New 'Superdiffusion' Proof Probes the Mysterious Math of Turbulence

They started by imagining a very fine grid superimposed on their fluid. They then computed how long particles spent in each square of the grid, on average. In some squares, the fluid acted like a rushing river: Particles tended to sweep straight across the square, spending only a brief period of time there. In other squares, small eddies might push particles around, slowing them down. The problem was that the numbers the mathematicians calculated might vastly differ from square to square — revealing precisely the kind of small-scale disorder that usually prevented mathematicians from using homogenization. Armstrong, Bou-Rabee and Kuusi needed to find a way around that. Ordering Disorder The mathematicians hoped to show that at slightly larger scales than the one their grid had captured, the fluid’s behavior would be a bit less noisy and disordered. If they could do that, they’d be able to use typical homogenization techniques to understand what was happening at the largest scale. ... Read full article.