High-resolution large eddy simulations and complementary laboratory experiments using particle image velocimetry were performed to provide a detailed quantitative assessment of flow response to gaps in cylinder arrays. The base canopy consists of a dense array of emergent rigid cylinders placed in a regular staggered pattern. The gaps varied in length from Δg/d=4 to 24, in intervals of 4d, where d is the diameter of the cylinders. The analysis was performed under subcritical conditions with Froude numbers Fr[0.08,0.2] and bulk Reynolds numbers Re[0.8,2]×104. Results show that the gaps affect the flow statistics at the upstream and downstream proximity of the canopy. The affected zone was Δx/d5 for the mean flow and Δx/d3 for the second-order statistics. Dimensionless time-averaged streamwise velocity within the gap exhibited minor variability with gap spacing; however, in-plane turbulent kinetic energy, k, showed a consistent decay rate when normalized with that at x/d1 from the beginning of the gap. The emergent canopy acts as a passive turbulence generator for the gap flow for practical purposes. The streamwise dependence of k follows an exponential trend within 1x/d2.5 and transitions to a power-law at x/d4. The substantially lower maximum values of k within the gap compared to k within the canopy evidence a limitation of gap measurements representative of canopy flow statistics. We present a base framework for estimating representative in-canopy statistics from measurements in the gap.

Whether located in floodplains, banks, or channels, vegetation has an extensive impact on the fluvial system and has long been the focus of river management activities. Aquatic vegetation is a source of hydraulic resistance, which impedes the conveyance of channels and aggravates flooding1 and has led to removal from streams, canals, and rivers. However, positive ecological effects of vegetation have been identified over the last few decades. Indeed, aquatic vegetation plays a vital role for many food webs2 and enhances local water quality by filtering nutrients and heavy metals.3 The drag created by vegetation canopies reduces bed shear stress, improving sedimentation and nutrient retention, which makes a suitable habitat for benthic fauna.4,5 Studies on the effects of aquatic vegetation on erosion control, bank stability, pollutant filtering, and wildlife habitat have established aquatic vegetation as stream ecosystem engineers,6 the main drivers of physical, chemical, and biological processes in the ecosystem.

Turbulence within vegetated channels is primarily produced in the wake of each plant and the entire canopy;7 thus, predictive models for flow statistics in open channel flows cannot be directly applied to vegetated channels. Numerous researchers8–15 have developed models for the mean and turbulent quantities in vegetated channel flows as a function of density, submergence ratio, and arrangement patterns of vegetation through experimental, numerical, and analytical approaches. However, many phenomena regarding their effects on the aquatic ecosystem remain unclear. Quantification of sediment transport in vegetated channels is one example that has been of particular interest. Classical models are based on bed shear stress, τb, or mean flow velocity, U. Yang et al.16 developed a linear stress model for estimating bed shear stress in vegetated flows, which is dependent on the thickness of the viscous layer, Hν. Etminan et al.17 improved the model by setting Hν as a function of production and dissipation of the turbulent kinetic energy, k, in the wake and channel bed. However, shear-based predictors can lead to conflicting results on sediment transport unless turbulence statistics are accounted for Ref. 18. Other studies19–21 suggest that sediment transport in vegetated channels is better explained by k rather than U and τb. Accurate quantification of k may improve prediction of sediment transport22 and other processes, such as interfacial gas transfer rate and scalar diffusivity.23 

Measurement of flow statistics within dense canopies is challenging. Experimental approaches are often limited by (i) the physical size of intrusive probes, e.g., acoustic Doppler velocimeter, ADV, or fluorometer, Fl, which may be larger than the spacing between the adjacent vegetation elements, and (ii) a lack of unobstructed field of view required for non-intrusive quantitative imaging, e.g., laser Doppler velocimetry, LDV, particle image/tracking velocimetry, PIV/PTV, optical back scatter sensor, OBS, or laser induced fluorometry, LIF. Clearing out a patch of vegetation for instrument access and unobstructed field of view9,16,22,24 is a common practice that may result in flow statistics not representative of those within a canopy. Table I summarizes past experiments on dense canopies having canopy gaps to enable flow measurement. The effect of such gaps on measured statistics is unexplored and forms the motivation for this study.

