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Mean turbulent momentum fluxes and wind deficits in nocturnal stable atmospheric boundary layers

Published online by Cambridge University Press:  11 August 2025

Zhouxing Shen ,
Luoqin Liu Open the ORCID record for Luoqin Liu [Opens in a new window] ,
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]  and
Richard J.A.M. Stevens Open the ORCID record for Richard J.A.M. Stevens [Opens in a new window]
Zhouxing Shen
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Luoqin Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China
Richard J.A.M. Stevens
Affiliation:
Physics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, J.M. Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, Enschede 7500 AE, The Netherlands
*
Corresponding authors: Luoqin Liu, luoqinliu@ustc.edu.cn; Xi-Yun Lu, xlu@ustc.edu.cn
Corresponding authors: Luoqin Liu, luoqinliu@ustc.edu.cn; Xi-Yun Lu, xlu@ustc.edu.cn
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Abstract

Accurately predicting the mean flow properties of wall-bounded turbulence is essential for both fundamental research and engineering applications. In atmospheric boundary layers, the mean flow within the surface layer is typically described by Monin–Obukhov similarity theory (MOST). However, beyond the surface layer, MOST no longer applies as the Coriolis effect becomes significant. To address this issue, this study introduces a novel analytical model for the mean turbulent momentum fluxes and geostrophic wind deficits in nocturnal stable atmospheric boundary layers (NSBLs), which are stably stratified near the surface and transition to neutrally stratified flow above. The model solutions are derived from the Ekman equations using the eddy viscosity approach and a new parametrisation of the flux Richardson number. The solutions show that the geostrophic wind deficits scale with $u_*^2/(hf)$, where $u_*$ is the friction velocity, $h$ is the boundary layer height, and $f$ is the Coriolis parameter. The model’s predictions align closely with recent large-eddy simulation studies, confirming the model’s accuracy. Combined with the geostrophic drag law, the model can reliably predict the wind speed profile above the surface layer of NSBLs. This work marks a significant step in modelling atmospheric turbulence and its fundamental dynamics.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Turbulent boundary layers

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JFM Papers
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Journal of Fluid Mechanics , Volume 1017 , 25 August 2025 , A5
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© The Author(s), 2025. Published by Cambridge University Press

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