Turbulence is very good at spreading things out. Drop dye into a turbulent flow and it will quickly disperse. Add in particles — like rubber ducks — and they can spread apart, often at speeds quicker than one would expect, based on the background flow. This is (roughly speaking) a phenomenon known as “superdiffusion,” where turbulence makes particles that start out as neighbors part ways.
Physicists conjectured that turbulence — including simplified and idealized versions of it that are simpler to deal with — had this superdiffusion property, but no one was able to show that in a mathematically rigorous way. But now a group of mathematicians has done so, using a technique known as homogenization. There’s a lot more on the story over at Quanta, or you can check out the original papers on arXiv. (Image credit: J. Richard; research credit: S. Armstrong et al. and S. Armstrong and T. Kuusi; see also Quanta)
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