where:
k
=
0.0041 SI
k
=
0.010 English
the sandbed river is braided. In these equations, S is the channel slope in m/m (ft/ft) and Q is
3
3
0.025
the mean discharge in m /s (ft /s). Between these values of S Q
is the transitional range.
Many of the U.S. rivers, classified as intermediate sandbed streams, plot in this zone. If a river
is meandering but its discharge and slope border on the transitional zone a relatively small
increase in channel slope may cause it to change to a transitional or braided river.
Leopold and Wolman (1960) plotted slope and discharge for a variety of natural streams. They
observed that a line could separate meandering from braided streams (Figures 18a and b).
The equation of this line is:
SQ0.44 = k
(5.3)
where:
S
=
Slope in m/m (ft/ft)
3
3
Bank-full discharge is m /s (ft /s)
Q
=
k
=
0.0125 SI
k
=
0.06 English
Streams classified as meandering by Leopold and Wolman are those whose sinuosity is
greater than 1.5. Braided streams are those which have relatively stable alluvial islands and,
therefore, two or more channels. Leopold and Wolman note that sediment size is related to
slope and channel pattern, but they do not try to account for the effect of sediment size on the
morphology of the streams. They further note that braided and meandering streams can be
differentiated based on combinations of slope, discharge, and width/depth ratio, but regard the
width as a variable dependent on mainly discharge.
Leopold and Wolman recognize that their analysis treats only two of the many variables
affecting morphology, therefore, they do not expect this method to apply in every condition.
However, because the data were all taken from natural streams, and because the analysis
obviously does indicate a significant relation between slope and discharge, the analysis should
give a reasonably effective prediction of channel pattern if slope and discharge are known.
Problem 1 in Section 5.9 gives an example of this type of prediction and Section 5.5.3 uses
these concepts in an engineering geomorphic analysis.
5.4.6 Hydraulic Geometry of Alluvial Channels
Hydraulic geometry is a general term applied to alluvial channels to denote relationships
between discharge Q and the channel morphology, hydraulics and sediment transport.
Channels forming in their own sediments are called alluvial channels. In alluvial channels, the
morphologic, hydraulic and sedimentation characteristics of the channel are determined by a
large variety of factors. The mechanics of such factors are not fully understood. However,
alluvial streams do exhibit some quantitative hydraulic geometry relations. In general, these
relations apply to channels within a physiographic region and can be obtained from data
available on gaged rivers. It is understood that hydraulic geometry relations express the
integral effect of all the hydrologic, meteorologic, and geologic variables in a drainage basin for
in-bank flows.
5.23
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