Sediment Movement in Alluvial Rivers - River Dynamics and Integrated River Management - page 278

of the bed material may be taken as the roughness size that characterizes the grain friction. The
roughness size representing the grain friction may be larger even than the particles. Scientists have
pointed out that even for a flat bed, the resistance of a movable stream bed may be quite different from
that on a rigid bed.
In the previous section, the channel bed was shown to take various forms for various flow conditions.
If ripples and dunes form, the flow separation at the peaks makes the pressure on the upstream face larger
than that on the downstream face, and in this way causes form resistance. With antidunes, although the
stream lines near the bed are almost parallel to the bed and are without separation, the water surface
wave corresponding to the antidune can break and cause intensive local turbulence with an increase in
the resistance loss. This kind of extra resistance is called form resistance (Rouse, 1965). The relation
between grain friction and form resistance can be illustrated as follows. For flow passing over a piece of
flat sand paper, the flow encounters only grain friction; if, however, the sand paper has a wavy shape, the
flow encounters not only grain friction, but also form resistance.
The materials of river banks and floodplains are normally finer than the bed material. On the floodplains
that are usually above the water level of normal floods, grasses and bushes often grow. The roughness
due to them not only changes with their characteristics, density, stem height, and season, but it is also
affected by the depth and velocity of the flow. In a shallow flow with a low velocity, the stems of grasses
and bushes are erect, and they offer the maximum resistance to the flow. If the water depth and velocity
are somewhat higher, the stems often bend down so that the flow area encountering resistance is less, and
the bank and floodplain resistances are correspondingly less. At high flows, the grasses and bushes tend
to lie flat on the bed, and the roughness is nearly constant and it changes very little with the discharge. If
the bank is protected or lined, its roughness is unaffected by vegetation.
The friction loss is also affected by the shape of a channel. For channels with sand bars, the flow can
be braided or meandering; the flow width is then variable and the resistance to flow is high. The resistance
is proportional to the square of velocity for flow in an open channel with a regular shape. But if a river
meanders and the flow Froude number exceeds a critical value, the resistance can be much higher and
would no longer follow the square law. A low flow tends to be meandering, and a high flow tends to be
straight. The channel form resistance for low flows, therefore, is higher than that for high flow.
Artificial structures built along a stream, like training and bank protection works, bridges, etc., tend to
create local resistance. The magnitude depends on the shape, size, and orientation of the structure. Due to
the complexity and variability of components of the friction loss in alluvial streams, and to the changeable
property of resistance for flow carrying sediment, a unified understanding of resistance in alluvial streams
does not exist at present.
Scientists use head loss and the Weisbach friction factor, f , to approach the resistance of open channel
flows, in the following way

2

U

(5.26)

h L f L

8 gR

where L is the distance of the flow and h L is the head loss for the flow over the distance. The energy
slope is given by the ratio of J = h L /L . For steady and uniform flows, the energy slope is equal to the bed
slope, and the formula can be transformed into the expression of the Weisbach friction factor
f 8 sgR / U 2 (5.27)

However, hydraulic engineers typically prefer the Manning roughness coefficient, n , to represent
the resistance of flow. In the calculation of the average velocity the Manning formula has been widely
accepted: