Fundamentals of Fluvial Geomorphology and Channel Processes
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:
L = 1890 Qm0.34 M-0.74
where Qm is the average annual flow. The width to depth ratio (F) is also related to the percentage silt and
clay:
F = 255 M-1.08
Channel slope (S) was found to be related to the mean annual discharge (Qm) and percentage silt and clay:
S = 60 M-0.38 Qm-0.32
Regime theory is an application of the idea that the width, depth, slope, and planform of a river are
adjusted to a channel-forming discharge. In his review of the history of regime theory, Lane (1955) states
that in 1895 Kennedy proposed the following relationship:
V = cDm
in which V is the mean channel velocity, D is the channel depth, and c and m are constants developed for
various channel locations. Much of the early work in developing regime relationships was conducted in the
irrigation canals of India, and since the early 1900s, many relationships have been proposed.
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