Multiple states in the flow through a sluice gate

This paper addresses the problem of hydraulic hysteresis for a supercritical open channel flow approaching a sluice gate when subcritical flow can establish downstream, against the gate. The possible flow configurations across the gate are classified on the basis of the Froude number of the incoming and downstream flows, and of the ratio of gate opening to the upstream supercritical flow depth. Within the above parameter space, two regions exist in which the problem admits a dual solution, that is, two different flow configurations can establish for the same gate opening and undisturbed flow conditions. In one of these regions, both smooth flow (i.e. the fluid flows under the gate without interacting with the gate) and free outflow conditions can establish; in the other region, both smooth flow and submerged flow can establish. For flow conditions in the above regions, the configuration that actually establishes depends on the previous history of the flow, thus implying the hysteretic character of the flow.