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
ams2001glos-Re40
Kinematically, the velocity correlation -ams2001glos-Rex08 represents the momentum flux in direction ams2001glos-Rex09 across a plane perpendicular to direction ams2001glos-Rex10 or the momentum flux in direction ams2001glos-Rex11 across a plane perpendicular to direction ams2001glos-Rex12. 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, ams2001glos-Rex13 and ams2001glos-Rex14.
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