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

Ricardo Garc\'ia-Mayoral; Zishen Chen

arxiv: 2506.19223 · v3 · submitted 2025-06-24 · ⚛️ physics.flu-dyn

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

Zishen Chen , Ricardo Garc\'ia-Mayoral This is my paper

Pith reviewed 2026-05-19 08:28 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn

keywords canopy densityturbulence penetrationReynolds shear stressfrontal densitydirect numerical simulationdense regimesparse regimespanwise gap

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The pith

Turbulence penetration into canopies depends on spanwise gaps relative to eddy size rather than frontal density alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies turbulent flows over rigid canopy elements of varying geometries and Reynolds numbers to distinguish dense, intermediate and sparse regimes. Standard frontal density fails to predict penetration for anisotropic layouts such as streamwise-packed elements with wide spanwise gaps. Instead the work tracks the location and size of intense Reynolds shear stress eddies to define an effective spanwise gap. A penetration length is then set by the smaller of this gap or the eddy width. The regime follows directly: the length small compared with canopy height gives dense behaviour, comparable values give intermediate, and equal or larger values give sparse behaviour with easy penetration.

Core claim

A penetration length of order the minimum of the effective spanwise gap and the typical width of overlying eddies of intense Reynolds shear stress determines the canopy density regime. When this length is small relative to canopy height the canopy is dense and penetration is limited; when comparable it is intermediate; when roughly equal or larger it is sparse and penetration occurs relatively unhindered. This metric accounts for the observed dependence on Reynolds number and on preferential element orientation where frontal density does not.

What carries the argument

The penetration length, defined as the smaller of the effective spanwise gap between elements and the width of eddies carrying intense Reynolds shear stress.

If this is right

Streamwise-packed elements with large spanwise gaps allow significant penetration and register as sparse even at the same frontal density as isotropic layouts.
A fixed canopy geometry can shift from dense to sparser behaviour as Reynolds number rises because eddy size or penetration increases.
Turbulence is essentially blocked from the canopy interior when the spanwise gap is smaller than the eddy size.
The regime classification applies across isotropic and anisotropic layouts, different element heights, width-to-pitch ratios and Reynolds numbers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The penetration length could be measured in laboratory experiments at higher Reynolds numbers to test whether the regime transition continues as eddy scales grow.
Similar gap-versus-eddy comparisons might organise data for drag or scalar transport in canopy flows without requiring new simulations for each layout.
Field observations of natural vegetation could check whether the same length scale separates dense and sparse regimes when element flexibility is present.

Load-bearing premise

The position and extent of eddies of intense Reynolds shear stress are the main quantities that set how far turbulence penetrates the canopy.

What would settle it

Direct observation of substantial turbulence penetration into a canopy whose measured spanwise gap is much smaller than the width of the intense Reynolds stress eddies would falsify the proposed classification.

read the original abstract

Turbulent flows over canopies of rigid elements with different geometries and Reynolds numbers (Re) are investigated to identify and characterise different canopy density regimes. In the sparse regime, turbulence penetrates relatively unhindered within the canopy, whereas in the dense regime, the penetration is limited. A common measure of canopy density is the ratio of frontal to bed area, the frontal density $\lambda_f$. This is effective for canopies with no preferential orientation, but we observe that it does not accurately predict the density regime for less conventional ones, so it may not encapsulate the governing physics. Instead, we propose density metrics based on the position and extent of eddies of intense Reynolds shear stress. We analyse a series of direct simulations for isotropic and anisotropic layouts, across a range of $\lambda_f$, height, element width-to-pitch ratio and Re. Canopies with streamwise-packed elements but large spanwise gaps allow significant turbulence penetration, and appear sparse compared to isotropic or spanwise-packed canopies with the same $\lambda_f$. Turbulence penetration depends on an effective spanwise gap, and increases with it, but depends also on Re. A canopy can behave as dense at low Re, but as sparser as Re increases. This suggests that turbulence penetration depends on the size of the spanwise gap relative to the typical width of the overlying eddies. Turbulence penetrates easily when the spanwise gap is larger than the eddy size, and is essentially precluded from penetrating in the opposite case. A penetration length can then be defined that is of the order of the effective spanwise gap or the eddy size, whichever is smaller. If the penetration length is small compared to the canopy height, the canopy behaves as dense; if it is comparable, as intermediate; and if it is roughly equal or larger, as sparse.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper replaces frontal density with a penetration length set by the smaller of spanwise gap and intense-RSS eddy size, which better handles anisotropy and Re effects in the DNS cases, but the eddy extraction step lacks an explicit reproducible method.

read the letter

Colleague, the main takeaway is that standard frontal density λ_f misses the mark for canopies with strong orientation, and the authors instead tie the regime to whether the effective spanwise gap is larger or smaller than the width of intense Reynolds shear stress eddies. They define a penetration length as roughly the min of those two scales, then classify the canopy as dense, intermediate, or sparse depending on how that length compares to canopy height. The DNS runs across isotropic and anisotropic layouts plus a range of Re show that streamwise-packed elements with wide spanwise gaps let turbulence in more than isotropic cases at the same λ_f, and that higher Re can shift a canopy toward sparser behavior. That observation is useful and not just a restatement of prior work. The simulations cover enough variations in geometry and Re to make the qualitative trends credible, and the point that penetration depends on gap-to-eddy comparison follows directly from the data they present. The soft spot is the missing detail on how the eddies are actually located and sized. The abstract gives no threshold for “intense,” no spatial filter, no connected-component rule, and no test of whether small changes in those choices flip the regime assignments. Without that, it is hard to judge how robust the metric really is or to reproduce the classification on new data. The concern about an algorithmic definition is fair and not minor if the claim is meant to be predictive rather than descriptive. This is aimed at people who model or measure canopy turbulence in environmental or engineering flows, where anisotropy and Reynolds-number dependence show up regularly. A reader working on vegetation or urban roughness would find the new organizing idea worth looking at. It deserves a serious referee because the simulations are direct, the limitation of λ_f is shown with concrete cases, and the proposed alternative is grounded in observable flow features. I would send it for review and ask the authors to supply the exact procedure for extracting eddy size and to check sensitivity to reasonable variations in that procedure.

