Transport Dynamics and Multiscale Turbulence Analysis of Vegetation Canopies Based on Wind Tunnel Experiments

Abstract

The momentum transport and scale-dependent motion characteristics within vegetation canopies play a crucial role in shaping near-surface turbulent structures and exchange processes, yet the interactions among different turbulent scales and their statistical representations remain insufficiently understood. Based on a series of controlled wind tunnel experiments, this study identifies coherent turbulent structures using a phase-space algorithm constructed from streamwise velocity fluctuation u′, acceleration a, and jerk j, and compares transport efficiency (exuberance η). This study uses scale-wise (cut-off frequency) momentum flux contribution analysis, natural visibility graph (NVG), and large–small-scale amplitude modulation to examine transport and multiscale behaviors across different canopy densities, array layouts, and inflow conditions. Results show that canopy density (different C_d drag coefficient) is a primary factor governing transport efficiency. Under low-wind staggered configurations, increasing canopy density strengthens the contribution of low-frequency large-scale motions to total momentum flux. In contrast, high-wind aligned configurations intensify canopy-top shear, enhancing small-scale motions and thereby reducing the relative contribution of large-scale motions. NVG analysis further reveals that in high-density canopies, large-scale acceleration and deceleration events tend toward equilibrium, whereas deceleration events dominate consistently in low- and medium-density cases. Amplitude modulation results indicate that high-density cases exhibit highly consistent modulation behavior, followed by low-density cases, while medium-density cases display a pronounced height-dependent variation, characterized by a distinct modulation critical point. This study proposes a unified analytical framework integrating coherent structure detection, graph-theoretic analysis, multiscale transport characterization, and large–small-scale modulation, providing a comprehensive description of momentum transport and scale motions within canopy flows, and it offers new insight into the mechanisms governing complex vegetation canopy turbulence.

1. Introduction

Urban environments are increasingly shaped by complex roughness elements that regulate airflow, turbulence, and pollutant transport near the surface. Among these elements, vegetation has become a critical component as cities adopt more green infrastructure for environmental and climatic benefits [1,2]. Vegetation behaves as a porous, permeable obstacle whose distributed drag and multiscale interactions generate flow adjustments far more complex than those produced by solid building walls.

Wind tunnel, numerical, and field studies have explored vegetation effects on airflow and pollutant transport. Conan et al. [3] linked coherent structures to momentum and scalar fluxes over vegetation canopies. Mo et al. [4] analyzed turbulence across canopies of varying densities and validated a wind-profile model for the RSL and ISL. Liu et al. [5], using LES, examined scalar transport downstream of fractal trees, highlighting vegetation-induced mixing. However, the impact of vegetation on urban air quality remains inconsistent. Canopy arrangement, porosity, and leaf area density have been associated with both pollutant accumulation and removal in street canyons [1,2,6,7]. Several studies report reduced ventilation and increased pollutant levels due to trees [8,9,10], while field observations show that vegetation can trap pollutants in deep or confined street canyons [11,12].

A variety of approaches have been developed to identify coherent turbulent motions responsible for transport and mixing in wall-bounded and urban flows, like U-level detection [13] and quadrant analysis [14]. However, such methods typically rely on user-defined thresholds. Based on a filtering technique used in 1D data [15], refined phase-space techniques have been developed to objectively identify extreme turbulent events characterized by large velocity, acceleration, or jerk, providing a more systematic description of turbulence dynamics [16].

Natural visibility graph (NVG) methods provide a network-based framework for analyzing turbulence signals beyond conventional statistical approaches. Lacasa et al. [17] established that time series can be transformed into complex networks that preserve structural properties of periodic, random, and fractal signals. Subsequent studies demonstrated that NVGs capture multiscale organization in wall-bounded turbulence and reveal large–small-scale modulation through topological metrics [18,19,20,21]. Together, these works position visibility-graph analysis as a robust and parameter-free tool for extracting structural information from turbulent flows.

