  Standard eddy viscosity models, while robust, cannot represent backscatter
and have severe difficulties with complex turbulence not at statistical
equilibrium. This report gives a new derivation of eddy viscosity models from
an equation for the evolution of variance in a turbulent flow. The new
derivation also shows how to correct eddy viscosity models. The report proves
the corrected models preserve important features of the true Reynolds stresses.
It gives algorithms for their discretization including a minimally invasive
modular step to adapt an eddy viscosity code to the extended models. A
numerical test is given with the usual and over diffusive Smagorinsky model.
The correction (scaled by $10^{-8}$ ) does successfully exhibit intermittent
backscatter.
