= K-epsilon turbulence front
{title2=$p=1/(2-\sigma),\quad q=\sigma/(2-\sigma)$}
A stationary turbulence edge with no production has an advection–turbulent-diffusion leading balance. For $k\propto x^p$, $\epsilon\propto x^q$ and $\nu_T=C_\mu k^2/\epsilon$, this balance gives $2p-q=1$ and $q/p=\sigma_\epsilon/\sigma_k=\sigma$. The integral length $k^{3/2}/\epsilon$ and turnover frequency $\epsilon/k$ both tend to zero when $1<\sigma<3/2$. The front viscosity is linear, with $\nu_T'(0^+)=(2\sigma_k-\sigma_\epsilon)U_0$. This is formal high-Reynolds-number consistency, not a uniform justification for neglecting molecular viscosity at the exact edge.
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