turbulence

Turbulence is chaotic, churning fluid motion full of swirls and eddies that mix and tumble unpredictably. It is the roiling white water of a rapid, the buffeting that shakes a plane, the billowing chaos of rising smoke once its smooth thread breaks up. It answers the question: what happens when flow stops being calm and orderly and instead becomes wild?

Precisely, turbulent flow is irregular and disorderly: the velocity at any point changes rapidly and randomly in both size and direction, and the fluid forms eddies of many sizes, swapping energy between them and mixing vigorously. Turbulence sets in when the destabilising inertia of the flow overwhelms the smoothing effect of viscosity, that is, at high Reynolds number, which means high speeds, large sizes, or low viscosity. Unlike laminar flow, the detailed motion cannot be predicted moment by moment; only its statistical, averaged behaviour can be described.

Turbulence is the normal state of most flows we meet, wind around buildings, water in rivers, air over wings and cars, and it strongly increases mixing and drag. It matters enormously in weather, engineering, and astrophysics. One honest admission: turbulence is famously one of the great unsolved problems of classical physics. We have the governing equations, the Navier-Stokes equations, yet a full understanding of turbulence remains beyond us, so engineers rely heavily on experiment, approximation, and computer simulation.