Reynolds stresses

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Reynolds stresses

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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