Amplitude modulation (AM) has been extensively studied to understand large–small-scale interactions in boundary-layer turbulence. Experimental studies have documented how large-scale motions (LSMs and VLSMs) influence near-wall turbulence [22,23,24,25,26,27], though certain AM metrics may be biased or sensitive to signal characteristics [22]. Both laboratory and rough-wall experiments indicate that modulation strength depends on Reynolds number, surface roughness, and flow configuration [23,24,25,26,27]. Numerical simulations offer further mechanistic insight: LES studies link modulation to systematic phase relationships between scales [28,29], while DNS confirms that AM intensifies with increasing Reynolds number and enhances near-wall extreme events [30]. Methodological evaluations suggest that spectral filtering provides reliable scale separation [31], and simulations over realistic urban geometries highlight strong spatial variability in modulation [32].

In current vegetation canopy turbulence research, two important gaps remain. First, momentum transport has rarely been decomposed by scale, and most studies report only the total momentum flux, without quantifying the contributions of different turbulence scales. Second, large–small-scale interactions in canopy turbulence have been explored only to a limited extent. The present study provides a partial contribution to two gaps.

To provide a unified analytical framework, the present study integrates phase-space detection, NVG-based temporal characterization, amplitude modulation analysis, and scale-wise momentum flux contribution. These complementary methods together quantify how canopy density and array configuration regulate coherent structures, large-scale motions, and momentum transport. The organization of this paper is as follows: Section 2 presents the wind tunnel experimental setup and parameter details. Section 3 focuses on the presentation and analysis of the results, including transport efficiency, contributions to momentum flux, the acceleration and deceleration effects of large-scale motions, and large–small-scale amplitude modulation. Finally, Section 4 summarizes the main conclusions.

2. Wind Tunnel Experiments

The experiment was carried out in an open-circuit, isothermal wind tunnel located in the Department of Mechanical Engineering at The University of Hong Kong (Figure 1). The airflow is generated by a three-phase blower, whose output is adjusted through a variable-frequency drive, allowing reference wind speeds between approximately 0.5 m and 19 m/s. Upstream of the test section, a flow-conditioning system—comprising a straightening element followed by a honeycomb layer positioned between the settling chamber and the contraction—was implemented to maintain a low ambient turbulence level (kept under 5%). The working section measures 6 m in length and 0.56 m × 0.56 m in cross-section. Artificial tree elements were mounted across the entire floor of the test section to ensure the formation of a fully developed turbulent boundary layer.

The canopy models were constructed using arrays of identical plastic tree elements. Each element was fitted onto a LEGO^® brick, allowing the vegetation density to be properly controlled. The representative dimensions of a single tree unit are approximately 25 mm in length and width, and 30 mm in height (including the LEGO^® connector at the base; see Figure 1a–d). These elements were subsequently arranged on LEGO^® baseplates that were fixed to the entire floor of the wind tunnel test section. Six different spatial configurations of the tree arrays were examined (Figure 2a–i). The streamwise spacing b was systematically varied, yielding three distinct height-to-spacing ratios (h/b = 0.47 in high-density cases, 0.23 in medium-density cases, and 0.12 in low-density cases). The streamwise spacing b was systematically varied, yielding three distinct height-to-spacing ratios (h/b = 0.47, 0.23, and 0.12). Two plan arrangements—aligned and staggered—were considered. For the staggered setups, experiments were further conducted under two nominal wind speed ranges: a lower-speed band (approximately 9–12 m/s) and a higher-speed band (approximately 14–16 m/s). Two levels of freestream wind speeds are employed to test Reynolds number independence. In total, nine experimental cases were carried out. The complete categorization of these cases has been summarized in

Table 1. TBL parameters in the wind tunnel experiments.

