23.6 : Hydraulic Jump

A hydraulic jump is a sudden rise in fluid depth in open channels, occurring when high-velocity (supercritical) flow transitions to low-velocity (subcritical) flow. This phenomenon requires an upstream Froude number greater than 1, as flows with Fr₁<1 remain subcritical, making a hydraulic jump impossible due to the need for negative head loss, which violates thermodynamic principles.

The characteristics of a hydraulic jump depend on the upstream Froude number and are classified as follows:

1. Jump Impossible (Fr₁<1): Subcritical flow prevents a hydraulic jump from forming.

2. Standing Wave or Undulant Jump (Fr₁​=1 to 1.7): Barely supercritical flow causes minimal depth changes, forming a standing wave.

3. Weak Jump (Fr₁​=1.7 to 2.5): A mild increase in depth occurs with low energy dissipation.

4. Oscillating Jump (Fr₁=2.5 to 4.5): Unstable with regular oscillations, this jump moderately dissipates energy.

5. Stable Jump (Fr₁​=4.5 to 9.0): Steady and well-balanced, this jump causes significant energy loss.

6. Strong Jump (Fr₁​>9.0): Highly turbulent with substantial energy dissipation.

The depth ratio and head loss across the jump depend on the Froude number​. Higher Froude number​ values result in considerable depth changes and greater energy dissipation.

Hydraulic jumps are vital in engineering for dissipating energy in structures like dam spillways. High-speed water exiting spillways can damage downstream channels, but hydraulic jumps convert supercritical flow to subcritical flow, reducing energy and protecting structures.

In sloped or obstructed channels, hydraulic jumps, such as submerged jumps or standing waves, can adapt to channel conditions in unique ways. Submerged jumps occur when downstream depth is artificially raised by structures like weirs or gates, dissipating energy over a longer distance. On the other hand, standing waves form with minimal depth changes, offering localized energy dissipation in steep or constricted sections. These types are tailored solutions for specific engineering needs, differing in behavior, efficiency, and spatial requirements.