Near-neutral log-linear surface-layer profiles ($K_{M,B}=u_{\ast }z{f}_{M,B}(z/\ell )$)

If the similarity functions of a turbulent boundary layer are differentiable at zero and have finite positive neutral values, expanding $f=a+dz/\ell +O((z/\ell {)}^2)$ gives a shear proportional to $1/z-d/(a\ell )$. Integration yields a logarithmic term plus a linear correction. Dimensional reasoning alone does not fix the coefficients or guarantee this regular neutral limit. The gradient Richardson number is of order $z/\ell$, so $|z/\ell |\ll 1$ is a shear-dominated, nearly neutral regime on either side of stability.