Reynolds averaging refers to the process of averaging a variable or an equation in time. Let be any dependent variable that varies in time. This variable can be decomposed into a fluctuating part, and an average part in the following way:
Where is a long enough time to average out the typical fluctuations in .
Reynolds averaging is often used in fluid dynamics to separate turbulent fluctuations from the mean-flow. The term "Reynolds averaging" originates from Osborne Reynolds, who was the first to use this type of averaging in fluid dynamics.