An approximate model of de Saint-Venant equations is proposed to study the motion of a flood wave down a channel. Its validity is not restricted to mild bottom slopes and the resulting parabolic equation can be integrated even if the variation of the wave speed with the flow rate is taken into account.
The phenomenon of the free overfall at the sharp drop of a channel bed has been deeply investigated experimentally since the pioneering work of Rouse (1933). Its behaviour is well known at least in the usual case of a wide rectangular channel. However, no complete theoretical solution has yet been obtained. Assuming the steady flow to be two-dimensional, irrotational and frictionless, an analytical solution for the flow field is obtained accounting for the presence of two free boundaries. By applying...
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