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

Error estimates for the Smagorinsky turbulence model: enhanced stability through scale separation and numerical stabilization