Reynolds decomposition - Definition and Overview

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 <math>u<math> the decomposition woud be:

<math>

u = \overline{u} + u'<math> where <math>\overline{u}<math> denotes the time average of <math>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 which gives rise to turbulence.

See also

• Reynolds-averaged Navier-Stokes equations

Example Usage of decomposition