Vertical mass and momentum transport in open-channel flows with submerged vegetations

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Journal of Hydro-environment Research 6 (2012) 287e297 www.elsevier.com/locate/jher

Vertical mass and momentum transport in open-channel flows with submerged vegetations Taka-aki Okamoto a,*, Iehisa Nezu b, Hirokazu Ikeda a a

Department of Civil Engineering, Utsunomiya University, Utsunomiya 321-8585, Japan b Department of Civil Engineering, Kyoto University, Kyoto 615-8540, Japan Received 30 June 2011; revised 12 March 2012; accepted 19 March 2012

Abstract The importance of flow and turbulence to the ecology of aquatic benthic organism has been widely reported. Aquatic vegetation is one of environmental variables that influence turbulence and the ecological condition of rivers. Aquatic canopies have the potential to greatly improve water quality through the removal of nutrients and trace metals. To describe the efficiency of this removal, we must be able to quantify the rate of vertical mixing. In fully submerged vegetation flows, coherent turbulent motions are generated near the vegetation edge and these large-scale eddies control the vertical exchange of mass and momentum. It is therefore important for river management to investigate hydrodynamic characteristics and coherent eddies in open-channel flows with vegetation canopies. Turbulence structure and transport mechanism of momentum in vegetated flows have been investigated intensively in the past decade. However, the effect of the submerged vegetation on the vertical mass transport and turbulent diffusion has not been fully investigated. Therefore, in the present study, continuous dye injection experiments were conducted to evaluate the mass transport structure in open-channel flow with rigid vegetation models by changing the vegetation density. A combination technique between PIV and planar laser-induced fluorescence (LIF) was developed by using two sets of CCD cameras, to measure the instantaneous velocity and concentration field simultaneously. The technique is capable of determining the turbulent scalar flux as well as the Reynolds stress, mean and fluctuating velocity and concentration fields. Consequently, the effects of coherent vortices on the vertical turbulent diffusivity were examined in detail. Ó 2012 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved. Keywords: Submerged vegetation flow; Coherent vortex; Vertical mass transport; Scalar flux; Turbulent diffusivity; PIV; LIF

1. Introduction The importance of flow and turbulence to the ecology of aquatic benthic organism has been widely reported. Aquatic vegetation is one of environmental variables that influence turbulence and the ecological condition of rivers. Aquatic canopies have the potential to greatly improve water quality through the removal of nutrients and trace metals. To describe the efficiency of this removal, we must be able to quantify the

* Corresponding author. E-mail addresses: [email protected], t.a.okamoto1234@ gmail.com (T.-a. Okamoto).

rate of vertical mixing. In fully submerged vegetation flows, coherent turbulent motions are generated near the vegetation edge and these large-scale eddies control the vertical exchange of mass and momentum. It is therefore important for river management to investigate hydrodynamic characteristics and coherent vortex in open-channel flows with vegetation canopies. Turbulence structure and transport mechanism of momentum in vegetated flows have been investigated intensively in the past decade. In canopy flows, the time-averaged velocity profile contains the inflection point near the vegetation edge and consequently, the KelvineHelmholtz (KeH) instability generates the largescale organized vortices, e.g. see a review of Finnigan (2000). A great deal is known about the terrestrial canopy flows.

1570-6443/$ - see front matter Ó 2012 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.

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T.-a. Okamoto et al. / Journal of Hydro-environment Research 6 (2012) 287e297

