<p>Understanding the effect of vegetation on the dynamics of air motion in the lower atmosphere is essential across a wide range of contexts, from forest canopies to vegetated urban canyons. Wind tunnel and water channel experiments enable controlled investigations of these processes; however, the simplified, reduced-scale vegetation models commonly used raise important questions about their representativeness of real vegetated structures. Unlike classical bluff bodies, it is still uncertain whether the flow around porous and geometrically complex elements such as vegetation becomes independent of the Reynolds number, even at high values. Furthermore, the role of multiscale structural elements must be examined to determine what physical processes are lost when models include only one or a few characteristic scales. More broadly, identifying the key geometric parameters that govern flow–vegetation interactions is crucial for the design of realistic reduced-scale vegetation models. In this study, wind tunnel experiments were conducted to investigate the dynamics of a wake behind an isolated model tree immersed in a turbulent boundary layer using Particle Image Velocimetry (PIV) measurements. Various approach velocities and crown porosities were tested, and, unlike most studies, the models used here include elements of multiple sizes. Beyond standard one-point statistics, the pressure field and Eulerian length scales were estimated and found to be significantly affected by the crown porosity, but insensitive to the Reynolds number, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$Re=H\ u_{ref}/\nu $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mi>H</mi> <mspace width="4pt" /> <msub> <mi>u</mi> <mrow> <mi mathvariant="italic">ref</mi> </mrow> </msub> <mo stretchy="false">/</mo> <mi>ν</mi> </mrow> </math></EquationSource> </InlineEquation>, in the range 1.1<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\times \,10^{4}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>×</mo> <mspace width="0.166667em" /> <msup> <mn>10</mn> <mn>4</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> - 3.8<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\times \,10^{4}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>×</mo> <mspace width="0.166667em" /> <msup> <mn>10</mn> <mn>4</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> (with <i>H</i> the model height, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$u_{ref}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>u</mi> <mrow> <mi mathvariant="italic">ref</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> the mean velocity at the crown top and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\nu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ν</mi> </math></EquationSource> </InlineEquation> air viscosity). Finally, Proper Orthogonal Decomposition was applied to analyse flow structures and their temporal evolution, revealing a few dominant modes associated with a flapping/oscillating shear layer in the wake, which drives most of the Reynolds stresses <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\overline{u'u'}$</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mrow> <msup> <mi>u</mi> <mo>′</mo> </msup> <msup> <mi>u</mi> <mo>′</mo> </msup> </mrow> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\overline{u'w'}$</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mrow> <msup> <mi>u</mi> <mo>′</mo> </msup> <msup> <mi>w</mi> <mo>′</mo> </msup> </mrow> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>.</p>

The Dynamics of a Wake Behind an Isolated Model Tree Within an Atmospheric Boundary Layer

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2026年4月6日

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Livia Grandoni,
Marc Michard,
Nathalie Grosjean,
Pietro Salizzoni

摘要

Understanding the effect of vegetation on the dynamics of air motion in the lower atmosphere is essential across a wide range of contexts, from forest canopies to vegetated urban canyons. Wind tunnel and water channel experiments enable controlled investigations of these processes; however, the simplified, reduced-scale vegetation models commonly used raise important questions about their representativeness of real vegetated structures. Unlike classical bluff bodies, it is still uncertain whether the flow around porous and geometrically complex elements such as vegetation becomes independent of the Reynolds number, even at high values. Furthermore, the role of multiscale structural elements must be examined to determine what physical processes are lost when models include only one or a few characteristic scales. More broadly, identifying the key geometric parameters that govern flow–vegetation interactions is crucial for the design of realistic reduced-scale vegetation models. In this study, wind tunnel experiments were conducted to investigate the dynamics of a wake behind an isolated model tree immersed in a turbulent boundary layer using Particle Image Velocimetry (PIV) measurements. Various approach velocities and crown porosities were tested, and, unlike most studies, the models used here include elements of multiple sizes. Beyond standard one-point statistics, the pressure field and Eulerian length scales were estimated and found to be significantly affected by the crown porosity, but insensitive to the Reynolds number, $Re=H\ u_{ref}/\nu $ $R e = H u_{ref} / ν$ , in the range 1.1 $\times \,10^{4}$ $\times 10^{4}$ - 3.8 $\times \,10^{4}$ $\times 10^{4}$ (with H the model height, $u_{ref}$ $u_{ref}$ the mean velocity at the crown top and $\nu $ $ν$ air viscosity). Finally, Proper Orthogonal Decomposition was applied to analyse flow structures and their temporal evolution, revealing a few dominant modes associated with a flapping/oscillating shear layer in the wake, which drives most of the Reynolds stresses $\overline{u'u'}$ $\bar{u^{'} u^{'}}$ and $\overline{u'w'}$ $\bar{u^{'} w^{'}}$ .