Under natural conditions, a third type of bend is often encountered. This bend occurs when the
stream impinging on a erosion-resistant bank forms a forced curve which is gradually
transformed into a river bend of a more constricted shape. In all cases, the effect of the
character (density) of the bank material is important and, to a certain degree, determines the
radius of curvature of the channel in a free bend. The radius of curvature increases with the
density of the material. Considering both the action of the stream and the interaction between
the stream and the channel, as well as the general laws of their formation, one can distinguish
the following three types of bends of a natural river channel:
1. Free bends - Both banks are composed of alluvial floodplain material which is usually quite
mobile; the free bend corresponds to the common concept of a surface bend;
2. Limited bends - The banks of the stream are composed of consolidated parent material
which limits the lateral erosion by the stream. Limited bends are entrenched bends; and
3. Forced bends - The stream impinges onto an almost straight parent bank at a large angle
(60 to 90).
A typical feature of bends is a close relationship between the type of stream bend and the radius
of curvature. The forced bend has the smallest radius of curvature. Next in size are the radii of
free bends. The limited bends have the greatest radii. The average values of the ratios of the
radii of curvature to the width of the stream at bankfull stage for the three types of bends are: (1)
free bends 4.5 to 5.0; (2) limited bends 7.0 to 8.0; and (3) forced bends 2.5 to 3.0.
A second characteristic feature of bends is the distribution of depths along the length of the bend.
In free bends and limited bends, the depth gradually increases and the maximum depth is found
some distance below the apex of the bend. In the forced bend, the depth sharply increases at
the beginning of the bend and then gradually diminishes. In forced bends the greatest depth is
located in the middle third of the bend, where there appears to be a concentrated deep scour
hole.
2.7.2 Transverse Velocity Distribution in Bends
The transverse velocities in bends result from an imbalance of radial pressures on a particle of
fluid traveling around the bend. In Figure 2.26, a cross section through a typical bend is shown.
The radial forces acting on the shaded control volume are the centrifugal force mv2/r in which r is
the radius of curvature, and the differential hydrostatic force γdz caused by the superelevation of
the water surface dz. As shown in Figure 2.26a, the centrifugal force is greater near the surface
where the fluid velocity v is greater and less at the bed where v is small. The differential
hydrostatic force is uniform throughout the depth of the control volume. As shown in Figure
2.26b, the sum of the centrifugal and excess hydrostatic forces varies with depth and can cause
a lateral velocity component. The magnitude of the transverse velocity is dependent on the
radius of curvature and on the proximity of the banks. In the immediate vicinity of the banks,
there can be no lateral velocity if the river is narrow and deep.
2.46
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