The Mean Wind and Potential Temperature Flux Profiles in Convective Boundary Layers

Luoqin Liu aDepartment of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui, China
bPhysics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, J. M. Burgers Center for Fluid Dynamics, University of Twente, Enschede, Netherlands

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Srinidhi N. Gadde bPhysics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, J. M. Burgers Center for Fluid Dynamics, University of Twente, Enschede, Netherlands

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Richard J. A. M. Stevens bPhysics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, J. M. Burgers Center for Fluid Dynamics, University of Twente, Enschede, Netherlands

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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 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/z0 ∈ [3.6 × 102, 0.7 × 105], where L is the Obukhov length and z0 is the roughness length.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Luoqin Liu, luoqinliu@ustc.edu.cn

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 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/z0 ∈ [3.6 × 102, 0.7 × 105], where L is the Obukhov length and z0 is the roughness length.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Luoqin Liu, luoqinliu@ustc.edu.cn
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