3.3.3 Plane Bed Without Sediment Movement
Plane bed without movement has been studied to determine the bed configuration that would
form after beginning of motion. After the beginning of motion, for flat slopes and low velocity,
the plane bed will change to ripples for sand material smaller than 0.6 mm, and to dunes for
coarser material. Resistance to flow is small for a plane bed without sediment movement
and is due solely to the sand grain roughness. Values of Manning's n range from 0.012 to
0.014 depending on the size of the bed material.
If the bed material of a stream is not moving, the bed configuration will be a remnant of the
bed configuration formed when sediment was moving. The bed configurations after the
beginning of motion may be those illustrated in Figure 3.5, depending on the flow and bed
material. Prior to the beginning of motion, the problem of resistance to flow is one of
rigid-boundary hydraulics. After the beginning of motion, the problem relates to defining bed
configurations and resistance to flow.
Ripples are small triangle-shaped elements having gentle upstream slopes and steep
downstream slopes. Length ranges from 0.12 m to 0.6 m (0.4 ft to 2 ft) and height from 0.01
m to 0.06 m (0.03 ft to 0.2 ft) (Figure 3.5). Resistance to flow is relatively large (with
Manning's n ranging from 0.018 to 0.030). There is a relative roughness effect associated
with a ripple bed and the resistance to flow decreases as flow depth increases. The ripple
shape is independent of sand size and at large values of Manning's n the magnitude of grain
roughness is small relative to the form roughness. The length of the separation zone
downstream of the ripple crest is about ten times the height of the ripple. Ripples cause very
little, if any, disturbance on the water surface, and the flow contains very little suspended bed
material. The bed material discharge concentration is small, ranging from 10 to 200 ppm.
When the shear stress or the stream power is increased for a bed having ripples (or a plane
bed without movement, if the bed material is coarser than 0.6 mm), sand waves called dunes
form on the bed. At smaller shear-stress values, the dunes have ripples superposed on their
backs. These ripples disappear at larger shear values, particularly if the bed material is
coarse sand with D50 > 0.4 mm.
Dunes are large triangle-shaped elements similar to ripples (Figure 3.5). Their lengths range
from 0.6 m (2 ft) to many tens of meters (hundreds of feet), depending on the scale of the
flow system. Dunes that formed in the 2.4 m (8-foot) wide flume used by Simons and
Richardson (1963, 1966) ranged from 0.6 to 3 m (2 to 10 ft) in length and from 0.06 to 0.3 m
(0.2 to 1 ft) in height; whereas, those described by Carey and Keller (1957) in the Mississippi
River were 100 to 200 m (300 to 700 ft) long and as much as 12 m (40 ft) high. The
maximum amplitude to which dunes can develop is approximately the average depth.
Hence, in contrast with ripples, the amplitude of dunes can increase with increasing depth of
flow. With dunes, the relative roughness can remain essentially constant or even increase
with increasing depth of flow.