Anne (peridot_faceted) wrote,

Rayleigh-Taylor instability and kids' toys

Wikipedia is cool.

Rayleigh-Taylor instability

I'll admit that it is occasionally unreliable (for example, it claims that the speed of light is affected by gravity) and it's sometimes a mess but it's full of fascinating information. For example, Rayleigh-Taylor instability.

Rayleigh-Taylor instabilities occur when a less-dense fluid accelerates a more-dense fluid. This sounds fairly unexciting, I know. I had a toy in my room when I was a kid that demonstrates what happens: little variations in the interface amplify into interpenetrating "fingers". It made for a cool-looking little toy, but it never really seemed that interesting either.

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But then I go reading about it on Wikipedia.

Turns out that when a supernova goes off, a spherical shell of matter is flung off. That shell of relatively dense matter crashes into the not so dense interstellar medium, and the interface breaks up into "fingers", giving nebulas their characteristic "clotted" look. (I also had a picture of the Crab nebula on my wall as a kid.) So my little toy explains, in a very visual way, why nebulae look the way they do.

Using this description I should be able to estimate the "mean kinematic viscosity" and "Atwood number" of my little toy; it might even make it clear how to build one.

From looking at it, I'd say the e-folding time is about a tenth of a second, and the wavelength we see first is about two centimeters. This gives an Atwood number of about 0.06 (densities differ by a few percent) and a "mean kinematic viscosity" of about 800 square millimeters per second. Water has a kinematic viscosity of 0.9 square millimeters per second; glycerol and castor oil both have viscosities about a thousand times that, and olive oil is about a tenth what is needed. SAE 60 motor oil also has a suitably high viscosity. The trick, I suspect, will be getting the densities close enough, since that controls the timescale.

Of course all this calculation is bogus in the likely case that the thinness of the layer of liquid plays an important role. After all, if the liquids are as viscous as these calculations suggest, putting them between two walls will certainly slow down their motion.

Every time I tell people about things like this I had as a kid they tell me "no wonder you're like that".
Tags: fluids, physics
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