TABLE I.

Summary of laboratory experiments with rigid elements arranged in random (top) and staggered (bottom) layouts containing gaps oriented spanwise to the flow direction except in staggered cases where a region around the instrument was cleared by removing 2–3 dowels. Δg is the gap size, Red=Ud/ν is the diameter (d) based Re, ϕ is the canopy density, and H/h is ratio of water depth to canopy height.

AuthorsInstrumentΔg/dRedϕH/h
Nepf9  LDV Unknown 4000–10 000 0.006–0.06 
Tanino and Nepf31  LDV, LIF 0–2 70–1475 0.01–0.35 
Zhang and Nepf32  PIV 3.33 ∼1 0.03–0.15 
Tanino and Nepf33  LIF 48–390 0.2–0.35 
Tinoco and Cowen34  PIV 6–47 60–4550 0.01–0.08 
Tinoco and Coco19  ADV, OBS <5000 0.008–0.08 
Ricardo et al.35  PIV Unknown 1066–1685 0.09–0.15 
Ghisalberti and Nepf36  Fl. 70–240 0.01–0.04 
Ghisalberti and Nepf37  ADV 12.5 134–429 0.01–0.04 
Murphy et al.38  Fl. Unknown 36–594 0.01 1–5 
King et al.39  ADV, PIV 6–50 36–2016 0.01–0.08 1–2 
Tinoco and Coco20  ADV, OBS 200–20 000 0.008–0.08 
White and Nepf40  LDV 10–144 0.02–0.1 
White and Nepf41  LDV 10–144 0.02–0.1 
Zong and Nepf42  ADV 6–84 0.02–0.1 
Zong and Nepf43  ADV 18–84 0.02–0.1 
Rominger and Nepf44  ADV Unknown 640 0.026–0.4 
Yang et al.16  LDV ∼5–36 25–2200 0.003–0.125 
Liu and Nepf45  ADV 3.5 75–220 0.15 
Tseng and Tinoco22  PIV 12 112–384 0.005–0.025 
Tseng and Tinoco23  PIV 12 64–660 0.005–0.025 1–4 
Tinoco et al.46  PIV,PTV 15d 282–666 0.006 2–4 
Prada et al.47  PIV 16 282–1216 0.006 2–4 
Tseng and Tinoco48  PIV 12 109–600 0.005–0.025 1–4 
AuthorsInstrumentΔg/dRedϕH/h
Nepf9  LDV Unknown 4000–10 000 0.006–0.06 
Tanino and Nepf31  LDV, LIF 0–2 70–1475 0.01–0.35 
Zhang and Nepf32  PIV 3.33 ∼1 0.03–0.15 
Tanino and Nepf33  LIF 48–390 0.2–0.35 
Tinoco and Cowen34  PIV 6–47 60–4550 0.01–0.08 
Tinoco and Coco19  ADV, OBS <5000 0.008–0.08 
Ricardo et al.35  PIV Unknown 1066–1685 0.09–0.15 
Ghisalberti and Nepf36  Fl. 70–240 0.01–0.04 
Ghisalberti and Nepf37  ADV 12.5 134–429 0.01–0.04 
Murphy et al.38  Fl. Unknown 36–594 0.01 1–5 
King et al.39  ADV, PIV 6–50 36–2016 0.01–0.08 1–2 
Tinoco and Coco20  ADV, OBS 200–20 000 0.008–0.08 
White and Nepf40  LDV 10–144 0.02–0.1 
White and Nepf41  LDV 10–144 0.02–0.1 
Zong and Nepf42  ADV 6–84 0.02–0.1 
Zong and Nepf43  ADV 18–84 0.02–0.1 
Rominger and Nepf44  ADV Unknown 640 0.026–0.4 
Yang et al.16  LDV ∼5–36 25–2200 0.003–0.125 
Liu and Nepf45  ADV 3.5 75–220 0.15 
Tseng and Tinoco22  PIV 12 112–384 0.005–0.025 
Tseng and Tinoco23  PIV 12 64–660 0.005–0.025 1–4 
Tinoco et al.46  PIV,PTV 15d 282–666 0.006 2–4 
Prada et al.47  PIV 16 282–1216 0.006 2–4 
Tseng and Tinoco48  PIV 12 109–600 0.005–0.025 1–4 

