Hydraulic Jump
When a vertical jet of water strikes a flat surface, it spreads outward as a thin supercritical film. At some radius, the film abruptly thickens — the circular hydraulic jump. This is the same phenomenon as the ring you see when water from a faucet hits a sink.
About the Hydraulic Jump
Supercritical vs subcritical: Inside the jump radius, the Froude number Fr = v/√(gh) > 1 (flow is faster than gravity waves). Outside, Fr < 1 (subcritical). The jump is the sharp transition between these regimes, analogous to a shock wave in gas dynamics.
Watson's (1964) theory predicts the jump radius scales roughly as Rj ~ Q5/8 ν-3/8 H-1/8. Increasing flow rate pushes the jump outward; increasing viscosity brings it inward.
The side view (lower panel) shows the water film profile: thin and fast inside, thick and slow outside. The abrupt wall is the jump. Particles are advected to show the velocity field: fast near the jet, slow beyond the jump.