Some historical notes on the statistical dynamics of turbulence

Turbulence is a complex phenomenon that originates from local instabilities which are further amplified owing to non-linearity of the basic equations that govern fluid flow. For the latter reason, application of statistical techniques to basic hydrodynamic equations leads to a closure problem. This was demonstrated by Reynolds [1], who introduced turbulence decomposition into the mean motion and random fluctuations in the equations of fluid flow in an attempt to determine the criterion for the onset of transition and self-maintenance of the turbulence in round tubes.