Author(s): Susin Francesca Maria; Defina Andrea
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Keywords: Stability; Hydraulic jump; Upward sloping channel
Abstract: In this note, the physical reason why friction enhances the stability of a hydraulic jump in a prismatic channel of non-negligible adverse slope is theoretically investigated. The approach outlined by Defina and Susin (2003), which used the flow momentum function to describe the phenomenon of jump stability, is here further developed in both graphical and analytical terms. It is shown that the behaviour of the jump depends on the ratio between the slope of the supercritical upstream flow to that of the subcritical downstream flow, evaluated at the stationary equilibrium position of the jump. The case of a wide rectangular channel with flow regime from hydraulically smooth to fully rough is examined in detail. The results show that jump stability is affected by the rates at which upstream and downstream free surface slopes change due to friction. In particular, the higher is friction the ‘m ore stable’ is the jump, since a higher flow resistance increases the rate of growth of the rapid flow depth more than it reduces the rate of decrease of the tranquil flow depth.
Year: 2007