Fundamentals of Fluvial Geomorphology and Channel Processes
The radius of curvature (r) is the radius of the circle defining the curvature of an individual bend
measured between adjacent inflection points (Figure 3.9). The arc angle ( ) is the angle swept out by the
radius of curvature between adjacent inflection points. The radius of curvature to width ratio (r/w) is a very
useful parameter that is often used in the description and comparison of meander behavior, and in
particular, bank erosion rates. The radius of curvature is dependent on the same factors as the meander
wavelength and width. Meander bends generally develop a radius of curvature to width ratio (r/w) of 1.5
to 4.5, with the majority of bends falling in the 2 to 3 range.
3.1.3.4 Channel Slope
The slope (longitudinal profile) of a stream is one of the most significant parameters in the study
and discussion of river behavior. Slope is one of the best indicators of the ability of the river to do work.
Rivers with steep slopes are generally much more active with respect to bank erosion, bar building,
sediment movement, etc., than lower slope channels.
Slope can be defined in a number of ways. If sufficient data exists, the water surface slope may be
calculated using stage readings at gage locations along the channel. However, in many instances,
particularly in small streams, gage information is non-existent. In these cases, the thalweg slope is generally
calculated. Thalweg refers to the deepest point in a cross section. The thalweg slope not only provides
a good expression of the energy of the stream, but also may aid in locating areas of scour and fill, geologic
controls, and outcrops of non-erodible materials.
3.1.4
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 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 3.10 and 3.11. 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 planforms. 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 3.11 might be shifted to point `B' if the
slope is increased due to the construction of man-made cutoffs.
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