On the Flood Waves in a Prismatic Open Channel

Abstract

The unsteady flows in a prismatic open channel are treated by the theoretical analysis of one-dimensional equations of motion and continuity. The author has shown that unsteady flows in a prismatic channel can be classified by an index λ, where λ has the value of the order of the ratio of water stage variation velocity to the vertical component of long wave celerity. The critical value of λ, above which the wave breaks into a bore at the wave front has obtained. Below the critical value, the bore fomation is prevented, and in the case where the value of λi is of the order of unity or larger the wave is propagated as "dynamic" and Saint-Venant's equation must be modified for the effects of vertical acceleration, and if λi <<1 the wave is "kinematic." The author has obtained the second approximation of the kinematic wave in cases where λ<<1 and λi <<1 and has compared the results with those obtained directly by the computer. Then the flood characteristics, such as the variation of wave profile, propagation speed and stage-discharge relationship, are discussed in connection with the appropriate theoretical considerations and experiments.