K-epsilon turbulence front ($p=1/(2-\sigma ),q=\sigma /(2-\sigma )$)

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