Energy dissipation in the Smagorinsky model of turbulence

The Smagorinsky model often severely over-dissipates flows and, consistently, previous estimates of its energy dissipation rate blow up as Re -> infinity. This report estimates time averaged model dissipation, <epsilon(S)>, under periodic boundary conditions as <epsilon(S)> <= 2U(3)/L + Re-1 U-3/L + 32/27 C-S(2) (delta/L)(2) U-3/L, where U, L are global velocity and length scales and C-S similar or equal to 0.1, delta < 1 are model parameters. Thus, in the absence of boundary layers, the Smagorinsky model does not over dissipate. (C) 2016 Elsevier Ltd. All rights reserved.