Field observations indicate that dunes can form in any sand channel, irrespective of the size
of bed material, if the stream power is sufficiently large to cause general transport of the bed
material without exceeding a Froude number of unity.
Resistance to flow caused by dunes is large. Manning's n ranges from 0.020 to 0.040. The
form roughness for flow with dunes is equal to or larger than the sand grain roughness.
Dunes cause large separation zones in the flow. These zones, in turn, cause boils to form
on the surface of the stream. Measurements of flow velocities within the separation zone
show that velocities in the upstream direction exist that are l/2 to l/3 the average stream
velocity. Boundary shear stress in the dune trough is sometimes sufficient to form ripples
oriented in a direction opposite to that of the primary flow in the channel. With dunes, as with
any tranquil flow over an obstruction, the water surface is out of phase with the bed surface
(Figure 3.6).
3.3.6 Plane Bed With Movement
As the stream power of the flow increases further, the dunes elongate and reduce in
amplitude. This bed configuration is called the transition or washed out dunes. The next bed
configuration with increased stream power is plane bed with movement. Dunes of fine sand
(low fall velocity) are washed out at lower values of stream power than are dunes of coarser
sand. With coarse sands larger slopes are required to affect the change from transition to
plane bed and the result is larger velocities and larger Froude numbers. In flume studies
with fine sand, the plane-bed condition commonly exists after the transition and persists over
a wide range of Froude numbers (0.3 < Fr < 0.8). If the sand is coarse and the depth is
shallow, however, transition may not terminate until the Froude number is so large that the
subsequent bed form may be antidunes rather than plane bed. In natural streams, because
of their greater depths, the change from transition to plane bed may occur at a much lower
Froude number than in flumes. Manning's n for plane bed sand channels range from 0.010
to 0.013.
3.3.7 Antidunes
Antidunes form as a series or train of inphase (coupled) symmetrical sand and water waves
(Figure 3.5). The height and length of these waves depend on the scale of the flow system
and the characteristics of the fluid and the bed material. In a flume where the flow depth was
about 0.15 m (0.5 ft) deep, the height of the sand waves ranged from 0.01 to 0.15 m (0.03 to
0.5 ft). The height of the water waves was 1.5 to 2 times the height of the sand waves and
the length of the waves, from crest to crest, ranged from 1.5 to 3 m (5 to 10 ft). In natural
streams, such as the Rio Grande or the Colorado River, much larger antidunes form. In
these streams, surface waves 0.6 to 1.5 m (2 to 5 ft) high and 3 to 12 m (10 to 40 ft) long
have been observed.
Antidunes form as trains of waves that gradually build up from a plane bed and a plane water
surface. The waves may grow in height until they become unstable and break like the sea
surf or they may gradually subside. The former have been called breaking antidunes, or
antidunes; and the latter, standing waves. As the antidunes form and increase in height,
they may move upstream, downstream, or remain stationary. Their upstream movement led
Gilbert (1914) to name them antidunes.
3.18
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