Multiple states in open channel flow

Steady flow regimes in a free surface flow approaching an obstacle are described and extensively discussed. Attention is focused on the phenomenon of hydraulic hysteresis, and a simple one-dimensional theory to predict its occurrence in a supercritical channel flow is proposed. It is shown that in many cases knowledge of the Froude number of the undisturbed approaching flow and of a geometric characteristic of the obstacle allows for a reliable prediction of the flow state. In the region of multiple regimes, however, the previous history of the flow must also be known. Three different obstacles in a rectangular channel are considered, namely a sill, a vertical sluice gate, and a circular cylinder, and the theoretical boundaries of the hysteresis region are specified for each obstacle. The experimental results show that the theoretical predictions are consistent with experiments in the case of obstacles that do not affect channel width (i.e. sills and gates). On the contrary, in the case of channel contraction, a further parameter, which the presented theory does not account for, was found to affect the behavior of the flow, namely the ratio of undisturbed flow depth to contraction width. Finally, in the case of a vertical sluice gate it was found that hysteresis develops in a subcritical undisturbed approaching flow as well.