Cases	Figure 2	U∞ (m/s)	u* (m/s)	Cd (×10−3)	δ (mm)	ISL (mm)	RSL (mm)	Re∞ (×103)	Re * (×103)
HDLW-S	(a)	11.94	0.71	7.02	250	106	84	298	17
MDLW-S	(b)	9.71	0.6	7.56	235	117	94	228	14
LDLW-S	(c)	11.48	0.56	4.73	220	98	82	252	12
HDHW-S	(d)	15.77	0.93	7.01	250	100	82	394	23
MDHW-S	(e)	14.09	0.87	7.6	235	117	98	331	20
LDHW-S	(f)	14.6	0.73	4.95	225	112	92	328	16
HDHW-A	(g)	14.73	0.79	5.72	240	94	76	353	18
MDHW-A	(h)	14.43	0.84	6.76	225	102	84	324	18
LDHW-A	(i)	14.74	0.66	4.07	250	100	82	368	16

, and a representative example is the LDLW-S case, referring to low density, low wind speed, and staggered arrangement.

Some parameters are defined as follows: U_∞ is the freestream wind speed. The friction velocity is estimated by the spatio-temporal average of downward momentum flux, i.e., u*² = − <u″ w″> [33,34]. The drag coefficient is calculated by C_d = u*²/2U_∞². The TBL thickness δ is defined at the height z where the spatio-temporal average of wind speed converges to 99% of the freestream value <u>|_z=δ = 0.99U_∞. The top and the bottom of ISLs are identified at the heights where the mean wind speeds no longer follow the log-law, and the RSL top is then taken at the ISL bottom. The Reynolds numbers based on the freestream wind speed and friction velocity are Re_∞ (= U∞δ/ν) and Re_* (= u*δ/ν).

The relatively low turbulence intensity in the wind tunnel represents a limitation of the present study, as it does not fully reproduce the energetic and intermittent turbulence typically observed in real atmospheric boundary-layer flows. This difference may restrict the direct applicability of the results to natural environments. Nevertheless, the primary objective of this work is to investigate relative transport mechanisms under controlled laboratory conditions, where the influence of canopy density and configuration can be systematically examined without external variability. Within this experimental framework, the observed trends remain physically consistent and meaningful. Future studies will consider higher background turbulence levels to further assess the robustness and broader applicability of the findings.

Another limitation of the present study is that the canopy models are rigid and therefore cannot capture the dynamic responses of real vegetation, such as bending and oscillation under wind loading. These flexible behaviors may alter wake development, turbulence generation, and momentum exchange in ways that rigid models cannot represent. Incorporating flexibility into the experimental setup would require more complex design considerations, including material properties and dynamic similarity requirements. This will be an important direction for future work aimed at achieving a more realistic representation of canopy–flow interactions.

3. Results and Discussion

3.1. Transport Efficiency and Phase-Space Algorithm

The three-dimensional distribution of exuberance η, scale coefficient k (the analytical approach follows Wu et al. [16] and Chen et al. [35]), and drag coefficient C_d for different tree arrays is illustrated in Figure 3. The scale coefficient k is introduced to control the size based on streamwise velocity fluctuation u′, acceleration a, and jerk j [16] of the detection ellipsoid in phase space. For a given dataset, all other parameters are fixed, and k is the only free parameter determining the volume of the detection ellipsoid. As k increases, the ellipsoid expands in phase space and encloses an increasing number of data points. Consequently, fewer data points remain on the surface of, or outside, the ellipsoid and are identified as coherent structure data points. Therefore, k effectively represents the scale employed in the phase-space detection and is defined as a scaling coefficient.

The momentum flux fraction

$$S_i={\displaystyle \frac{\overline{{〈u^{\prime }{w}^{\prime }〉}_{Qi}}}{\overline{〈u^{\prime }{w}^{\prime }〉}}}$$

(1)

quantifies the contribution from the i-th quadrant Q_i to the spatio-temporal average of vertical momentum flux $⟨\overline{u^{\prime }{w}^{\prime }}⟩$. Subsequently, the exuberance

$$\eta ={\displaystyle \frac{S_1+S_3}{S_2+S_4}}$$

(2)

is used to compare the turbulent transport efficiency [36,37,38,39,40] and is defined as a measure of the relative contribution of momentum-enhancing (Q₂ and Q₄) versus momentum-reducing (Q₁ and Q₃) turbulent events, and therefore represents the intrinsic capability of the canopy flow to support vertical momentum transfer. In view of the transport direction of Q_i, less negative exuberance implies more efficient vertical transport.

