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When it rains and water flows down an inclined street, ripples may form that are carried along with the current. Here's a picture with an example of what I'm talking about

enter image description here

I'd like to know what the fluid mechanical mechanism is for the formation of these waves. A quick google search reveals that they've been identified in some scientific literature as "rain waves" (if you have a jstor subscription you can see http://www.jstor.org/stable/4297089?seq=1) but I've only been able to find phenomenological descriptions of their properties without any details of the physics giving rise to them. In particular, I'm curious if people think that the surface on which the water is flowing must have a particular texture in order to give rise to the waves.

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This answer will be my hopthesis, I am by no means absolutely sure about this answer, but want to share my thoughts.

Considering the thickness of the liquid film and the inclination of the surface, it may be an interplay between gravity and surface tension. This may be an example of the Plateau-Rayleigh instability, which can for example be seen at the break-up of the stream out of a faucet into droplets.

Except surface tension itself, you also encounter wetting behaviour here, which may be the reason that you see the long vertical streaks. So my intuition would be that gravity controls the speed of the streaks, the wetting/contact line the shape and surface tension controls the width or wavelength.

In other words. If you have a liquid film due to the rain, gravity is the downward force. The wetting behaviour at the front of the film, is a force acting opposite to it. Surface tension now controls that liquid behind it. At some points, the film breaks up, again by surface tension (Plateau-Rayleigh), giving you a new front and the story repeats.

Your asking about the texture to the surface, and the most important aspect of the texture of the surface is in the contact line behaviour. Different textures cause different opposing or breaking forces. I assume rough surfaces (as a street) have higher opposing forces.

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thanks very much for your answer. Your mention of wetting behavior led me to the wikipedia article on how wetting is affected by rough surfaces (en.wikipedia.org/wiki/Wetting#Non-ideal_rough_solid_surfaces) which is very useful. I am less sure about the application of the Plateau-Rayleigh instability and would love to hear other opinions as to whether this is the case. I also wonder whether the ripples are hydraulic jumps (with important contributions from surface tension) or if there is better way to think of them –  kleingordon Mar 29 '12 at 1:11

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