Universal Wind Profile for Conventionally Neutral Atmospheric Boundary Layers

TL;DR

This paper derives an analytic wind profile for the complex, neutral atmospheric boundary layers by combining classical similarity theory with local scaling, validated against high-fidelity simulations.

Contribution

It introduces a novel analytic expression for the wind profile in CNBLs using a stability correction function and local scaling, advancing predictive capabilities.

Findings

Analytic wind profile matches high-fidelity simulation data.

Derived stability correction function accurately captures CNBL behavior.

Provides a new tool for weather, climate, and wind energy modeling.

Abstract

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.