Transport efficiency remains comparable across different experimental conditions because its physical meaning is unchanged, and the definition and interpretation of η do not depend on canopy density, inflow conditions, or turbulence intensity, ensuring that all cases are evaluated under the same physical framework. The uncertainty of η is small because the quadrant contributions are derived from long, well-converged time series and averaged over multiple measurement points. These procedures ensure statistical stability, so the computed η is reliable and suitable for cross-case comparison despite variations in experimental conditions.

In general, arrays with lower planting density exhibit reduced drag coefficients. The transport efficiency at roof level rises as the drag coefficient increases (Figure 3). However, when the scale coefficient k exceeds approximately 0.35 (a transition point in the phase-space detection scale, beyond which the characteristics of the detected coherent structures change markedly), the transport efficiency decreases markedly.

This behavior is associated with the role of k in the phase-space detection algorithm. As k increases, the detection ellipsoid expands (major half-axis $e_{u^{\prime }}=k\lambda {\sigma }_{u^{\prime }}$, median half-axis $e_a=k\lambda {\sigma }_a$, minor half-axis $e_j=k\lambda {\sigma }_j$, $\lambda$ is the characteristic size of coherent structures, u′ is the streamwise velocity fluctuation, a is the acceleration, and j is the jerk, and detailed calculation procedures for the relevant parameters are provided in [16]), data points satisfying this criterion (u′/eu′2 + a/ea′2 + j/ej′2 ≥ 1) are identified as coherent structures, and more data points are enclosed within the ellipsoid and are, therefore, excluded from the coherent structure analysis. Consequently, the analysis increasingly relies on data points located on the ellipsoid surface or outside it.

In Figure 4, the classification uses k₃ = 1 as the reference boundary. As the value of k decreases from this state, a portion of the previously black non-coherent points will be out of the ellipsoid and is therefore reclassified as brown coherent structures. When k is small (e.g., k₁ = 0.2), the ellipsoid is compact and excludes only a small portion of data near the origin, leaving many points on or outside the surface to be identified as coherent structures. As k increases (e.g., k₂ = 0.5 or k₃ = 1.0), the ellipsoid expands substantially, reducing the number of effective points outside the surface. The remaining points are typically associated with lower momentum-transport efficiency, explaining the progressive decline in overall transport efficiency with increasing k. In the analysis, each phase-space point is represented by a three-dimensional vector (u′, a, j), corresponding to streamwise velocity fluctuation u′, acceleration a, and jerk j.

At larger values of k, these remaining points are predominantly distributed farther from the phase-space origin and are associated with structures that exhibit intrinsically lower momentum transport efficiency. As a result, the overall transport efficiency decreases progressively with increasing k.

The phase-space method plays a central role in interpreting the momentum-transport behavior revealed in this study. By jointly considering the multi-order quantities (u′, a′, j′), the phase-space framework identifies coherent structures based on their intrinsic dynamical signatures rather than single-variable thresholds. The ellipsoidal criterion provides a geometrically rigorous separation to quantify how canopy density and array configuration regulate the transport efficiency of coherent structures. Specifically, by capturing how the dynamical trajectory of a structure evolves in phase space, the method reveals whether coherent structures enhance or suppress vertical momentum exchange. This capability is essential for explaining the transition in transport efficiency observed at k = 0.35, as only the phase-space method can explicitly reveal how the momentum-transport capability of coherent structures degrades when the detection scale expands.

3.2. Momentum Flux Contribution

Figure 5 illustrates momentum flux contributions to the total flux at various low-pass filtered frequencies. Under low-wind configurations (Figure 5a–c), increasing tree canopy density primarily enhances drag and wake interference, suppressing small-scale turbulence and strengthening the dominance of low-frequency large-scale structures, thereby increasing their contribution to total momentum flux. In high-wind aligned configurations (Figure 5g–i), higher density intensifies the shear layer at the canopy top, strengthening more small-scale motions, which moderately reduces the relative contribution of low-frequency large-scale motions.