Raupach et al. (1986) found that velocity spectra above and within the canopy show the dominance of large-scale eddies occupying much of the boundary layer. Gao et al. (1988) have proposed a ramp-jump structure and humidity within and above a terrestrial canopy. They revealed that coherent structures consisted of a weak ejection from the canopy top followed by a strong sweep into the canopy. Further, Raupach et al. (1996) observed that the mean streamwise spacing of ramp-jump structures in canopy flow is equal to the streamwise wavelength of a KelvineHelmholtz wave derived from the instability theory of a plane-mixing-layer. These terrestrial canopy flow models can also be applied to the open-channel flows with submerged vegetation. Ghisalberti and Nepf (2002) revealed that the submerged vegetation flows can be patterned on a mixing-layer than a boundary layer. Poggi et al. (2004) classified the whole flow depth region in submerged vegetation flow into three layers on the basis of the laser Doppler anemometer (LDA) measurement data. The lower layer is primary dominated by small-scale vortices due to Karman vortex. The second layer, which is near the canopy top, is dominated by Kelvine Helmholtz waves due to inflection instability. The third is the upper layer, which is similar to boundary layers. Nezu and Sanjou (2008) compared the experimental results with those of terrestrial canopy flows and a general agreement is concluded. Pokrajac et al. (2008) pointed out the importance of double-averaging method (DAM), i.e., both time-average and space-average, in the within-canopy region. Many aquatic canopies have great flexibility and the passage of large-scale coherent vortex generates coherent waving motion of plants, which is called the “Monami” phenomena. Ikeda and Kanazawa (1996) have investigated the open-channel flows with flexible vegetation by PIV and observed that the coherent vortex shows the three-dimensional structure. Ghisalberti and Nepf (2006) revealed that the highly-organized vertical transport within flexible canopy is dominated by Sweep (to degree dependent upon the vegetation density), while the over-canopy region is dominated by Ejections. Recently, Okamoto and Nezu (2009) analyzed the instantaneous tip motion of flexible vegetations and quantified the “Monami” phenomena by applying PTV technique. The results show that much larger space-time correlation between vegetation elements are observed for Monami canopy than for Swaying canopy. The objective of this study is to quantify the vertical mixing in submerged vegetation flows. Planar laser-induced fluorescence (LIF) is non-intrusive technique for measuring spatial and temporal scalar structure in fluid flows. A fluorescent dye is used as a scalar proxy, and local fluorescence caused by excitation from a thin laser sheet can be related to dye concentration (see Crimaldi (2008)). The LIF measurement technique has been adapted for use to investigate the mixing processes in various flows. For open-channel flow study, Chen and Jirka (1999) have measured the instantaneous concentration field of plane jet by LIF to examine the role of turbulence structure in the mixing processes. Crimaldi and Koseff (2001) conducted two techniques for quantifying the scalar structure of turbulent flows. The full-field planar LIF image technique

was capable of making highly resolved measurements of spatial structure, and the single-point LIF probe resolved the temporal structure. Rahman and Webster (2005) and Jackson et al. (2007) conducted planar LIF measurements in turbulent open-channel flows and examined the effect of bed roughness on a chemical plume. In contrast, as aquatic canopy study, Ghisalberti and Nepf (2005) conducted continuous dye injection experiments to characterize vertical mass transport in submerged vegetation flow. Through the absorbance-concentration relationship of the Beer Lambert law, a digital imaging was used to provide highresolution concentration profiles of the dye plumes. They suggested that vertical mass transport is dominated by the coherent vortices in the vegetation shear layer and turbulent diffusivity is directly proportional to the shear layer thickness. Reidenbach et al. (2007) have measured fine-scale mixing and mass transport within a coral canopy by using planar LIF. They showed that the action of surface waves could increase instantaneous shear and mixing up to six times compared to that of non-conditional flow. In addition, LIF technique has been recently coupled with a velocimetry technique to calculate the local covariance between the concentration and velocity. Shiono and Feng (2003) conducted simultaneous turbulence measurements of velocity and fluorescence concentration using a combination of LDA and LIF in rectangular and compound channel flows. The results show that the diffusivity calculated from the measured data were scattered around the eddy viscosity values. Crimaldi et al. (2007) investigated how the aggregations of bed roughness can alter the structure of both the overlaying momentum and concentration fields by using LDA and LIF. They observed that the vertical turbulent flux of scalar mass to the bed was approximately proportional to the rate of clam pumping. As mentioned, turbulent mixing process in vegetated openchannel flows has received much attention in many years. However, there are no data available for simultaneous turbulent fluctuations of velocity and scalar estimating the scalar flux in open-channel flow with submerged vegetation. Therefore, in the present study, continuous dye injection experiments were conducted to evaluate the vertical turbulent diffusion in open-channel flow with rigid vegetation models by changing the vegetation density. A combination technique between PIV and LIF was developed by using two sets of highspeed CCD cameras to measure the instantaneous velocity and concentration field simultaneously. The technique is capable of determining the scalar flux as well as the Reynolds stress, mean and fluctuating velocity and concentration fields. Consequently, the effects of coherent vortices on the vertical turbulent diffusivity were examined in detail. 2. Experimental method 2.1. Experimental setup and vegetation model The experimental setup and the coordinate system are indicated in Fig. 1. The present experiments were conducted in

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289

U( y). The dye absorbed the green laser-light (lw ¼ 537 nm) and reemitted light with the different longer wavelengths (lw ¼ 580 nm). The instantaneous distribution of dye was captured by one CCD camera (for LIF). An optical cut-off filter (lw > 550 nm) blocked the scattered light from PIV tracer (lw ¼ 537 nm) and passed the fluoresced light (lw ¼ 580 nm) to the camera sensor. The intensity ~Iði; jÞ recorded by the camera was transformed to the local chemical concentration ~cði; jÞ by an appropriate calibration function using the slope A(i, j ) and the intercept B(i, j ) (e.g. see Rahman and Webster (2005)). ~cði; jÞ ¼ Aði; jÞ~Iði; jÞ þ Bði; jÞ

