar[sub max]/h[sub n] occurred at smaller values of l/h[sub n] as the Froude number was increased. For a given value of hbar[sub max] /h[sub n] the growth rate d hbar[sub max]/d l of the shock waves increased as the Froude number was increased. A laboratory channel was also used to measure the wave properties of periodic permanent roll waves. For a given Froude number and channel slope the h[sub max] /h [sub n] vs. T' relation did not agree with a theory in which the weight of the shock front was neglected. After the theory was modified to include this weight, the observed values of h[sub max] /h[sub n] were within an average of 6.5 percent of the predicted values, and the maximum discrepancy was 13.5 percent. For hbar[sub max] /h[sub n] sufficiently large (hbar[sub max] /h[sub n] > approximately 1.5) it was found that the hbar[sub max] /h[sub n] vs. T' relation for natural roll waves was practically identical to the h[sub max] /h[sub n] vs. T' relation for periodic permanent roll waves at the same Froude number and slope. As a result of this correspondence between periodic and natural roll waves, the growth rate d hbar[sub max]/d l of shock waves was predicted to depend on the channel slope, and this slope dependence was observed in the experimen
Item Type:  Report or Paper (Technical Report) 

Group:  W. M. Keck Laboratory of Hydraulics and Water Resources 
Record Number:  CaltechKHR:KHR16 
Persistent URL:  http://resolver.caltech.edu/CaltechKHR:KHR16 
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ID Code:  25977 
Collection:  CaltechKHR 
Deposited By:  Imported from CaltechKHR 
Deposited On:  01 Jun 2004 
Last Modified:  26 Dec 2012 13:50 
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