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Express the large scale length in terms of k and ε.

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Express the large scale length in terms of k and ε.

(a) (k/ε)^3/2

(b) k^3/2/ε

(c) ε/k^3/2

(d) (ε/k)^3/2

I had been asked this question during an online exam.

Origin of the question is Turbulence Modelling topic in portion Turbulence Modelling of Computational Fluid Dynamics

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Right answer is (b) k^3/2/ε

The explanation: The length scale of the large eddies can be given as k^3/2/ε. The small scale dissipation rate of the turbulent kinetic energy can be used to represent the large scale length as the rate at which the large eddies extract energy from the mean flow is matched with the rate of energy transfer to small eddies.

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