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The global properties of nocturnal stable atmospheric boundary layers

Published online by Cambridge University Press:  14 November 2024

Zhouxing Shen ,
Luoqin Liu Open the ORCID record for Luoqin Liu [Opens in a new window] ,
Xiyun Lu Open the ORCID record for Xiyun 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 230027, Anhui, PR China
Luoqin Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, Anhui, PR China
Xiyun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, Anhui, 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, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

Accurate prediction of the global properties of wall-bounded turbulence holds significant importance for both fundamental research and engineering applications. In atmospheric boundary layers, the relationship between friction drag and geostrophic wind is described by the geostrophic drag law (GDL). We use carefully designed large-eddy simulations to study nocturnal stable atmospheric boundary layers (NSBLs), which are characterized by a negative potential temperature flux at the surface and neutral stratification higher up. Our simulations explore a wider range of the Kazanski–Monin parameter, $\mu = L_f / L_s = [16.7, 193.3]$, with $L_f$ the Ekman length scale and $L_s$ the surface Obukhov length. We show collapse of the GDL coefficients onto single curves as functions of $\mu$, thereby validating the GDL's applicability to NSBLs over a very wide $\mu$ range. We show that the boundary-layer height $h$ scales with $\sqrt {L_f L_s}$, while both the streamwise and spanwise wind gradients scale with $u_*^2 / (h^2 f)$, where $u_*$ represents the friction velocity and $f$ the Coriolis parameter. Leveraging these insights, we developed new analytical expressions for the GDL coefficients, significantly enhancing our understanding of the GDL for turbulent boundary layers. These formulations facilitate the analytical prediction of the geostrophic drag coefficient and cross-isobaric angle.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 999 , 25 November 2024 , A60
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© The Author(s), 2024. Published by Cambridge University Press

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