The SAM program assigns 20 base widths for the calculation, each with an
increment of 0.1B. Calculations for these conditions are displayed as output.
Stability curves can then be plotted from these data.
A solution for minimum stream power is also calculated by the model. This
solution represents the minimum slope that will transport the incoming sediment
load. Solution for minimum slope is obtained by using a second-order
Lagrangian interpolation scheme. Opinions are divided regarding the use of
minimum stream power to uniquely define channel stability.
An optional use of the analytical method is to assign a value for slope, thereby
obtaining unique solutions for width and depth. Typically there will be two
solutions for each slope.
Meander Program
Langbein and Leopold (1966) proposed the sine-generated curve as an
analytical descriptor for meander planform in sand-bed rivers. Their "theory of
minimum variance" is based on the hypothesis that the river will seek the most
probable path between two fixed points, which is described by the following
equation:
2 sπ
φ = ω cos
Equation 2-57
M
where:
φ=
angle of the meander path with the mean longitudinal axis
ω=
maximum angle a path makes with the mean longitudinal axis
s =
the curvilinear coordinate along the meander path
M=
the meander arc length
These variables are shown in Figure 2.11.
Meander planform may thus be described with a shape parameter, ω, and a
scale parameter, M. The sine generated curve has been shown to effectively
replicate meander patterns in a wide variety of natural rivers. (Langbein and
Leopold, 1966)
The purpose of the meander algorithm in SAM is to provide both curvilinear
and Cartesian coordinates for a meander planform based on the sine-generated
curve. Required input are the meander arc length, M, and the meander wave
length, λ. The meander arc length can be determined from the valley slope, the
meander wave length, and the design stable channel slope.
45
Chapter 2
Theoretical Basis for SAM.hyd Calculations
Previous Page
