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Reynolds decomposition is a mathematical separation of a quantity (an evolving field, i.e., a field as a function of time) into its time-averaged and its fluctuating parts. For example:
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u(x,y,z,t) = u(x,y,z) + u'(x,y,z,t)
Reynolds decomposition is a technique for dealing with the Navier-Stokes equations. In that case, the fluctuating component includes a non-linear component which is called the Reynolds stress or Reynolds stresses, which account(s) 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.