Large eddy simulation, LES, has been used extensively as a tool to understand the hydrodynamics of the flow through vegetated channels. Stoesser et al.25 and Etminan et al.26 investigated the flow through a staggered emergent vegetation patch of varying density to gain insight into the dominant physical mechanisms controlling the drag on the canopy. Ricardo et al.27 performed LES of the flow through random arrays of rigid emergent cylinders and evaluated the minimum grid resolution and domain size required for representative measurement of flow statistics. Chang et al.28 reported flow structures in a rigid cylindrical array over flat and deformed beds, and Kim et al.29 investigated scour depths within and around vegetation patches of varying density. Liu et al.30 used LES to resolve the flow through a circular patch of cylinders and investigated the effects of array density on the mean flow field and bleeding flow through the canopy.

Here, we use a combination of high-resolution LES and laboratory experiments in a dense, emergent canopy composed of rigid cylinders to explore the flow statistics within the canopy and the impact of gap size (Δg/d = 4–24) on the measurement of an in-canopy flow. The diameter-based Re, Red in the simulations range from 500 to 1200, which is in the observed range for freshwater and coastal ecosystems.9 We characterize the gap canopy region, which is required to assess the practice of using gap measurements as representative of in-canopy flow statistics. We derive a simple relationship that may estimate the maximum level of k within the canopy from measurements in the gap. Section II describes the experimental and numerical setups. Section III presents the results from the numerical simulations and experiments. Section IV provides the main remarks.

We performed six flume experiments and five complementary high-resolution LES. The experiments focused on the effect of gap length for a given Reynolds number, whereas the simulations explored the effect of Reynolds number for a given gap configuration.

The experiments were conducted on an Odell-Kovasznay type racetrack flume at the Ecohydraulics and Ecomorphodynamics Laboratory at the University of Illinois. The recirculating racetrack flume has a 2 m long straight test section, 0.15 m wide, and 0.6 m deep. A vertical axis disk pump drives a flow with a uniform velocity profile and minimal vertical disturbances.

Smooth rigid acrylic cylinders of diameter d =6.25 mm were attached to a smooth plate at the flume bed. The mean streamwise and transverse spacing between the cylinders was sx/d=2 and sy/d=4, respectively. A total of 672 cylinders of height h = 0.1 m were arranged in a staggered pattern resulting in a L/H=15 long canopy with H = 0.1 m as the mean free surface height; see basic schematics of Fig. 1. The canopy density resulted in ϕ=0.088, similar to mangroves and seagrass.7 Gaps of Δg/d=4–24, defining cases E1–E6, were set by separating the base plates and placing smooth plates to maintain the bed level; see Table II. The flow rate was maintained constant in all the cases; the corresponding bulk mean speed was Ub=0.08 m s−1 or Reb8000 based on H =0.1 m.

FIG. 1.

Schematic of the actual experimental setup illustrating basic dimensions and the field of view (FOV) covering the gap region (drawings at scale).

FIG. 1.

Schematic of the actual experimental setup illustrating basic dimensions and the field of view (FOV) covering the gap region (drawings at scale).

Close modal
TABLE II.

Experimental (top) and numerical (bottom) cases. The experimental cases share the Reb = 8000, whereas the numerical simulations consider a fixed gap spacing of Δg/d=8. Ub is the bulk velocity of the incoming flow impinging the canopy.

