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

What is the relationship between SGS viscosity (μSGS), density (ρ),

1.	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
Answer» Right answer is (d) μSGS=ρ(CΔ)^2\(\MID\overline{S}\mid \) EASY EXPLANATION: The equation for SGS viscosity is obtained by the dimensional analysis. It is given by the equation μSGS=ρ(CΔ)^2\(\mid\overline{S}\mid \) . Where, C is the CONSTANT of SGS viscosity.

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