What is the relationship between SGS viscosity (μSGS), density (ρ), characteristic length (Δ) and the average strain rate of the resolved flow (\(\mid\overline{S}\mid \) ) in the Smagorinsky-Lilly SGS model?
(a) μSGS=ρ(C)^2 Δ\(\mid\overline{S}\mid \)
(b) μSGS=ρC(Δ)^2\(\mid\overline{S}\mid^2\)
(c) μSGS=ρ(CΔ)^2\(\mid\overline{S}\mid \)
(d) μSGS=ρ(CΔ)^2\(\mid\overline{S}\mid \)
I had been asked this question in a national level competition.
Origin of the question is Turbulence Modelling topic in division Turbulence Modelling of Computational Fluid Dynamics