Fundamentals of Fluvial Geomorphology and Channel Processes
2.1.5 RELATIONSHIPS IN RIVERS
One interesting aspect of meandering rivers is the similarity in the proportion of
planform characteristics. Various empirical relationships have been developed which relate
radius of curvature and meander wavelength to channel width and discharge. Brice (1984)
suggested that these similarities regardless of size, account for the fact that the meandering
planform is sensibly independent of scale. In other words, if scale is ignored all meandering
rivers tend to look alike in plan view. This fact provides us with a glimmer of hope that we
might be able to develop some relationships to help explain the behavior of complex river
systems.
Investigation by Lane (1957) and Leopold and Wolman (1957) showed that the
relationships between discharge and channel slope can define thresholds for indicating which
rivers tend to be braided or meandering, as shown in Figures 2.10 and 2.11. Lane's
relationship is somewhat more realistic because an intermediate range is included; however,
both relationships are very similar in the variables used and the appearance of the graphs.
Rivers that are near the threshold lines may exhibit segments that transitions between the two
plan forms. These relationships can be useful if the planform of a river is to be changed. For
instance, a meandering river positioned at point `A' in Figure 2.11 might be shifted to point
`B' if the slope is increased due to the construction of man-made cutoffs. Shifting the channel
into the transition zone would cause some concern about the possibility of the channel
becoming braided.
Another set of empirical relationships is related to meander geometry. Leopold et al.
(1964) reported the relationship between meander wave length (L) and channel width (w),
meander amplitude (A) and channel width (w), and meander wave length (L) and bendway
radius of curvature (Rc ) as defined by Leopold and Wolman (1960). The relationships are:
L = 10.9 w1.01
A = 2.7 w1.1
L = 4.7 Rc0.98
Leopold et al. (1964) stated that the exponents for the relationships are approximately
unity, and these relationships can be considered linear. Also, they pointed out that channel
meander form is affected by the cohesiveness of the channel boundaries. Dury (1964) found
that meander wave length is related to the mean annual flood (Qma ):
L = 30 Qma0.5
Schumm (1960, 1977) investigated the effect of the percentage silt and clay (M) in
the stream boundaries and reported the following relationship for meander wave length:
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