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 versus the fluctuations might be done for a single directional component, e.g., specifically for the meridional flow.