Damping Functions correct over-dissipation of the Smagorinsky Model

Abstract

This paper studies the time-averaged energy dissipation rate $⟨{\epsilon }_{SMD}(u)⟩$ 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 $⟨{\epsilon }_{SMD}(u)⟩$ 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.

14 pages, 5 figures, Mathematical Methods in the Applied Sciences, ISSN 1099-1476 2017