 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-84/4/c/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

k = k_{0} ξ^{1/ (2 - σ)}, ϵ = ϵ_{0} ξ^{σ / (2 - σ)} .

Its characteristic integral length and the specified frequency scale are

L = δ_{0} ξ^{(3/2 - σ) / (2 - σ)}, ω = \frac{ϵ _{0}}{k _{0}} ξ^{(σ - 1) / (2 - σ)} .

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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