Kevin Hartnett in Quanta:
Picture a calm river. Now picture a torrent of white water. What is the difference between the two? To mathematicians and physicists it’s this: The smooth river flows in one direction, while the torrent flows in many different directions at once.
Physical systems with this kind of haphazard motion are called turbulent. The fact that their motion unfolds in so many different ways at once makes them difficult to study mathematically. Generations of mathematicians will likely come and go before researchers are able to describe a roaring river in exact mathematical statements.
But a new proof finds that while certain turbulent systems appear unruly, they actually conform to a simple universal law. The work is one of the most rigorous descriptions of turbulence ever to emerge from mathematics. And it arises from a novel set of methods that are themselves changing how researchers study this heretofore untamable phenomenon.