Theoretical model for the onset condition of a steady hydraulic jump

A hydraulic jump constitutes a transition from supercritical to subcritical flow. At the jump a roller forms, the water level suddenly increases, the flow velocity reduces, and power is dissipated. The type of hydraulic jump varies with the upstream Froude number. Experimental observations showed that for Froude numbers below F1 = 4.5 the jump is unstable and oscillatory, and from this value onwards it becomes steady. In this article, a novel theoretical model of the hydraulic jump is described which allows the transition point to be determined theoretically. The simple model assumes the power dissipation to occur through a counteracting moment at the roller. With an extended momentum balance approach, where the moments instead of the forces acting on the control volume are considered, the limit point is determined at F1 = 4.4. This correlates well with the experimentally derived value given in the literature of F1 = 4.5.