Theoretical investigation of hysteresis loops in free-surface flow under sluice gates for power-law channels

ABSTRACT In the present study, a new theoretical framework and analytical solutions to the problem of hysteresis loops due to hydraulic jump in power-law open channels under supercritical flows are introduced. This investigation primarily focuses on the flow dynamics encountered at a vertical sluice gate across channels of various shapes: rectangular, parabolic, and triangular. By the application of energy and momentum conservation principles, the dual flow configurations emerging under identical initial conditions are shown. An intensive analytical computational analysis led to the development of approximate theoretical models, facilitating the prediction of hysteresis loops for a wide range of Froude numbers and dimensionless channel geometry parameters. Several illustrative examples were treated and the results show a high degree of accuracy of the proposed models in predicting the hysteresis loops. The present research contributes to a novel methodology for enhancing predictions regarding the behavior of supercritical flows and the design of open channels for specific scenarios of the hysteresis phenomenon.