Circular Hydraulic Jump: The Sink-Ring Shock That Behaves Like a White-Hole Horizon (Field Guide)

Date: 2026-03-14
Category: explore

The weird claim

That bright circular ring you see in a kitchen sink is not just “splash geometry.”
It is a hydrodynamic jump: a sharp transition between two flow regimes, and in shallow-water language it can act like a white-hole horizon for surface waves.

What is actually changing at the ring?

Water from the jet spreads radially as a thin, fast film. At some radius, the film abruptly thickens and slows down: that discontinuity is the jump.

A useful control parameter is the shallow-water Froude number:

[ \mathrm{Fr} = \frac{u}{\sqrt{g h}} ]

• (u): local radial flow speed
• (h): local film depth
• (\sqrt{g h}): long-wave speed on a shallow layer

Interpretation:

• Inner region: typically supercritical (Fr > 1)
• Outer region: subcritical (Fr < 1)

So the jump is a supercritical → subcritical transition.

Why a sharp jump forms instead of smooth slowing

The incoming thin film carries strong radial momentum. A smooth deceleration would require enough downstream pressure/force feedback to travel upstream, but in supercritical flow that feedback is limited.

So the system “resolves” the mismatch at a narrow annulus where:

• thickness rises,
• speed drops,
• viscous dissipation spikes,
• momentum balance closes abruptly.

Classic models (Watson) captured jump radius scaling via thin-film boundary-layer physics. Later work emphasized that surface tension curvature forces can materially shift the radius, especially for smaller jumps.

Gravity vs surface tension: old intuition vs modern nuance

A common classroom line is: “hydraulic jumps are gravity-driven.”

That is often true in deeper/open-channel settings. But for thin-film circular jumps (sink-scale), experiments and scaling analyses show that viscous + capillary effects can dominate or strongly compete with gravity, depending on regime.

Practical takeaway: don’t assume one universal balance; check dimensionless groups and film thickness scale first.

Why people call it a hydrodynamic white hole

In analogue-gravity language:

• Surface-wave perturbations outside the jump cannot freely propagate into the inner supercritical region.
• The jump behaves like a one-way kinematic barrier for certain wave modes.

That is the fluid analogue of a white-hole horizon (time-reversed black-hole picture): signals are blocked in one direction by flow kinematics.

Important caveat: this is an analogy in wave propagation and effective geometry, not literal general relativity in your sink.

Common misconceptions

• “It’s just where water gets deeper.”
  No—there is a regime transition and a momentum-balance discontinuity.

• “Jump radius is set only by gravity.”
  Not in many thin-film circular jumps; capillarity and viscosity matter a lot.

• “White-hole analogy means exotic spacetime is proven in the lab.”
  No—what is tested is analogue horizon kinematics for waves in a moving medium.

Quick experiment checklist (kitchen version)

1. Use a steady vertical jet on a flat plate/sink bottom.
2. Adjust flow rate and note ring radius changes.
3. Change liquid properties (e.g., mild surfactant/temperature shifts) and observe radius sensitivity.
4. Disturb the outer region with tiny ripples and watch whether they penetrate inward.
5. Record top-view video; ring radius is stable enough for frame-by-frame scaling checks.

References

1. E. J. Watson (1964), The radial spread of a liquid jet over a horizontal plane, Journal of Fluid Mechanics 20(3), 481–499.
   https://doi.org/10.1017/S0022112064001367

2. J. W. M. Bush, J. M. Aristoff (2003), The influence of surface tension on the circular hydraulic jump, Journal of Fluid Mechanics 489, 229–238.

3. R. K. Bhagat, N. K. Jha, P. F. Linden, D. I. Wilson (2018), On the origin of the circular hydraulic jump in a thin liquid film, Journal of Fluid Mechanics 851, R5.
   https://doi.org/10.1017/jfm.2018.558
   arXiv preprint: https://arxiv.org/abs/1712.04255

4. G. Jannes, R. Piquet, P. Maïssa, C. Mathis, G. Rousseaux (2011), Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole, Physical Review E 83, 056312.
   https://doi.org/10.1103/PhysRevE.83.056312
   arXiv: https://arxiv.org/abs/1010.1701

5. G. Jannes (2012), The circular jump as a hydrodynamic white hole (review/chapter).
   https://arxiv.org/abs/1203.6505

One-line takeaway

Your sink’s circular ring is a compact fluid-dynamics lab: a visible supercritical-to-subcritical jump that also serves as a tabletop analogue horizon for waves.