Discussion of “Laboratory Investigation of Mean Drag in a Random Array of Rigid, Emergent Cylinders” by Yukie Tanino and Heidi M. Nepf

Tanino, Yukie; Nepf, Heidi

doi:10.1061/(asce)hy.1943-7900.0000021

Cited by 33 publications

(25 citation statements)

References 3 publications

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“…Cheng and Nguyen [] reported a monotonic decline in C d but with an increasing vegetation‐related Reynolds number ( Re v ) for canopies composed of cylinders. These experiments, presumed to represent uniform and nonuniform flow conditions, are dominated by the “blocking effect” [ Ishikawa et al ., ; James et al ., ; Tanino and Nepf , ; Liu et al ., ; Ferreira et al ., ; Kothyari et al ., ; Stoesser et al ., ]. Their empirical drag coefficient for vegetation array (labeled as C d‐array ) fitted to a large library of experiments (the range of

ϕ_{v}_{e g}

is 0.0022–0.35, and range of Re v is 50 − 6 × 10 5 ) is given as [ Cheng and Nguyen , ]

C_{d ‐ a r r a y} = 50 {(R e_{v})}^{- 0.43} + 0.7 true[1 - \exp true(- \frac{R e_{v}}{15000} true) true],

where

R e_{v} = U R_{v} / ν

is the vegetation‐related Reynolds and R v (that differs from R ) is a vegetation‐related hydraulic radius given by

R_{v} = \frac{π}{4} \frac{1 - ϕ_{v e g}}{ϕ_{v e g}} D .

…”

Section: Theorymentioning

confidence: 98%

Steady nonuniform shallow flow within emergent vegetation

Wang

Huai

Thompson

et al. 2015

Water Resources Research

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Surface flow redistribution on flat ground from crusted bare soil to vegetated patches following intense rainfall events elevates plant available water above that provided by rainfall. The significance of this surface water redistribution to sustaining vegetation in arid and semiarid regions is undisputed. What is disputed is the quantity and spatial distribution of the redistributed water. In ecohydrological models, such nonuniform flows are described using the Saint-Venant equation (SVE) subject to a Manning roughness coefficient closure. To explore these assumptions in the most idealized setting, flume experiments were conducted using rigid cylinders representing rigid vegetation with varying density. Flow was induced along the streamwise x direction by adjusting the free water surface height H(x) between the upstream and downstream boundaries mimicking the nonuniformity encountered in nature. In natural settings, such H(x) variations arise due to contrasts in infiltration capacity and ponded depths during storms. The measured H(x) values in the flume were interpreted using the SVE augmented with progressively elaborate approximations to the roughness representation. The simplest approximation employs a friction factor derived from a drag coefficient (C d ) for isolated cylinders in a locally (but not globally) uniform flow and upscaled using the rod density that was varied across experiments. Comparison between measured and modeled H(x) suggested that such a ''naive'' approach overpredicts H(x). Blockage was then incorporated into the SVE model calculations but resulted in underestimation of H(x). Biases in modeled H(x) suggest that C d must be varying in x beyond what a local or bulk Reynolds number predicts. Inferred C d (x) from the flume experiments exhibited a near-parabolic shape most peaked in the densest canopy cases. The outcome of such C d (x) variations is then summarized in a bulk resistance formulation that may be beneficial to modeling runon-runoff processes on shallow slopes using SVE.

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ϕ_{v}_{e g}

is 0.0022–0.35, and range of Re v is 50 − 6 × 10 5 ) is given as [ Cheng and Nguyen , ]

C_{d ‐ a r r a y} = 50 {(R e_{v})}^{- 0.43} + 0.7 true[1 - \exp true(- \frac{R e_{v}}{15000} true) true],

where

R e_{v} = U R_{v} / ν

is the vegetation‐related Reynolds and R v (that differs from R ) is a vegetation‐related hydraulic radius given by

R_{v} = \frac{π}{4} \frac{1 - ϕ_{v e g}}{ϕ_{v e g}} D .

