Math breakthrough: boundary layer turbulence.

This is a pretty big deal.

Mathematicians have been trying for a century or more to understand the turbulence that arises when a flow interacts with a boundary, but a formulation has proven elusive.

Now an international team of mathematicians, led by UC Santa Barbara professor Björn Birnir and the University of Oslo professor Luiza Angheluta, has published a complete description of boundary layer turbulence. The paper appears in Physical Review Research, and synthesizes decades of work on the topic. The theory unites empirical observations with the Navier-Stokes equation — the mathematical foundation of fluid dynamics — into a mathematical formula.

So what, you say? Well, every liquid or gas that flows over, around or through anything is affected by boundary layer turbulence. Airplane wings, windmill blades, fuel injection and engine intake manifolds, any sort of pipe or container, anything from helium to treacle, all experience the energy-robbing phenomenon of turbulence at their surface. It is the thing that creates friction and the detaching of laminar flow.

If you have a complete mathematical model of it, you can accurately simulate it with a digital computer. You don't need a wind tunnel to do experiments, which means you can start doing things like applying machine learning and evolutionary modeling to your optimization efforts. Run ten million examples of your pipe elbow to find the minimum drag version.

Which means you don't have to be Boeing anymore. Compute power is cheap, you can optimize laminar flow on a PC and build it in your shop with CNC machinery and 3D printing.

That is what we call a breakthrough.