However, in the high-wind staggered configurations (Figure 5d–f), increasing canopy density leads to only minor changes in the scale-wise contributions to the momentum flux. At high velocity, wake turbulence is already strong and nearly saturated, so the flow remains wake-dominated regardless of density. The staggered geometry disrupts the continuity required for a well-defined drag discontinuity at the canopy top, preventing the formation of a coherent shear layer. As a result, small-scale motions originate mainly from wake shedding rather than shear-layer breakdown, which explains the weak sensitivity of the momentum flux distribution to density. This interpretation is consistent with the mechanisms described by Ghisalberti and Nepf [41] and Nepf [42].

3.3. Natural Visibility Graph Analysis of Large-Scale Motions

Natural visibility graphs provide a useful framework for examining the volatility of turbulent signals and are applicable to both large- and small-scale motions [18]. The large-scale motions are determined jointly by the cut-off frequency based on TBL thickness δ [29,32] and the low-pass filter. Following Iacobello et al. [18], the natural visibility graph (NVG) is constructed from the velocity fluctuation time series. To quantitatively distinguish acceleration and deceleration events at large scales, two NVG-based degrees are defined as: Kp = (1/Npos) ∑ (k_j|u’_LS > 0), Kn = (1/Nneg) ∑ (k_j|u’_LS < 0), where k_j denotes the degree of the j-th node in the NVG, and Npos and Nneg represent the number of data points with positive and negative large-scale velocity fluctuations, respectively. In practice, the differences between the small-scale indicators Kn and Kp are minor, so the present discussion focuses on their behavior at larger scales. In Figure 6, the primary difference between density cases becomes most evident within the roughness sublayer (RSL), where high-density configurations tend to show a near balance between large-scale acceleration and deceleration events. However, as the height increases from the upper RSL toward the ISL, this balance progressively weakens, large-scale deceleration motions strengthen, and as a result, even in the highest-density cases, deceleration motion begins to dominate over acceleration motion.

Under dense canopy conditions, the strong mean shear above the canopy and the frequent interactions among adjacent wakes generate a saturated turbulence environment within the roughness sublayer (RSL), which results in wake-generated turbulence and the shear-layer continuously replenishing the energy of large-scale motions, allowing them to maintain a balanced alternation between acceleration and deceleration. However, under sparse canopy conditions, the weakened canopy drag and the reduced overlap of wakes lead to incomplete turbulence saturation and an under-energized shear, causing large-scale motions to become deceleration-dominated.

The NVG method effectively captures this imbalance because its visibility-based degree reflects how prominently a point stands out relative to its surrounding values. Comparing the degree of acceleration and deceleration reveals whether canopy density causes systematic differences in the fluctuation structure of large-scale motions. Although these differences do not measure momentum transport directly, they indicate the dynamical state of the large-scale flow: balanced acceleration and deceleration suggest more active motions that favor vertical momentum exchange, whereas a dominance of deceleration reflects weaker transport capability. Thus, NVG asymmetry provides a concise statistical indicator of how canopy structure influences large-scale turbulence dynamics relevant to momentum transport.

3.4. Amplitude Modulation of Large- and Small-Scale Motions

Figure 7 describes the amplitude modulation coefficients of motion at different scales under various circumstances. The large-scale and small-scale motions are determined jointly by the cut-off frequency based on TBL thickness δ [29,32] and the low-pass filter. Overall, canopy density is the dominant factor affecting the amplitude modulation coefficient R_AM, a trend that is also observed in roughness-dependent modulation studies [27]. The three high-density cases almost entirely overlap across the full height range, demonstrating that dense arrays produce highly consistent modulation behavior. Their values decrease from about 0.35 near the canopy base to approximately 0 at RSL top, where a distinct turning point occurs. Across all high-density cases, the modulation behavior is nearly insensitive to canopy arrangement and inflow wind speed, consistent with observations that stronger surface resistance suppresses variability in modulation intensity [26]. The three low-density cases remain relatively close throughout most of the RSL, although their internal variability is slightly larger than that of the high-density group. Within the RSL, their values generally vary from around 0.1 to approximately –0.1. However, once the height exceeds the IRS top, the three low-density curves begin to separate more clearly, which is not present at lower heights.

