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Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 84 / 4 / c / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2008 iii Paper 84 4 c
Created 2026-10-03 Updated 2026-10-14  0 By others on same topic  0 Discussions Create my own version
The K-epsilon turbulence front has
k=k0​ξ1/(2−σ),ϵ=ϵ0​ξσ/(2−σ).​
(1)
Its characteristic integral length and the specified frequency scale are
L=δ0​ξ(3/2−σ)/(2−σ),ω=k0​ϵ0​​ξ(σ−1)/(2−σ).​
(2)
The ratio ϵ/k is an inverse eddy-turnover time. The PDF calls it turbulent vorticity, but it should not be identified with the exact root-mean-square vorticity at dissipative scales, which involves molecular viscosity as well.

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