Nicole Sharp<p><strong>Proving Superdiffusion</strong></p><p>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 “<a href="https://en.wikipedia.org/wiki/Anomalous_diffusion" rel="nofollow noopener" target="_blank">superdiffusion</a>,” where turbulence makes particles that start out as neighbors part ways.</p><p>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 <a href="https://www.quantamagazine.org/new-superdiffusion-proof-probes-the-mysterious-math-of-turbulence-20250516/?__readwiseLocation=" rel="nofollow noopener" target="_blank">Quanta</a>, or you can check out the original papers on arXiv. (Image credit: <a href="https://unsplash.com/photos/yellow-and-red-plastic-toy-VTvnoNBowZs" rel="nofollow noopener" target="_blank">J. Richard</a>; research credit: <a href="https://arxiv.org/abs/2404.01115" rel="nofollow noopener" target="_blank">S. Armstrong et al.</a> and <a href="https://arxiv.org/abs/2405.10732" rel="nofollow noopener" target="_blank">S. Armstrong and T. Kuusi</a>; see also <a href="https://www.quantamagazine.org/new-superdiffusion-proof-probes-the-mysterious-math-of-turbulence-20250516/?__readwiseLocation=" rel="nofollow noopener" target="_blank">Quanta</a>)</p><p><a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://fyfluiddynamics.com/tagged/diffusion/" target="_blank">#diffusion</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://fyfluiddynamics.com/tagged/fluid-dynamics/" target="_blank">#fluidDynamics</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://fyfluiddynamics.com/tagged/mathematics/" target="_blank">#mathematics</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://fyfluiddynamics.com/tagged/physics/" target="_blank">#physics</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://fyfluiddynamics.com/tagged/science/" target="_blank">#science</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://fyfluiddynamics.com/tagged/turbulence/" target="_blank">#turbulence</a></p>