CaseΔg/d
E1 
E2 
E3 12 
E4 16 
E5 20 
E6 24 
CaseΔg/d
E1 
E2 
E3 12 
E4 16 
E5 20 
E6 24 
CaseRebRedUb (m s−1)
S1 8000 500 0.08 
S2 12 000 750 0.12 
S3 15 000 938 0.15 
S4 18 000 1125 0.18 
S5 20 000 1250 0.20 
CaseRebRedUb (m s−1)
S1 8000 500 0.08 
S2 12 000 750 0.12 
S3 15 000 938 0.15 
S4 18 000 1125 0.18 
S5 20 000 1250 0.20 

For each setup, the flow in the gap was characterized using planar PIV. It consisted of a continuous-wave 5 W OptoEngine LLC laser, Model PIV01251, which provided illumination to a 1 mm thick vertical plane at the center of the gaps. The flow was seeded with 55 μm Nylon 12 particles. For each case, 7200 instantaneous fields were collected at a frequency of 120 Hz using an Edgertronic SC2+ high-speed camera at 1 MP resolution. Images were processed using PIVlab.49 Three consecutive 50% size passes with 50% overlapped interrogation areas were used to obtain the vector fields. The final interrogation window had a size of 16 × 16 pixels with 50% overlap, resulting in a vector grid spacing of Δx=Δy= 2 mm.

High-resolution large-eddy simulations (LES) were performed using Nek5000, a spectral element method (SEM) based solver.50 The SEM is a high-order weighted residual method that combines the geometric flexibility of the finite element method (FEM) with the high-order accuracy and fast convergence of spectral methods. The basis functions in the SEM are N-order tensor-product Lagrange polynomials on Gauss–Lobatto–Legendre quadrature points in each element, which leads to fast operator evaluation, O(Nd+1), and low operator storage of O(Nd). Higher-order polynomial-based methods, such as SEM, are especially suited for turbulent flow simulations; they eliminate dispersion errors, which is very important for large-scale and long-term turbulence calculations.

The incompressible Navier–Stokes equations are solved in the velocity–pressure form using semi-implicit kth-order backward difference formula (BDFk)/kth-order extrapolation (EXTk) time-stepping in which the time derivative is approximated using a kth-order backward difference formula (BDFk), the non-linear terms are treated explicitly using kth-order extrapolation (EXTk), and the viscous and pressure terms are treated implicitly. This approach leads to a linear unsteady Stokes problem to be solved at each step, which is split into independent viscous and pressure updates. Details of the time integration scheme are given in Mittal et al.51 Spectral filtering was used to dissipate the fraction of unresolved sub-grid scale eddies.52 More information about the solver is given in Fischer et al.53 

The numerical simulations resembled the experimental setup but were constrained to a canopy length of 445 mm containing 192 cylinders (Fig. 2). Periodic boundary conditions were applied along the streamwise and spanwise boundaries. The flow through a staggered canopy exhibits periodic statistics,26 thus using periodic boundary conditions on the given domain allowed us to contain the expense of the simulations without penalty on the quality of the results. The gap size was fixed at Δg/d=8 and the H based Reynolds number varied from Reb=800020000; this defined the cases S1–S5 given in Table II. This corresponds to bulk flow velocity in the range of 0.080.2 m s−1, which is similar to flow conditions in rigid emergent vegetation (e.g., reeds, rushes, papyrus, and rice) of natural habitats.54 

FIG. 2.

(a) A view of the computational domain illustrating coherent structures for an arbitrary instantaneous velocity field for the S5 case (Reb = 20 000). (b) Velocity spectra at half-channel depth in the center of the gap (black), wake of a cylinder near the gap (blue), and preferential path between two rows of cylinders (red).

FIG. 2.

(a) A view of the computational domain illustrating coherent structures for an arbitrary instantaneous velocity field for the S5 case (Reb = 20 000). (b) Velocity spectra at half-channel depth in the center of the gap (black), wake of a cylinder near the gap (blue), and preferential path between two rows of cylinders (red).

Close modal

Numerical simulations were performed on a three-dimensional hexahedral mesh using a Laplacian- and optimization-based mesh-improvement method developed for high-order finite- and spectral-element method.55 The mesh resolution was sufficient to resolve the boundary layer around individual cylinders and along the bed of the channel with at least 10 points within the viscous sublayer of the cylinders and the channel bed. The total number of computational points was over 144 million, which warranted using the petascale BlueWaters supercomputer to conduct the simulations. No-slip boundary conditions were applied along the channel bed and on the surface of the cylinders with frictionless condition at the top of the computational domain.