ð1Þ

The calibration images were used to calculate a slope A(i, j ) and intercept B(i, j ) at each location using a linear leastsquare fit. Consequently, the planar concentration field ~cðx; y; tÞ is calculated from the captured images by one CCD camera (for LIF). 2.2. Hydraulic condition Fig. 1. Experimental setup.

a 10 m long and 40 cm wide tilting flume. y and z are the streamwise, vertical and spanwise coordinates, respectively. H is the water depth and h is the vegetation height. Bv and Lv are the neighboring vegetation spacings in the spanwise and streamwise directions, respectively. The elements of vegetation model were made of rigid-strip plates (h ¼ 50 mm height, b ¼ 8 mm width and th ¼ 1 mm thickness) in the same manner as conducted in laboratory experiments by Nezu and Sanjou (2008). The time-averaged velocity components in each direction are defined as U, V and W, and the corresponding turbulent fluctuations are u, v and w, respectively. ~cðtÞhC þ cðtÞ is the instantaneous dye concentration, which is defined in the same manner as velocity components. In the present study, a combination technique between PIV and LIF was developed by using two sets of CCD cameras (1024  1024 pixels), to measure the instantaneous velocity components ð~ u; ~vÞ and the instantaneous concentration ~cðx; yÞ simultaneously. The 2 mm thickness laser-light sheet (LLS) was generated by 3 W Argon-ion laser. The illumination point is 7.0 m downstream of the leading edge of the vegetation zone. The illuminated flow pictures were taken by two sets of high-speed cameras with 500 Hz frame-rate and 60 s sampling time. The instantaneous velocity components ð~ u; ~vÞ in the xey plane (20 cm  20 cm) were analyzed by the PIV algorithm for the whole flow depth region. The diameter and specific density of tracer particles (Nylon-12) were 100 m m and 1.02, respectively. These PIV methods are the same as used previously by Nezu and Sanjou (2008). The instantaneous concentration field ~cðx; yÞ was quantified by using the planar LIF technique. Dye (Rhodamine B) was injected through a 3 mm diameter stainless nozzle. The dye injection velocity was adjusted to match the local flow velocity

Table 1 shows the hydraulic condition. The bulk mean velocity Um and the submergence depth ratio H/h were kept constant for all cases, i.e., Um ¼ 12 (cm/s) and H/h pffiffiffiffiffiffi¼ 3.0. RehUmH/n is the Reynolds number, and FrhUm = gH is the Froude number. U* is the friction velocity, which was evaluated from the Reynolds stress distribution as shown later. In this study, only the vegetation density F was varied to examine the effects of the coherent vortex on the vertical mass transport, i.e., F ¼ 0.0, 0.015 and 0.061. In this study, the vegetation density F is defined as follows: n P

F¼

i

Ai bi

S$h

¼ ab

ð2Þ

in which, Ai is the frontal area of the vegetation element, bi is the vegetation element width and S is the referred bed area. n is the number of vegetation elements occupied in S. The vegetation density a (1/m) was defined as the total frontal area per vegetation volume Vo ¼ S  h. In the present study, the nozzle tip position y0 was changed ( y0/h ¼ 0.2, 0.6, 1.0, 1.4, 2.0, 2.4) to examine the turbulent diffusion properties in all three sub-zones of the vegetated open-channel flow, as shown in Fig. 2. Nepf and Vivoni (2000) and Poggi et al. (2004) have pointed out that the whole depth region in submerged vegetation flow could be classified into several layers on the basis of the vertical profiles of mean streamwise velocity and Reynolds stress. Nezu and Sanjou Table 1 Hydraulic condition. Case

F

H(cm)

h(cm)

H/h

Um (cm/s)

Re

Fr

S R1 R2

0.0 0.015 0.061

15.0

e 5.0

e 3.0

12.0

30,000

0.17

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H

y h

y 3

Nozzle Tip Position Log-law zone Coherent Vortex

2

hlog Mixing-layer zone

h

2.5

Vegetation edge

vegetation edge

1.5

=0.061

1

=0.015

hp

0.5

=0.061

Wake zone

=0.015

U /U h − uv/U*2

0

Vegetation Elements

0

0.5

1

1.5

2

2.5

U / Uh − uv /U *2

Fig. 2. Flow zone model in vegetated open-channel flow.

Fig. 3. Mean velocity and Reynolds stress.

