Reynolds decomposition is a mathematical separation of a quantity (an evolving field) into its average and its fluctuating parts. For example:
________ u(x,y,z,t) = u(x,y,z) + u'(x,y,z,t)
It is used to help deal with the Navier-Stokes equations. The fluctuating component has a non-linear component which is called the Reynolds stress or Reynolds stresses. It accounts for turbulence. In analysis of fluid motions (e.g., atmospheres), this sort of decomposition (a partitioning of fluid motion into the mean motion versus the fluctuations) might be done for a single directional component, e.g., specifically for the meridional flow.