What is the difference between the Reynolds decomposition and LES filtering?
The Reynolds decomposition separates the velocity field into an average component and a fluctuating component. The time average of the fluctuating component is identically zero. In LES, a filtering operation is performed to decompose the velocity field into a filtered velocity field and a filtered residual field. The crucial difference between both methods is • The filtered velocity field is a random variable while the average field (Reynolds) is not • The time average of the residual field is generally nonzero while it is identically zero for fluctuating component in the Reynolds decomposition.
