In fluid dynamics and the theory of turbulence, Reynolds decomposition is a mathematical technique to separate the average and fluctuating parts of a quantity. For example, for a quantity <math>\scriptstyle u</math> the decomposition woud be
- <math>
u(x,y,z,t) = \overline{u(x,y,z)} + u'(x,y,z,t)</math> where <math>\scriptstyle\overline{u}</math> denotes the time average of <math>\scriptstyle u\,</math> (often called the steady component), and <math>u'\,</math> 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 known as the Reynolds stresses which gives rise to turbulence.
