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<p>The atmospheric boundary layer is characterized by a logarithmic increase in wind speed within the surface layer and a turning of the wind vector aloft. The simplest canonical configuration featuring both <i>a logarithmic layer and wind turning</i> is Ekman flow. A formulation of the mean velocity profile was derived from scaling considerations and calibrated using direct numerical simulation (DNS) in Part I of this work. Here, we explore the extrapolation of this formulation to atmospheric Reynolds numbers (<i>Re</i>) using large-eddy simulation (LES). Theoretical profiles of the wind vector are compared to LES results at intermediate <i>Re</i>, which require consideration of viscous effects along with modifications to the standard bottom boundary condition. A grid convergence analysis shows that LES data converge towards the theoretical profiles for intermediate and high <i>Re</i>. The LES thus confirms that (i) the spanwise velocity scales as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10546_2025_933_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left. Re_\tau \right. ^{-1}\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10546_2025_933_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(Re_\tau \)</EquationSource> </InlineEquation> is the friction Reynolds number, and (ii) one third of the wind veer is confined to the surface layer. Such agreement between the theoretical formulation and LES data increases confidence in the underlying scaling assumptions, reinforcing the utility of the theoretical profiles as a reference for intermediate and a quasi-reference for both idealized simulation and field observation.</p>

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Wind Veer and Speed in Turbulent Ekman Flow–Part II: Comparison to LES for Atmospheric Reynolds Numbers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月28日

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  • Hauke Wurps,
  • Gerald Steinfeld,
  • Cedrick Ansorge

摘要

The atmospheric boundary layer is characterized by a logarithmic increase in wind speed within the surface layer and a turning of the wind vector aloft. The simplest canonical configuration featuring both a logarithmic layer and wind turning is Ekman flow. A formulation of the mean velocity profile was derived from scaling considerations and calibrated using direct numerical simulation (DNS) in Part I of this work. Here, we explore the extrapolation of this formulation to atmospheric Reynolds numbers (Re) using large-eddy simulation (LES). Theoretical profiles of the wind vector are compared to LES results at intermediate Re, which require consideration of viscous effects along with modifications to the standard bottom boundary condition. A grid convergence analysis shows that LES data converge towards the theoretical profiles for intermediate and high Re. The LES thus confirms that (i) the spanwise velocity scales as \(\left. Re_\tau \right. ^{-1}\) , where \(Re_\tau \) is the friction Reynolds number, and (ii) one third of the wind veer is confined to the surface layer. Such agreement between the theoretical formulation and LES data increases confidence in the underlying scaling assumptions, reinforcing the utility of the theoretical profiles as a reference for intermediate and a quasi-reference for both idealized simulation and field observation.