Hysteretic behavior of the flow under a vertical sluice gate

In the paper, the phenomenon of hysteresis which can develop in a supercritical channel flow approaching an obstacle is analyzed, and a simple theory to predict the occurrence of hysteresis is described. The results of an in-depth theoretical and experimental study of the case of flow under a vertical sluice gate in a rectangular channel are then presented. Possible flow regimes in the vicinity of a gate are classified on the basis of the nondimensional gate opening and the Froude number of the undisturbed approaching flow. It is shown that within a wide range of flow parameters both undisturbed and free outflow conditions may exist for the same gate opening. Within this range, the actual regime depends on the previous history of the flow, thus implying the hysteretic character of the flow. It is worth noting that a subcritical approaching flow may also exhibit such a hysteretic behavior provided the Froude number is greater than approximately 0.8. This occurrence, which has not previously been reported in the literature, is probably a result of the contraction affecting the flow issuing from under the gate. The results of an extensive series of experiments, performed over a wide range of flow parameters, are detailed in the paper and confirm theoretical predictions.