  Conventionally neutral atmospheric boundary layers (CNBLs), which are
characterized with zero surface potential temperature flux and capped by an
inversion of potential temperature, are frequently encountered in nature.
Therefore, predicting the wind speed profiles of CNBLs is relevant for weather
forecasting, climate modeling, and wind energy applications. However, previous
attempts to predict the velocity profiles in CNBLs have had limited success due
to the complicated interplay between buoyancy, shear, and Coriolis effects.
Here, we utilize ideas from the classical Monin-Obukhov similarity theory in
combination with a local scaling hypothesis to derive an analytic expression
for the stability correction function $\psi = -c_\psi (z/L)^{1/2}$, where
$c_\psi = 4.2$ is an empirical constant, $z$ is the height above ground, and
$L$ is the local Obukhov length based on potential temperature flux at that
height, for CNBLs. An analytic expression for this flux is also derived using
dimensional analysis and a perturbation method approach. We find that the
derived profile agrees excellently with the velocity profile in the entire
boundary layer obtained from high-fidelity large eddy simulations of typical
CNBLs.
