Extended Theory of Hydraulic Hysteresis in Open-Channel Flow

The occurrence of hysteresis in a supercritical, open-channel flow approaching an obstacle has been recognized and investigated both experimentally and theoretically over the last few decades. However, the available theory and experimental investigations in the literature do not include the case when subcritical flow, controlled from downstream, can establish across the obstacle. The present work fills this gap by proposing a new theory that includes this occurrence and shows that two different steady flow states can establish for the same obstacle geometry and flow conditions—one with supercritical to subcritical transition far downstream from the obstacle, and the other with supercritical to subcritical transition far upstream from the obstacle. The proposed, more general theory includes the existing theory as a special case. Finally, two specific examples are illustrated and discussed, i.e., the case of flow over a raised bed hump, and the case of flow through a channel contraction.