The mean wind and potential temperature flux profiles in convective boundary layers

TL;DR

This paper introduces new analytical profiles for mean wind and potential temperature fluxes in convective boundary layers, validated against large-eddy simulations, with applications in weather, climate, and wind energy modeling.

Contribution

The authors develop analytical expressions for flux profiles in convective boundary layers using a perturbation approach and integrate them with Monin-Obukhov theory, providing accurate modeling tools.

Findings

Profiles agree well with large-eddy simulation data.

The method captures flux profiles across a wide range of stability conditions.

Analytical expressions improve boundary layer modeling accuracy.

Abstract

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.