= Solution
The <K-epsilon turbulence front> has
$$
\boxed{k=k_0\xi^{1/(2-\sigma)},\qquad
\epsilon=\epsilon_0\xi^{\sigma/(2-\sigma)}.}
$$
Its characteristic integral length and the specified frequency scale are
$$
\boxed{L=\delta_0\xi^{(3/2-\sigma)/(2-\sigma)},
\qquad\omega=\frac{\epsilon_0}{k_0}
\xi^{(\sigma-1)/(2-\sigma)}.}
$$
The ratio $\epsilon/k$ 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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