Reynolds stresses
From Glossary of Meteorology
The mean forces (per unit area) imposed on the mean flow by turbulent fluctuations.
They arise from the nonlinear advection term when the Navier–Stokes equations are Reynolds decomposed and Reynolds averaged. The general form of the Reynolds stress tensor is 
represents the momentum flux in direction 
across a plane perpendicular to direction 
or the momentum flux in direction 
across a plane perpendicular to direction 
. In a turbulent flow, the divergence of the Reynolds stresses are of leading order in the mean momentum budgets. Typically they are several orders of magnitude larger than the viscous stresses. In the boundary layer, the most important Reynolds stresses are the vertical fluxes of horizontal momentum, 
and 
.
Kinematically, the velocity correlation -
represents the momentum flux in direction across a plane perpendicular to direction or the momentum flux in direction across a plane perpendicular to direction . In a turbulent flow, the divergence of the Reynolds stresses are of leading order in the mean momentum budgets. Typically they are several orders of magnitude larger than the viscous stresses. In the boundary layer, the most important Reynolds stresses are the vertical fluxes of horizontal momentum, and .
