A systematic characterisation of canopy density based on turbulent-structure penetration.

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Title: A systematic characterisation of canopy density based on turbulent-structure penetration.
Authors: Chen, Zishen1 (AUTHOR), García-Mayoral, Ricardo1 (AUTHOR) r.gmayoral@eng.cam.ac.uk
Source: Journal of Fluid Mechanics. 4/25/2026, Vol. 1033, p1-41. 41p.
Subjects: Turbulence, Coherent structures, Flow simulations, Reynolds number, Turbulent flow
Abstract: We investigate turbulent flows over canopies of rigid elements with different geometries, spacings and Reynolds numbers to identify and characterise different canopy density regimes. In the sparse regime, the overlying turbulence penetrates relatively unhindered within the canopy, whereas in the dense regime, this penetration is limited. The frontal density, $\lambda _f$ , a common a measure of canopy density, is effective for e.g. conventional vegetation with no preferential orientation, but we observe that it does not fully characterise the density regime for some less conventional topologies, suggesting it may not always capture the underlying physics. To address this, we propose to quantify turbulence penetration directly, from the position and extent of individual turbulent eddies, particularly those associated with intense Reynolds shear stress. We analyse a series of direct simulations for isotropic- and anisotropic-layout canopies with frontal densities $\lambda _f\approx 0.01$ – $2.04$ , heights $h^+\approx 44$ – $266$ , element width-to-pitch ratios $w/s\approx 0.06$ – $0.7$ and Reynolds numbers ${\textit{Re}}_{\tau} \approx 180$ – $2000$. For the same $\lambda _f$ , canopies with elements closely packed in the streamwise direction but large spanwise gaps result in deeper turbulence penetration, appearing sparser than isotropic or spanwise-packed ones. For the same spanwise gap, turbulence penetration remains similar across canopies independently of their streamwise pitch and gap. As the spanwise gap increases, eddies penetrate deeper and more vigorously into the canopy. Turbulence penetration is also Reynolds-number-dependent: the same canopy can behave as dense at low ${\textit{Re}}_{\tau}$ , but increasingly sparse as ${\textit{Re}}_{\tau}$ increases. Our results suggest that turbulence penetration depends essentially on the ability of turbulent eddies to fit within the canopy as they travel downstream, and that this can be characterised by an effective spanwise gap, and its ratio to the typical eddy size; turbulence penetration is substantial when this gap is larger than the eddy size, and negligible in the opposite case. A penetration length $d_p$ can then be defined from the effective gap or the eddy size, whichever is smaller. For small $d_p/h$ , the canopy behaves as dense; for moderate $d_p/h$ , as intermediate; and for $d_p/h\approx 1$ , turbulent eddies can penetrate all the way to the canopy bed and the canopy behaves as sparse. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: A systematic characterisation of canopy density based on turbulent-structure penetration.
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  Data: <searchLink fieldCode="AR" term="%22Chen%2C+Zishen%22">Chen, Zishen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22García-Mayoral%2C+Ricardo%22">García-Mayoral, Ricardo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> r.gmayoral@eng.cam.ac.uk</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 4/25/2026, Vol. 1033, p1-41. 41p.
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  Data: <searchLink fieldCode="DE" term="%22Turbulence%22">Turbulence</searchLink><br /><searchLink fieldCode="DE" term="%22Coherent+structures%22">Coherent structures</searchLink><br /><searchLink fieldCode="DE" term="%22Flow+simulations%22">Flow simulations</searchLink><br /><searchLink fieldCode="DE" term="%22Reynolds+number%22">Reynolds number</searchLink><br /><searchLink fieldCode="DE" term="%22Turbulent+flow%22">Turbulent flow</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We investigate turbulent flows over canopies of rigid elements with different geometries, spacings and Reynolds numbers to identify and characterise different canopy density regimes. In the sparse regime, the overlying turbulence penetrates relatively unhindered within the canopy, whereas in the dense regime, this penetration is limited. The frontal density, $\lambda _f$ , a common a measure of canopy density, is effective for e.g. conventional vegetation with no preferential orientation, but we observe that it does not fully characterise the density regime for some less conventional topologies, suggesting it may not always capture the underlying physics. To address this, we propose to quantify turbulence penetration directly, from the position and extent of individual turbulent eddies, particularly those associated with intense Reynolds shear stress. We analyse a series of direct simulations for isotropic- and anisotropic-layout canopies with frontal densities $\lambda _f\approx 0.01$ – $2.04$ , heights $h^+\approx 44$ – $266$ , element width-to-pitch ratios $w/s\approx 0.06$ – $0.7$ and Reynolds numbers ${\textit{Re}}_{\tau} \approx 180$ – $2000$. For the same $\lambda _f$ , canopies with elements closely packed in the streamwise direction but large spanwise gaps result in deeper turbulence penetration, appearing sparser than isotropic or spanwise-packed ones. For the same spanwise gap, turbulence penetration remains similar across canopies independently of their streamwise pitch and gap. As the spanwise gap increases, eddies penetrate deeper and more vigorously into the canopy. Turbulence penetration is also Reynolds-number-dependent: the same canopy can behave as dense at low ${\textit{Re}}_{\tau}$ , but increasingly sparse as ${\textit{Re}}_{\tau}$ increases. Our results suggest that turbulence penetration depends essentially on the ability of turbulent eddies to fit within the canopy as they travel downstream, and that this can be characterised by an effective spanwise gap, and its ratio to the typical eddy size; turbulence penetration is substantial when this gap is larger than the eddy size, and negligible in the opposite case. A penetration length $d_p$ can then be defined from the effective gap or the eddy size, whichever is smaller. For small $d_p/h$ , the canopy behaves as dense; for moderate $d_p/h$ , as intermediate; and for $d_p/h\approx 1$ , turbulent eddies can penetrate all the way to the canopy bed and the canopy behaves as sparse. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1017/jfm.2026.11446
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 41
        StartPage: 1
    Subjects:
      – SubjectFull: Turbulence
        Type: general
      – SubjectFull: Coherent structures
        Type: general
      – SubjectFull: Flow simulations
        Type: general
      – SubjectFull: Reynolds number
        Type: general
      – SubjectFull: Turbulent flow
        Type: general
    Titles:
      – TitleFull: A systematic characterisation of canopy density based on turbulent-structure penetration.
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            NameFull: Chen, Zishen
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            NameFull: García-Mayoral, Ricardo
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          Dates:
            – D: 25
              M: 04
              Text: 4/25/2026
              Type: published
              Y: 2026
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              Value: 1033
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