Reynolds decomposition
In fluid dynamics and turbulence, Reynolds decomposition is a mathematical
technique to separate the average and fluctuating parts of a quantity.
For example, for a quantity u the decomposition woud be:
where 
denotes the time average of 
(often called the steady component), and
the fluctuating part (or perturbations). The perturbations are defined such that their time average equals zero.
This allows us to simplify the Navier-Stokes equations by substituting in the sum of the steady component and perturbations to the velocity profile and taking the mean value. The resulting equation contains a nonlinear term which gives rise to turbulence.