[Physics] Why do rain waves form and what is their connection to the texture of the surface they’re on

everyday-lifefluid dynamicswaves

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

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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.

Best Answer

I have a very slightly different answer to that of Bernhard above, but it relies on the same Plateau-Raleigh Instability idea.

The speed of a thin layer of water flowing is going to be slower than a slightly thicker layer. So I expect that thin layer would flow more slowly and water in a thicker film would tend to catch up with the thin layer and build up to form a faster moving 'little wave' or 'ripple'. The wave would leave behind a very thin layer of water wetting the ground before the next 'ripple' comes along.

I guess this may be similar to how a flag flutters.

Ultimately I think if water is flowing down a flat surface the mechanism of flow will change as the flow rate changes from laminar to 'ripples' to some other type of flow and at some point turbulence will be important - this is classical behaviour of a non-linear system where changing a parameter (water flow rate, for example) can change the mechanism of what is going on. By contrast linear systems (e.g. SHM Simple Harmonic Motion) always show the same behaviour (eg for SHM - oscillatory behaviour, but with amplitude and frequency determined by initial conditions/system variables)

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