Water churns behind a rock in a river, air swirls behind an airplane wing: it seems like completely random motion. But the authors of the study found a rigid kitchen recipe in this [tag:chaos_theory]chaos.
They[/tag] decomposed the fluid's rotation (angular momentum) into two independent parts. The first, longitudinal, is like a layered cake of large, coherent vortices
The second, transverse, resembles the filling that fills all the space between the layers and behaves like a hot bath of small, chaotic motions. These two parts are strictly separated: their contributions are in a 1:2 ratio.
Then it gets more interesting. The velocity directed away from the vortex center (radial) does not participate in this rotation at all. It acts like a piston: it pushes energy into transverse motions, causing vortices to stretch. As a result, all energy is distributed among three parts: 1/3, 2/9, and 4/9. This is not an approximate estimate but an exact rule confirmed by computer simulations.
If you stir cream into coffee, you first get beautiful patterns, but then everything becomes uniform. Turbulence, on the contrary, creates stable structures — vortices that live long, even though the flow seems chaotic.
In Frank Herbert's novel "Dune," the sandstorms on Arrakis are described as turbulent flows capable of destroying everything in their path. If the locals had known the exact energy proportions, they might have built their shelters differently.