Free-surface undulations in open channel flows: undular jumps, undular bores, standing waves
In open channels, slow flow motion is called subcritical or fluvial flow motion, while rapid flows are termed supercritical flows. For intermediate conditions, the flow is said to be critical. Critical flow conditions correspond to a singularity, where the flow depth and velocity are function of the flow rate only, for a given cross-sectional shape. This singularity is unstable and critical flow conditions cannot be sustained over a long distance without the development of free-surface undulations. Undulations are stationary standing waves and they are often observed in hydraulics jumps and positive surges with low inflow Froude numbers. Undular jump A hydraulic jump is a stationary transition from a rapid (supercritical flow) to a slow flow motion (subcritical flow). Although the hydraulic jump was described by LEONARDO DA VINCI, the first experimental investigations were published by Giorgio BIDONE in 1820. It is extremely turbulent and characterised by the development of large-scale turbulence, surface waves and spray, energy dissipation and air entrainment (e.g. CHANSON and BRATTBERG 2000). The large-scale turbulence region is usually called the 'roller'. Experimental observations highlight different types of hydraulic jumps, depending upon the Froude number (footnote (1)) of the upstream flow. An undular hydraulic jump is observed at low Froude numbers (1< Fr <3): looking downstream (Fr=1.2) and sideview (Fr=1.6) (CHANSON and MONTES 1995, MONTES and CHANSON 1998). With increasing Froude numbers, other types of jumps include weak jump, oscillating jump (3.5< Fr <4.5), steady jump and strong jump (Fr >10). These photographs show surfers riding on a hydraulic jump roller in a river in Munich, Germany (Photo No. 1 : flow from right to left, Photo No. 2: looking downstream, Courtesy of Dale YOUNG).