Very stable surface-layer similarity ($U_z\sim c_m|B_0|/u_{\ast }^2,N^2\sim c_h|B_0{|}^2/u_{\ast }^4$)

In local continuously turbulent scaling at $z/{\ell }_O\gg 1$, dependence on the distance to the wall disappears at leading order. The velocity profile is linear and the buoyancy frequency is constant. Local energy balance gives $ϵ=(c_m-1)|B_0|$ and ${\mathrm{Ri}}_f=1/c_m$, with positive dissipation requiring $c_m>1$. The coefficients depend on a closure, and this regime should not be imposed on fully collapsed turbulence.