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.