# Reynolds averaging

Reynolds averaging refers to the process of averaging a variable or an equation in time. Let $\Phi$ be any dependent variable that varies in time. This variable can be decomposed into a fluctuating part, $\Phi'$ and an average part $\overline{\Phi}$ in the following way:
 $\overline{\Phi} \equiv \frac{1}{T} \int_T \Phi(t) dt$ (1) $\Phi' \equiv \Phi - \overline{\Phi}$
Where $T$ is a long enough time to average out the fluctuations in $\Phi$.