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 ${\displaystyle \scriptstyle u}$ the decomposition would be

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

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