  In the present work we show some results on the effect of the Smagorinsky
model on the stability of the associated perturbation equation. We show that in
the presence of a spectral gap, such that the flow can be decomposed in a large
scale with moderate gradient and a small amplitude fine scale with arbitratry
gradient, the Smagorinsky model admits stability estimates for perturbations,
with exponential growth depending only on the large scale gradient. We then
show in the context of stabilized finite element methods that the same result
carries over to the approximation and that in this context, for suitably chosen
finite element spaces the Smagorinsky model acts as a stabilizer yielding close
to optimal error estimates in the $L^2$-norm for smooth flows in the
pre-asymptotic high Reynolds number regime.
