  This paper studies the time-averaged energy dissipation rate $\langle
\varepsilon_{SMD} (u)\rangle$ for the combination of the Smagorinsky model and
damping function. The Smagorinsky model is well known to over-damp. One common
correction is to include damping functions that reduce the effects of model
viscosity near walls. Mathematical analysis is given here that allows
evaluation of $\langle \varepsilon_{SMD} (u)\rangle $ for any damping function.
Moreover, the analysis motivates a modified van Driest damping. It is proven
that the combination of the Smagorinsky with this modified damping function
does not over dissipate and is also consistent with Kolmogorov phenomenology.
