Free-convection surface-layer scaling (source code)

= Free-convection surface-layer scaling
{title2=$w_c\sim(B_0z)^{1/3},\quad\epsilon\sim B_0$}

For a positive approximately constant <vertical turbulent buoyancy flux>, dimensional turnover scaling gives $K_b\sim B_0^{1/3}z^{4/3}$ and $N^2\sim-B_0^{2/3}z^{-4/3}$. The negative squared frequency describes unstable overturning, not a real restoring oscillation. The leading dissipation is height-independent, unlike neutral wall turbulence.