# Patterns in laminar flow of tap water

This is a simple experiment that anyone can do at home. Open your tap so that the water maintains a laminar flow, and the cross section of flow is considerably thin. Place your finger 3-4 cm below the flow. A beautiful wave-like pattern is observed on surface of flowing water, near the region of your finger. Changing the position of finger changes the 'wave-length' of the wave.

The attached picture shows how to do this experiment, though the resolution is not clear.

What is the explanation for this phenomena? Probably a harder question would be if there is an intuitive explanation for it. Thanks!

${\bf Edit:}$ I observed a similar phenomena in the swimming pool...when the water is still, move your hand slowly along the surface of the water. It causes a 'bump' in the water, which decays away in a wave-like pattern in front of your hand. Clearly they are the same phenomena: water falling on the hand or hand moving against the water.

The answers below are very interesting (Thanks!). And as far as I can see, they are still being debated, suggesting that the phenomena is more non-trivial that it appears to be. I had accepted an answer earlier, but I am now taking it back, as I did not completely understand it. Looking forward to further discussion on it. It would be most exciting to find an answer that is elementary: without resorting to complex terminologies of fluid mechanics.

Astute observation, and very interesting phenomena. I do know for a fact that the reason the column of water narrows as it gets further from the faucet is due to acceleration by gravity and an increasing fluid velocity. The higher the velocity, the lower the pressure. Since the pressure outside everywhere along the column is essentially the same, the column is forced to a narrower cross section further down the column - a vena contracta.

But as for the ripple, I can only offer a hypothesis:

The presence of your finger causes a sudden slowing of the velocity and therefore increase in pressure leading to a discontinuity and a sort of circumferential hydraulic jump. Some energy redirects the flow radially along the surface of your finger, but some energy is dissipated into the boundary layer of the column above your finger, generating cylindrical surface waves that travel in the slower boundary layer a short distance upward but then dampen out. Normally surface waves use gravity as the restoring force, but in this case the restoring forces may be surface tension, pressure variations or both.

• Thanks for your comment. It is a plausible explanation, and i like the idea that pressure variation may be responsible for restoring force. It might explain the following observation: if we move our finger upwards, the 'wavelength' as well as effective range of wave-pattern increases. It could happen because damping due to pressure is less in upper stream. But what is quite mysterious is how this wave-pattern becomes a standing wave. Do you have an explanation? Apr 20 '15 at 9:47
• @anuraganshu If it's a standing wave that's observed then there is likely reflection and interference. I can't immediately explain how a reflection could occur. Apr 20 '15 at 14:26
• @David2000 ok, you are welcome to answer Sep 15 '15 at 12:55

What is the explanation for this phenomena?

"Water Hammer" https://en.wikipedia.org/wiki/Water_hammer

There is a study from "Hasson and Peck", 1964, which explains "Thickness distribution in a sheet formed by impinging jets." It's all basically Bernoulli's equation; "Velocity -> pressure -> velocity" and then simply continuity. Anouther good source is the Book "Zhang, Zhengji, Freistrahlturbinen" You can luckily preview these particular pages (53-54) here; http://www.springer.com/us/book/9783540707714 It's german, but the equations and a picture is there.

It should be noted that when the flow velocity is high enough these "water hammer" pressure waves cant't travel back anymore. Therefore the waves are bigger if the free fall is shorter and they get smaller, and finally disappears when the distance und thus velocity increases.

Very similar phenomenon is the "Free surface undulations" in MEL strucutres as explained by Hubert Chanson. Or the FR = 1 - 1.73 Hydraulic jump. These undulations after this Jump is bit different, the energy and continuity can't be fullfilled with the same waterlevel, so the surface must make waves in a way that the Energy and continuity avareges are fullfilled.

• I am not quite satisfied to this answer; more complete view is presented here; physics.stackexchange.com/questions/226441/… Dec 10 '16 at 22:09
• This phenomenon has nothing whatsoever to do with what is known as the "water hammer" effect. This is the so-called Rayleigh instability, which is surface-tension driven. And, no, the derivation of the stability equations requires the Euler equations, and cannot rely on Bernoulli.
– Pirx
Jan 31 '17 at 23:15

The accepted answer is incorrect: The surface undulations seen in the picture above are due to the Rayleigh (or Rayleigh-Plateau) instability, see here.

• Well, the Rayleigh instabilty is not able to travel upstream. You don't even seem to understand the question. pls. Try this once with the tap, and then come back with an solid answer which explains how the finger downstream can disturb the flow on upstream. Feb 4 '17 at 20:12
• You're wrong. This is an incompressible flow, where disturbances most certainly travel upstream.
– Pirx
Feb 4 '17 at 20:48
• Yes, I am never right. -The Nature is always right. Have you already tried this on the tap with you self? Feb 5 '17 at 5:04