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