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Article
Article Type:
Research Article

A New Wall Shear Stress Model for Atmospheric Boundary Layer Simulations

Marcus Hultmark Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey

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Marc Calaf School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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Marc B. Parlange School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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Print Publication:
01 Nov 2013
DOI:
https://doi.org/10.1175/JAS-D-12-0257.1
Page(s):
3460–3470
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Abstract

A new wall shear stress model to be used as a wall boundary condition for large-eddy simulations of the atmospheric boundary layer is proposed. The new model computes the wall shear stress and the vertical derivatives of the streamwise velocity component by means of a modified, instantaneous, and local law-of-the-wall formulation. By formulating a correction for the modeled shear stress, using experimental findings of a logarithmic region in the streamwise turbulent fluctuations, the need for a filter is eliminated. This allows one to model the wall shear stress locally, and at the same time accurately recover the correct average value. The proposed model has been applied to both unique high Reynolds number experimental data and a suite of large-eddy simulations, and compared to previous models. It is shown that the proposed model performs equally well or better than the previous filtered models. A nonfiltered model, such as the one proposed, is an essential first step in developing a universal wall shear stress model that can be used for flow over heterogeneous surfaces, studies of diurnal cycles, or analyses of flow over complex terrain.

Current affiliation: Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah.

Corresponding author address: Marcus Hultmark, Department of Mechanical and Aerospace Engineering, Princeton University, D222 Engineering Quadrangle, Olden Street, Princeton, NJ 08544. E-mail: hultmark@princeton.edu

Abstract

A new wall shear stress model to be used as a wall boundary condition for large-eddy simulations of the atmospheric boundary layer is proposed. The new model computes the wall shear stress and the vertical derivatives of the streamwise velocity component by means of a modified, instantaneous, and local law-of-the-wall formulation. By formulating a correction for the modeled shear stress, using experimental findings of a logarithmic region in the streamwise turbulent fluctuations, the need for a filter is eliminated. This allows one to model the wall shear stress locally, and at the same time accurately recover the correct average value. The proposed model has been applied to both unique high Reynolds number experimental data and a suite of large-eddy simulations, and compared to previous models. It is shown that the proposed model performs equally well or better than the previous filtered models. A nonfiltered model, such as the one proposed, is an essential first step in developing a universal wall shear stress model that can be used for flow over heterogeneous surfaces, studies of diurnal cycles, or analyses of flow over complex terrain.

Current affiliation: Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah.

Corresponding author address: Marcus Hultmark, Department of Mechanical and Aerospace Engineering, Princeton University, D222 Engineering Quadrangle, Olden Street, Princeton, NJ 08544. E-mail: hultmark@princeton.edu
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