Energy dissipation in the Smagorinsky model of turbulence. (September 2016)

• Record Type: Journal Article
• Authors: Layton, William
• Is Part Of: Applied mathematics letters. Volume 59(2016:Sep.)
• Page Start: 56
• Page End: 59
• Publication Date: 2016-09
• Subjects: Energy dissipation rate -- Smagorinsky model -- Turbulence; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.03.008
• Languages: English
• ISSNs: 0893-9659

Abstract

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.