Fully developed turbulence is the notion of the general or universal behavior in any physical situation of a violent fluid flow, be it a dust devil or a cyclone in the atmosphere, the water flow in a white-water river, the rapid mixing of the cream and the coffee when stirring in a coffee cup, or perhaps even the flow in gigantic interstellar gas clouds. It is generally believed that the developments of these different phenomena are describable through the Navier–Stokes equation with suitable initial or boundary conditions. The governing equation has been known for almost two centuries, and a lot of progress has been achieved within practical engineering in fields like aerodynamics, hydrology, and weather forecasting with the ability to perform extensive numerical calculations on computers. However, there are still fundamental questions concerning the nature of fully developed turbulence which have not been answered. This is perhaps the biggest challenge in classical physics. The literature on the subject is vast and very few people, if any, have a full overview of the subject. In the updated version of Monin and Yaglom's classic book the bibliography alone covers more than 60 pages (Monin & Yaglom, 1981).

The phenomenology of turbulence was described by Richardson (1922) and quantified in a scaling theory by Kolmogorov (1941b). This description stands today, and has been shown to be basically correct by numerous experiments and observations.