Hydraulic jump

Open-channel flow is commonly characterized by the Froude number, which compares flow speed with the speed of surface gravity waves. In supercritical flow, the Froude number exceeds one and surface disturbances cannot propagate upstream; subcritical flow has a Froude number below one. A hydraulic jump forms when conditions force a rapid transition from the former state to the latter. The water surface rises abruptly, often with a visible turbulent roller, waves and entrained air. The jump is not a wave moving along the channel but a localized change in flow depth and regime.

For a given channel and inflow, the deeper downstream flow is related to the shallower upstream flow through conservation of momentum; for a rectangular channel this relation is commonly expressed as the Bélanger equation using the upstream Froude number. Across the jump, mechanical energy is not conserved: intense turbulence, mixing and air-water motion dissipate a portion of it. The detailed structure can be complex, and observed jump shape and stability depend on inflow conditions, channel geometry and tailwater depth.

Hydraulic jumps commonly occur downstream of gates, weirs and spillways, where released water may otherwise strike the channel bed at high speed. Engineers design stilling basins to hold a jump in a controlled location, reducing energy before water continues downstream and helping protect structures and beds from scour. Basin layout and downstream water depth matter: if the jump is displaced or swept out of its intended basin, energy dissipation and protection may be inadequate. Jumps also promote mixing and aeration, uses noted in water and wastewater processes.

The phenomenon was noted in early observations of flowing water and was experimentally and analytically studied by Giorgio Bidone in the early nineteenth century. Later work developed momentum-based relationships for the upstream and downstream depths and examined turbulence and energy loss. Modern research combines laboratory measurements with numerical methods to investigate air entrainment, fluctuating surfaces and the effects of channel expansions, roughness and structures on jump position and stability.