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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:

$u = \overline{u} + u'$

where $\overline{u}$ denotes the time average of $u\,$ (often called the steady component), and $u'\,$ 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.

Reynolds decomposition

See also