Energy dissipation in the Smagorinsky model of turbulence. (September 2016) - Layton, William
Abstract: The Smagorinsky model often severely over-dissipates flows and, consistently, previous estimates of its energy dissipation rate blow up as R e → ∞ . This report estimates time averaged model dissipation, 〈 ε S 〉, under periodic boundary conditions as 〈 ε S 〉 ≤ 2 U 3 L + Re − 1 U 3 L + 32 27 C S 2 ( δ L ) 2 U 3 L, where U, L are global velocity and length scales and C S ≃ 0.1, δ < 1 are model parameters. Thus, in the absence of boundary layers, the Smagorinsky model does not over dissipate.