The numerical model was compared with the measured flow statistics in the Δg/d=8 gap for the Reb = 8000 scenario. Comparison of the zaveraged streamwise velocity along the xdirection [Fig. 3(a)] and xaveraged streamwise velocity profile in the zdirection [Fig. 3(b)] shows good agreement. We also compared the energy spectra at the center of the gap using the streamwise [Fig. 3(c)] and vertical [Fig. 3(d)] velocity components. A low pass filter with a cutoff frequency of 20 Hz was used to remove high-frequency noise from the experimental data. Velocity spectra were also calculated at three locations within the channel, namely, in the gap, wake of a cylinder, and local preferential path, to verify that the numerical method captures the relevant turbulence scales across the simulated domain. Figure 2(b) shows velocity spectra for the Reb = 20 000 case, with the simulations capturing the inertial subrange and a portion of the dissipative scales. Considering representative eddy scales of dimension d advects at the root mean square velocity, urms=2k/3, resulting in a Rerms=urmsd/ν=620 and a referential Kolmogorov timescale τητoRerms1/22×102 s, which corresponds to an equivalent frequency of 50 Hz, which is half of that from that solved by the simulations. A minor fraction of smaller scales is not resolved, but the associated energy is dissipated using the spectral filter mentioned earlier.

FIG. 3.

Comparison between the experiments and numerical simulations within the Δg/d=8 gap at Reb = 8000. (a) zaveraged streamwise velocity along the xdirection. (b) xaveraged streamwise velocity profile in the zdirection. (c) Streamwise and (d) spanwise velocity spectra at the half-channel depth in center of the gap. Note that the x/d origin is shifted to the beginning of the gap.

FIG. 3.

Comparison between the experiments and numerical simulations within the Δg/d=8 gap at Reb = 8000. (a) zaveraged streamwise velocity along the xdirection. (b) xaveraged streamwise velocity profile in the zdirection. (c) Streamwise and (d) spanwise velocity spectra at the half-channel depth in center of the gap. Note that the x/d origin is shifted to the beginning of the gap.

Close modal

Wall parallel distributions of the time-averaged streamwise velocity, U, in-plane turbulent kinetic energy, k=(u2¯+v2¯+w2¯)/2, and kinematic shear stress, uv¯, at the mid height, z/H=1/2, for the Δg/d=8 gap are illustrated in Fig. 4. Here, u,v, and w represent the streamwise, transverse, and vertical velocity fluctuation components.

FIG. 4.

Half-height wall parallel distributions of the time-averaged (a) streamwise velocity component, U, (b) in-plane turbulent kinetic energy, k, and (c) kinematic shear stress uv¯ for the Δg/d=8 gap case.

FIG. 4.

Half-height wall parallel distributions of the time-averaged (a) streamwise velocity component, U, (b) in-plane turbulent kinetic energy, k, and (c) kinematic shear stress uv¯ for the Δg/d=8 gap case.

Close modal

These quantities reveal various flow features and the impact of the gap. The narrow preferential streamwise paths of comparatively high momentum induce a sharp shear layer resulting in enhanced turbulence with maximum value on the order of k/Ub20.75 and kinematic shear of uv¯/Ub2±0.15. These quantities exhibit lateral and streamwise periodicity except in the upstream and downstream vicinity of the gap. The flow adjusts within a relatively short distance downstream of the gap due to the narrow path that filters potential large turbulent coherent motions formed in the gap. It is also worth noticing the significant reduction of the transverse and streamwise inhomogeneity of the turbulence in the gap compared to that within the canopy. This is highlighted with selected transverse profiles in Fig. 4. Note that the merging of preferential paths in the gap further contributes to reduce the mean shear; however, this high-momentum merging is not possible at sufficiently large transverse separation of the cylinders.

