Currents and bed load in channel forks and in channel bends

For the central part of channel bends with a relatively small ratio of water depth (D) to width and to radius of curvature (j), the norm in nature, one may use the following simplified formula for determination of the bottom flow deviation angle (j) from the mean flow direction:

tg j = C(D/r)

where the values of the constant C vary somewhat with the roughness, the distribution of longitudinal velocities, and with other factors. In general C ha a value of 10 – 12.

In channel forks as well as in ordinary channel bends where the flow velocities are normally asymmetrically distributed, the shape of the channel cross-sections is usually asymmetric. The highest flow velocities and the greatest depths normally occur near the outside bank, and the bed is mainly sloping from the inside towards the outside. The deviation angle of the bottom currents from the mean flow direction varies with the ratio of water depth to radius of curvature. It will normally also vary both along and across the channels.

As regards the transport direction of bed load, one also has to consider that particles on a sloping bed will have a gravitational force component directed down the slope, equal to m´g sine S, where m´ is the immersed weight of the particles, and S the slope angle of the bed. When this force component has attained a value equal to the transverse fluid-force component directed up the slope, no further net deflection of the bed load takes place towards the inside, which may probably be the case when the bed at channel forks and channel bends has attained a state of temporary equilibrium.

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