Within the medium-density group, a clear contrast emerges between the low-wind staggered case and the high-speed aligned case. At lower heights, the low-wind staggered configuration exhibits the largest modulation coefficient, while the high-wind aligned configuration shows the smallest value, consistent with the well-known enhancement of near-wall large–small-scale coupling [43]. However, once the flow reaches the critical height (lower RSL height), where the modulation coefficient crosses 0, this ordering reverses: the high-wind aligned case becomes dominant, and the low-wind staggered case drops to the lowest level, reflecting the height-dependent transition of modulation characteristics observed in wall turbulence [25]. This inversion indicates a fundamental shift in the governing mechanism. At lower heights, local wake interactions dominate under low-wind staggered conditions, producing stronger small-scale responses and therefore larger modulation. Above the critical height, where canopy influence weakens and outer-layer large-scale structures become more influential, the coherent shear-layer motion in the high-wind aligned configuration provides a stronger large-scale forcing, in agreement with evidence that outer-layer structures strongly condition small-scale structures [24]. Thus, the medium-density regime reveals a unique crossover behavior where the controlling mechanism transitions from wake-induced modulation below the critical point to shear-layer-driven modulation above it, which is consistent with the role of coherent shear-layer vortices [44].

Based on the present dataset, the critical point is better interpreted as a transitional state arising from the combined influence of shear-layer development, turbulence interactions, and canopy geometry. It is not governed by any single physical parameter in a monotonic manner. This transitional state appears only in the medium-density configuration, where different flow mechanisms coexist and collectively maintain an intermediate regime between the sparse and dense canopy conditions. In addition, a frequency of 2000 Hz is sufficiently high for resolving the turbulent fluctuations relevant to the AM analysis. The potential influence of alternative sampling frequencies will be explored in future work.

4. Conclusions

This study summarizes the transport efficiency characteristics and multiscale momentum-transfer mechanisms in canopy flows based on a series of controlled wind tunnel experiments. By integrating multiple quantitative analysis methods, it examines momentum flux contributions and the interactions between large- and small-scale motions under different canopy conditions. The main results are presented as follows:

• Transport efficiency at the canopy top increases with drag coefficient, with the strongest enhancement near the canopy–top interface. Stronger vegetation-induced drag enhances momentum exchange and turbulent mixing in the upper canopy, promoting vertical transport. The canopy top, therefore, acts as a sensitive transition layer linking canopy turbulence to the overlying boundary layer.
• The influence of canopy density on momentum flux contributions depends on wind speed and array configuration. Under low-wind conditions, higher density strengthens drag, suppresses small-scale motions, and enhances low-frequency large-scale contributions. In high-wind aligned cases, increased density promotes shear-layer activity, moderately increasing small-scale motions and reducing the relative contribution of large-scale motions. In high-wind staggered cases, wake turbulence is already saturated, and no continuous shear layer develops at the canopy top, resulting in minimal sensitivity of scale-wise flux distribution to density changes.
• NVG analysis indicates that canopy density primarily modulates large-scale acceleration and deceleration within the roughness sublayer (RSL). In high-density cases, these motions remain nearly balanced in the RSL but become increasingly deceleration-dominated toward the inertial sublayer (ISL). This highlights the canopy-top transition layer as a density-sensitive region governing large-scale flow behavior.
• Increasing canopy density is the primary factor that strengthens the amplitude modulation coefficient. For high-density cases, all configurations show nearly identical behavior: the amplitude modulation coefficient decreases from about 0.35 near the canopy base to nearly 0 at the RSL top. Low-density cases show a similar height-dependent pattern, but with smaller magnitudes (from about 0.1 to –0.1) and slightly larger variability between configurations. In the medium-density group, the amplitude modulation coefficient shows a clear crossover: the ordering between cases reverses around the lower RSL, where the coefficient changes sign.

However, this study also has a clear limitation: the canopy models used in the experiments are made of rigid materials, which cannot adequately represent the flow–structure interactions that occur in real vegetation. Future work should consider incorporating flexible materials to better capture these flow–solid coupling effects.