Birth of a hydraulic jump

The hydraulic jump, i.e., the sharp transition between a supercritical and a subcritical free-surface flow, has been extensively studied in the past centuries. However, ever since Leonardo da Vinci asked it for the first time, an important question has been left unanswered: How does a hydraulic jump form? We present an experimental and theoretical study of the formation of stationary hydraulic jumps in centimeter wide channels. Two starting situations are considered: The channel is, respectively, empty or filled with liquid, the liquid level being fixed by the wetting properties and the boundary conditions. We then change the flow-rate abruptly from zero to a constant value. In an empty channel, we observe the formation of a stationary hydraulic jump in a two-stage process: First, the channel fills by the advancing liquid front, which undergoes a transition from supercritical to subcritical at some position in the channel. Later the influence of the downstream boundary conditions makes the jump move slowly upstream to its final position. In the pre-filled channel, the hydraulic jump forms at the injector edge and then moves downstream to its final position.