A closer inspection of the canopy regions affected by the gap and flow development in the gap is given in Fig. 5. It illustrates U/Ub,k/Ub2, and uv¯/Ub2 along the preferential path and the line connecting the center of the cylinders (wake center). The gap affected the mean velocity in a region roughly within ±4Δx/d from the gap boundaries in the preferential path; however, it was negligible in the line connecting the center of the cylinders. The second-order statistics evidence a different trend compared to the mean flow. Indeed, the downstream region was significantly more affected in the preferential path reaching an area of 7Δx/d. The upstream effect was 3Δx/d, i.e., a reduced region. It is worth highlighting that the short impact of the gap in the in-canopy turbulence statistics also indicates that relatively short emergent canopies produce adjusted turbulence within the canopy. Here, three rows upstream and downstream are sufficient for that, which hints at the requirements for simulations of emergent canopies. Note that this does not necessarily apply to submerged canopies since the development of the internal boundary layer is monotonic with distance.

FIG. 5.

Profiles of the streamwise velocity component, U, in-plane turbulence kinetic energy, k, and kinematic shear stress uv¯ along the “wake” (black) and the preferential path (blue) lines at the half flow depth for the Δg/d=8 gap case.

FIG. 5.

Profiles of the streamwise velocity component, U, in-plane turbulence kinetic energy, k, and kinematic shear stress uv¯ along the “wake” (black) and the preferential path (blue) lines at the half flow depth for the Δg/d=8 gap case.

Close modal

As pointed out in Sec. I, clearing a region to obtain flow statistics within the canopy is a common practice. The underlying assumption is a negligible effect induced by the gap. Figures 4 and 5 show that this practice may lead to erroneous flow characterization when measuring in the gap. High redistribution of momentum and turbulence promoted by a gap in a short spatial region may reduce turbulence levels and spatial flow heterogeneity. In addition, the dominant impact of the vertical structures, here cylinders, leads to negligible vertical mean shear that inhibits the production of turbulence in the gap resulting in turbulence decay in the direction of the mean flow within the gap. See the similar and monotonically decreasing k along the preferential path and wake of the last cylinder in Fig. 5(b).

The change in the flow statistics in the gap makes it challenging to use it as representative of the canopy. Early studies by Olsson56 indicate a mean velocity deficit in the wake of an array of equally spaced row of cylinders in crossflow following a power law U0Ux1, where U0 is the mean velocity in the far field and U is the mean velocity in the wake. Bragg et al.57 suggested an exponential decay of flow statistics with a x1/2 sufficiently downstream; this was attributed to a lateral redistribution of the mean momentum by turbulence. Townsend58 suggested a decay with an exponential trend of mean velocity, assuming that small velocity perturbations are advected and diffused as passive scalars. These insights support the idea of characterizing in-canopy turbulence from flow measurements in gaps with a proper extrapolation.

The preferential path extended to the gap can be used to obtain the maximum velocity within the canopy despite the sharp reduction of velocity of about ΔU/Ub0.25 within 0x/d3. This reduction corresponds to the area recovered in the gap by the absence of the cylinders and by the high momentum redistribution in the lateral direction in that region. However, estimating a representative value of k is not straightforward. A candidate for such a value is the maximum level, which is instrumental to estimating gas transfer rates and sediment resuspension within vegetated channels.22,23 Transverse inhomogeneity of this quantity at the beginning of the gap [see Fig. 4(b)] makes it particularly difficult to extrapolate a value from the gap. Unlike the case of the maximum velocity, the preferential path region does not provide a direct way to estimate the maximum k; see Fig. 5. Turbulence levels remain relatively constant along the path and well within the gap. In contrast, k in the wake region (Fig. 1) near the gap provides a close estimation of the maximum values.

From a practical standpoint, a regular and even irregular arrangements of emergent canopies act as like passive grid for the flow in the gap. This analogy, together with the negligible vertical and minor lateral mean shear in the gap, implies a minor production of turbulence there. As a result, the streamwise variability of the turbulent kinetic energy may be represented by a power law of the form,

k/k0(x/dx0/d)n.
(1)

Within the transition region along the wake centerline (see Fig. 1), the turbulence decay may be expressed by the simplified steady-state equation for k, given by

Udkdx=ϵ,
(2)

where the turbulence production, transport, and other advection terms are considered minor as a first approximation. Following Nepf9 turbulence dissipation, ϵk3/2d1, and Uk1/2, the solution of Eq. (2) is

k(x)=c1exp[α(xd)],
(3)

where c1 is an integration constant and α0.7 for rigid emergent vegetation.9 This relationship may be used to estimate the maximum levels of k in the canopy from measurements made at the beginning of the gap that allows obtaining c1. For example, the maximum value of k/Ub2 within the canopy for case E2 (Δg/d=8) estimated using Eq. (3) is 0.63, which is within 10% of the maximum value observed within the canopy in the corresponding simulation.

