Diffusion Solutions to Flows with Upstream Control

A diffusion solution to a simplified form of the St. Venant equations is used to predict the passage of a flood wave along the Clutha River in New Zealand. Hayami’s diffusion analogy is extended to nonprismatic moderately irregular channels with lateral inflows, thus allowing more realistic simulation of floods in natural channels. For waves produced by artificial controls the diffusion theory predicts constant travel times for a given part of any such wave. The extended solution was applied to two floods produced artificially by the operation of hydroelectric station. The first was used as a calibration flood to determine channel constants. These were then used to predict the stage-time curves for the second flood which had a different discharge-time relationship. Excellent agreement between predicted and measured travel times was obtained.