Referee Report

1 major / 1 minor

Summary. The manuscript uses DNS to examine turbulent flows over rigid canopy elements with isotropic and anisotropic layouts across varying frontal densities λ_f, heights, width-to-pitch ratios, and Reynolds numbers. It shows that λ_f does not reliably predict density regimes for anisotropic configurations, and instead proposes new metrics based on the position and extent of intense Reynolds shear stress eddies. A penetration length is defined as being of the order of the smaller of the effective spanwise gap or the typical eddy width; the canopy is classified as dense, intermediate, or sparse according to whether this length is small, comparable, or equal/larger relative to canopy height. The work also notes Re dependence, with canopies appearing denser at low Re and sparser at higher Re.

Significance. If the penetration length can be shown to be a reproducible and robust classifier that cleanly separates observed penetration behaviors, the result would supply a physically motivated alternative to λ_f that incorporates anisotropy and Reynolds-number effects, with potential value for improved modeling of canopy turbulence in environmental and engineering contexts.

major comments (1)

[Abstract] Abstract (and the corresponding results section): the central claim introduces a penetration length 'of the order of the effective spanwise gap or the eddy size, whichever is smaller' without an explicit, reproducible extraction procedure (threshold for 'intense' Reynolds shear stress, spatial filtering, connected-component criteria, or fitting method) for locating and sizing the eddies from the simulation fields. Because the regime classification rests on this length scale, the absence of an algorithmic definition and of sensitivity tests to reasonable variations in that definition makes the metric difficult to verify or reproduce.

minor comments (1)

The abstract states that turbulence penetration 'depends also on Re' and that a canopy 'can behave as dense at low Re, but as sparser as Re increases,' yet no quantitative measure of this dependence (e.g., scaling of penetration length with Re) is supplied in the summary; a concise statement or figure reference would strengthen the presentation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the major comment point by point below and have revised the manuscript to incorporate the requested clarifications where appropriate.

read point-by-point responses

Referee: [Abstract] Abstract (and the corresponding results section): the central claim introduces a penetration length 'of the order of the effective spanwise gap or the eddy size, whichever is smaller' without an explicit, reproducible extraction procedure (threshold for 'intense' Reynolds shear stress, spatial filtering, connected-component criteria, or fitting method) for locating and sizing the eddies from the simulation fields. Because the regime classification rests on this length scale, the absence of an algorithmic definition and of sensitivity tests to reasonable variations in that definition makes the metric difficult to verify or reproduce.

Authors: We agree that the current presentation would benefit from greater explicitness to ensure reproducibility. In the revised manuscript we will add a dedicated subsection in the methods that provides the full algorithmic definition: the precise threshold used to identify intense Reynolds shear stress regions (a multiple of the local rms value of u'w'), the spatial filtering or smoothing applied prior to identification, the connected-component labeling criteria (including minimum volume and connectivity rules) used to isolate individual eddies, and the geometric measure adopted for eddy width (principal-axis extent of the connected region). We will also report a sensitivity analysis demonstrating that the resulting penetration length and regime classifications remain stable under modest variations of the threshold and filtering parameters. These additions will be referenced from both the abstract and the results section. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of penetration length from eddy observations

full rationale

The paper performs direct numerical simulations across geometries and Re, identifies positions/extents of intense Reynolds shear stress eddies from the flow fields, and defines a penetration length as the smaller of effective spanwise gap or typical eddy width. This length is then compared to canopy height to assign dense/intermediate/sparse labels. The eddy identification and length definition are extracted from the simulation data independently of the final regime classification; the classification is a post-analysis comparison rather than an input that constrains the eddy metrics. No self-citations, fitted parameters renamed as predictions, or self-definitional loops appear in the provided text. The central claim remains an observational characterization supported by the simulation results themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on standard incompressible Navier-Stokes assumptions plus the modeling choice that intense Reynolds-shear-stress eddies dominate penetration physics. No free parameters are introduced in the abstract; the penetration length is defined directly from observed scales.

axioms (2)

standard math Incompressible Navier-Stokes equations govern the flow at the simulated Reynolds numbers.
Implicit in any DNS of turbulent canopy flow.
domain assumption Eddies of intense Reynolds shear stress are the dominant structures controlling vertical momentum transport into the canopy.
Stated as the basis for the new density metrics in the abstract.

invented entities (1)

Penetration length no independent evidence
purpose: Scalar measure of turbulence access into canopy, taken as min(effective spanwise gap, typical eddy size).
Defined in the abstract as the quantity that determines dense/intermediate/sparse behavior when compared to canopy height.

pith-pipeline@v0.9.0 · 5866 in / 1469 out tokens · 39500 ms · 2026-05-19T08:28:12.718638+00:00 · methodology

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

Core claim

What carries the argument

If this is right

Where Pith is reading between the lines

Load-bearing premise

What would settle it

discussion (0)