  We develop innovative analytical expressions for the mean wind and potential
temperature flux profiles in convective boundary layers (CBLs). CBLs are
frequently observed during daytime as the Earth's surface is warmed by solar
radiation. Therefore, their modeling is relevant for weather forecasting,
climate modeling, and wind energy applications. For CBLs in the convective-roll
dominated regime, the mean velocity and potential temperature in the bulk
region of the mixed layer are approximately uniform. We propose an analytical
expression for the normalized potential temperature flux profile as a function
of height, using a perturbation method approach in which we employ the
horizontally homogeneous and quasi-stationary characteristics of the surface
and inversion layers. The velocity profile in the mixed layer and the
entrainment zone is constructed based on insights obtained from the proposed
potential temperature flux profile and the convective logarithmic friction law.
Combining this with the well-known Monin-Obukhov similarity theory allows us to
capture the velocity profile over the entire boundary layer height. The
proposed profiles agree excellently with large-eddy simulation results over the
range of $-L/z_0 \in [3.6\times10^2, 0.7 \times 10^5]$, where $L$ is the
Obukhov length and $z_0$ is the roughness length.
