ABSTRACT
In fluid dynamics, turbulence means a flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. Flow that is not turbulent is called laminar flow. The turbulent motion is not entirely without regularity, but the regularity is statistical in character and appears only when long-term time averages are examined. For conservative systems describable by a Lagrangian function there is Noether's theorem which gives a rationale for this association. Other more local conservation laws, such as the conservation of circulation, may be even more important but have found surprisingly few applications to turbulence theory. Possibly most ingenious attempt to understand the statistics of turbulence is due to Kolmogorov who proposed the idea of universality based on the notion of the inertial range. Fusion rules in turbulence specify the analytic structure of many-point correlation functions of the turbulent field when a group of coordinates coalesce.
