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What is the velocity scale taken in the Smagorinsky-Lilly SGS model?

(a) The ratio of the length scale and the time scale

(b) The square of the average strain rate of the resolved flow

(c) The product of the length scale and the average strain rate of the resolved flow

(d) The square of the length scale

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My question is from Turbulence Modelling topic in portion Turbulence Modelling of Computational Fluid Dynamics

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The correct choice is (c) The product of the length scale and the average strain rate of the resolved flow

The best I can explain: The Smagorinsky-Lilly SGS model assumes a velocity scale equal to the Product of the length scale and the average strain rate of the resolved flow. It is given by the equation Δ×\(\mid\overline{S}\mid \) .

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