Turbulence
Fluid motion organised into nested vortices across a vast range of scales. The last unsolved problem of classical physics.
Definition
Turbulence is the chaotic, eddy-rich state of flow that dominates at high Reynolds number. It is characterised by nested whorls of motion, from the largest scale set by the flow geometry down to the viscous dissipation scale, and by rapid mixing, diffusion, and dissipation of energy.
It is the default state of almost every flow that matters at human scales: atmosphere, ocean, rivers, pipe flow above Re ≈ 2300, aircraft wakes, stellar interiors. And it is unsolved in the deepest sense. The Navier-Stokes equations describe it exactly, but we cannot even prove those equations always have smooth solutions in three dimensions — that is a Millennium Prize Problem. Kolmogorov gave the universal scaling of the inertial range in 1941, but a full theory of turbulence remains out of reach eighty years later.