…”

Section: Theorymentioning

confidence: 98%

Steady nonuniform shallow flow within emergent vegetation

Wang

Huai

Thompson

et al. 2015

Water Resources Research

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“…Traditionally, C D is obtained from experimental results for emergent cylinder arrays by equating driving forces with resistance caused by cylinders (Ferreira, Ricardo, & Franca, 2009;Kim & Stoesser, 2011;Tanino & Nepf, 2008a). Assuming wall and bed stresses are negligible, for emergent cylinders this equates to the balance of gravity and drag forces:…”

Section: Existing Measurements Of C Dmentioning

confidence: 99%

Estimating drag coefficient for arrays of rigid cylinders representing emergent vegetation

Sonnenwald

Stovin

Guymer

2018

Journal of Hydraulic Research

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Flow resistance due to vegetation is of interest for a wide variety of hydraulic engineering applications. This note evaluates several practical engineering functions for estimating bulk drag coefficient (C D) for arrays of rigid cylinders, which are commonly used to represent emergent vegetation. Many of the evaluated functions are based on an Ergun-derived expression that relates C D to two coefficients, describing viscous and inertial effects. A re-parametrization of the Ergun coefficients based on cylinder diameter (d) and solid volume fraction (φ) is presented. Estimates of C D are compared to a range of experimental data from previous studies. All functions reasonably estimate C D at low φ and high cylinder Reynolds numbers (R d). At higher φ they typically underestimate C D. Estimates of C D utilizing the re-parametrization presented here match the experimental data better than estimates of C D made using the other functions evaluated, particularly at low φ and low R d .

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“…Other works have applied PIV to measure the velocity field within the canopy (e.g., Zhu et al 2007;Reynolds and Castro 2008;Yue et al 2008) but did not quantify the dispersive stresses. The only study that we are aware of that used PIV to estimate the dispersive stresses based on measured subscale velocities field deep inside the canopy is that of Ferreira et al (2009), though no experimental details were provided.…”

Section: Introductionmentioning

confidence: 99%

Dispersive Stresses at the Canopy Upstream Edge

Moltchanov

Bohbot-Raviv

Shavit

2011

Boundary-Layer Meteorol

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The derivation of flow and mass transfer models in canopy and porous media environments involves the spatial-averaging of the flow properties and their subscale equations. The averaging of the momentum equation generates the dispersive stress terms that represent the subscale spatial variations of the unresolved velocity field. While previous studies ignored the dispersive stresses in their flow models, recent evidence indicates that the dispersive stresses may be important. Here we focus our attention on the magnitude of the normal dispersive stresses in the entry region of a 'forest patch', where the in-canopy velocities are large and the longitudinal derivatives do not cancel out. Highly detailed particle image velocimetry measurements, at a temporal and spatial resolution of 5 Hz and 1.4 mm, are obtained inside and around a 1-m long model canopy which consists of transparent vertical cylinders 6 mm in diameter and 74.3 mm high (h). The cylinders are randomly distributed to form a relatively sparse forest patch with a leaf area density of 7.56 m −1 and a fluid volume fraction (porosity) of 0.965. We present results of the double averaged flow properties at three different regions of the forest patch; the upstream edge (x ≈ 0), the fully-developed interior region (x ≈ 10h) and the downstream edge (x ≈ 13h). We find that the normal dispersive stresses around the entry region of the forest patch are significantly larger than the normal Reynolds stresses. An order of magnitude analysis of the relevant terms in the momentum equation indicates that the longitudinal derivatives of the dispersive stresses are of the same order of magnitude as that of the drag force and similar to that of the horizontal convection term. The longitudinal derivatives of the Reynolds stresses are smaller, though cannot be ignored. Comparing these results with the characteristic profiles measured in the fully-developed region indicates that the dispersive stresses, which are generated at the forest patch entrance, decrease along an adjustment region while maintaining their profile shape. We find that the dispersive stresses influence the rate at which momentum penetrates into the 123 334 S. Moltchanov et al. canopy. These observations suggest that under certain flow conditions, dispersive stresses may dominate the momentum balance and therefore must be considered in future canopy and porous media flow models.

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Discussion of “Laboratory Investigation of Mean Drag in a Random Array of Rigid, Emergent Cylinders” by Yukie Tanino and Heidi M. Nepf

Cited by 33 publications

References 3 publications

Steady nonuniform shallow flow within emergent vegetation

Steady nonuniform shallow flow within emergent vegetation

Estimating drag coefficient for arrays of rigid cylinders representing emergent vegetation

Dispersive Stresses at the Canopy Upstream Edge

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