The great Italian scientist Leonardo da Vinci was the first person to use the word "turbulence" (or turbolenza) to describe the complex motion of water or air. By carefully examining the turbulent wakes created behind obstacles placed in the path of a fluid, he found that there are three key stages to turbulent flow. Turbulence is first generated near an obstacle. Long-lived "eddies" - beautiful whirls of fluid - are then formed. Finally, the turbulence rapidly decays away once it has spread far beyond the obstacle.
However, it was not until the early 19th century that Claude Navier was able to write the basic equations governing how the velocity of a turbulent fluid evolves with time. Navier realized that the earlier equations of Leonhard Euler for ideal flow had to be supplemented by a diffusion term that took into account the viscosity of the fluid.
Modelling turbulent transport thus became - and remains to this day - a major challenge.
In the December issue of Physics World magazine, Uriel Frisch from the Observatoire de la Côte d'Azur, Nice, France writes about the complexity of turbulence and our attempts to model it.