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# Reynolds decomposition

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 $\scriptstyle u$ the decomposition woud be

$u(x,y,z,t) = \overline{u(x,y,z)} + u'(x,y,z,t)$

where $\scriptstyle\overline{u}$ denotes the time average of $\scriptstyle u\,$ (often called the steady component), and $u'\,$ the fluctuating part (or perturbations). The perturbations are defined such that their time average equals zero.