Figure 6(b) shows that distributions of k are independent of the gap length past one diameter downstream of the canopy, as evidenced with the k(x/d=1)=k(1) normalization. In the near field, at 1x/d2.5, collapsed k distributions first follow an exponential trend of the form k/k(1)eαx/d, as predicted by Eq. (3). The power-law relation of the type given in Eq. (1) occurs in the intermediate field at x/dx0/d4, where the flow exhibits a larger degree of transverse homogeneity. Interestingly, the maximum levels of k occur at d/2 downwind of the second to the last row of cylinders (Fig. 5), consistent with other arrangements.59 There, the turbulence level is about 70% higher than that of the maximum value in the gap (at x/d=0). Finally, inspection on the effect of Reynolds number on the local dynamics, or Froude number on the bulk flow, shows that the normalized mean flow, U/Ub, and turbulence levels, k/Ub2, undergo minor changes within Reb = 8×103 and 2×104. Figure 7 illustrates selected transverse profiles of the quantities within the undisturbed canopy region. Given that open-channel flows with emergent canopies are mostly subcritical, the low impact of the Reb in the mean flow and turbulence indicates that the geometrical features of the canopy are the primary factor defining the flow statistics within the canopy.

FIG. 6.

Streamwise variation of the in-plane time-averaged (a) U and (b) k with size of the gap, Δg, along the preferential path.

FIG. 6.

Streamwise variation of the in-plane time-averaged (a) U and (b) k with size of the gap, Δg, along the preferential path.

Close modal
FIG. 7.

Comparison of (a) U and (b) k profiles within the upstream canopy for Reb= 8000 and 20 000 at half-channel height.

FIG. 7.

Comparison of (a) U and (b) k profiles within the upstream canopy for Reb= 8000 and 20 000 at half-channel height.

Close modal

We conducted a unique numerical study of highly resolved flow statistics in developed (upstream of a gap) and developing (through and downstream of a gap) canopy flows at scales prohibitive for most studies on vegetated flows and complementary laboratory experiments. The combined numerical and experimental inspection of the impact of gaps and dimensions on the turbulence statistics within an emergent canopy revealed various phenomena. In particular, turbulence levels in the gap are significantly lower than those within the canopy. The upstream and downstream regions affected by the gap have a short extent and turbulence in the gap transitions from an exponential to power-law decay. Also, the size of the gap did not induce a substantial effect on the in-canopy flow. Indeed, in-plane turbulent kinetic energy in the gap collapses when normalized by a value past just one blade diameter. From a practical point of view, emergent canopies may be conceptualized as passive filters or turbulence generators for the flow in the gap. It opens possibilities to develop formulations for representative turbulence levels within the canopy; the maximum value is a candidate for that. Using simplified arguments, we present a first-order formulation that estimates the maximum turbulence levels in the canopy, which provides one of the first frameworks for estimating representative in-canopy statistics from measurements within a gap. Despite that it exhibits good agreement with data, much work is necessary to account for canopy characteristics, including spacing, blade geometry, and heterogeneous layouts, among others.

Future work will explore these relevant parameters to improve the assessment of vegetated flow conditions from experimental data that require the use of gaps to infer flow features in emergent canopies.

We want to thank Professor P. Fischer and Professor S. Dutta for their insight in setting up the simulations. This research is part of the Blue Waters sustained-petascale computing project, supported by the National Science Foundation (NSF) (Award Nos. OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois and its National Center for Supercomputing Applications. This study was partially supported by NSF through CAREER EAR 1753200.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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