(2008) found that the submerged canopy flow can be divided into the following three sub-zones on the basis of previous experimental results. 9   Wake zone 0  y  hp = ð3Þ Mixing  layer zone hp  y  hlog  ; Log  law zone hlog  y  H In the Wake zone (0  y  hp), the velocity profile is almost constant and turbulence is generated in strong wakes of individual vegetation elements. Consequently, the vertical turbulent momentum transport is negligibly small. Nepf and Vivoni (2000) defined the extent of the Wake zone ( y ¼ hp) as the point within the canopy, at which the Reynolds stress has decayed to 10% of its maximum value. In the Mixing-layer zone (hp  y  hlog), the velocity profile has an inflection point near the vegetation edge and turbulence structure is analogous to pure mixing-layer. A large-scale coherent vortex is generated near the vegetation edge and the vertical turbulent exchange contributes largely to the momentum transfer between over- and the within-canopies. Poggi et al. (2004) suggested that the relative enhancement of turbulent diffusivity near the vegetation edge depends on the vegetation density. In the Log-law zone (hlog  y  H ), the mean velocity obeys the log-law profile and turbulence characteristics are analogous to those of boundary layers. The lower limit position of the Log-law zone hlog is defined as the elevation of the starting deviation from the log-law profile. 3. Results 3.1. Mean-flow structure Before examinations of the concentration field, it is very important to examine the mean-flow and turbulence characteristics in vegetated open-channel flows. Fig. 3 shows the vertical profile of streamwise velocity U for dense canopy (F ¼ 0.061) and sparse canopy (F ¼ 0.015). These values are normalized by the mean velocity at the vegetation edge Uh. The velocity data were averaged over time and space (i.e.

double-averaging method (DAM)). The averaging window in time was 60 s. The size of the averaging window in space was 200  4  2 (mm) in the streamwise (x-axis), vertical ( y-axis) and spanwise (z-axis) directions, respectively. Near the top of the vegetation ( y/h ¼ 1.0), both the local velocity U( y) and its gradient vU/vy increase rapidly, which induces a strong shear layer and a significant inflection point instability, as pointed by many researchers. Note that the near-constant velocity within the canopy decreases with an increase of the vegetation density F, which implies that the drag force due to the vegetation elements become stronger. Fig. 3 also shows the vertical distributions of the timeaveraged and space-averaged Reynolds stress uv, normalized by the friction velocity U*. The value of U* was evaluated as the peak value of uv in the same way as conducted by Poggi et al. (2004). It should be noticed that the value of uv attains maximum near the vegetation edge, i.e., y/h ¼ 1.0. The Reynolds stress decays rapidly in the canopy layer ( y/h < 1) and becomes negligibly small near the channel bed. This indicates that the vertical turbulent transport becomes negligibly small in the Wake zone, which is consistent with Nepf and Vivoni (2000). Fig. 3 also shows that the values of Reynolds stress within the vegetation layer ( y/h < 1.0) decrease with an increase of the vegetation density F. Due to the dense spacing of vegetation elements, turbulent transport imparts minimum momentum into the canopy layer for F ¼ 0.061. As such a measure, Nepf and Vivoni (2000) defined the penetration depth hp as the elevation of 10% of the maximum Reynolds stress. In the present study, hp/h ¼ 0.25 for dense canopy (F ¼ 0.061) and hp/h ¼ 0.15 for sparse canopy (F ¼ 0.015). 3.2. Quadrant conditional analysis To elucidate the impact of the vegetation density on turbulence structures, the quadrant analysis was conducted for the instantaneous Reynolds stress u(t)v(t). The quadrant Reynolds stress RSi is defined as follows:

T.-a. Okamoto et al. / Journal of Hydro-environment Research 6 (2012) 287e297

1 RSi ¼ lim T/N T

ZT ðuvÞIi dt

ð4Þ

0

If (u, v) exists in a quadrant i, then Ii ¼ 1, and otherwise Ii ¼ 0. Each quadrant of (u, v) corresponds to the following coherent events: i i i i

¼ ¼ ¼ ¼

1 2 3 4

(u (u (u (u

> < > <

0, 0, 0, 0,

v v v v

> > < <

0): 0): 0): 0):

Outward interaction Ejection Inward interaction Sweep

density is sufficient to produce an inflection point in the velocity profile, i.e. CDah >z 0.1 (CD: canopy drag coefficient). In the present study, the vegetation density is CDah >z 0.38 for dense canopy and CDah >z 0.0975 for sparse canopy. In order to compare the contributions of Sweeps and Ejections to vertical momentum transport in submerged vegetation flow, Ghisalberti and Nepf (2006) proposed the following parameter RS/E. 1 RS=E ¼ h  hp

Fig. 4 shows the vertical distributions of the quadrant Reynolds stress RSi, which is normalized by the bulk mean velocity U*. The ratio of RSi =U2 is a measure of momentum exchange efficiency. For dense canopy flow (F ¼ 0.061), the distributions of RS4 (Sweep) and RS2 (Ejection) have the peak value near the vegetation edge. RS4 is much larger than RS2 within the canopy layer ( y/h < 1.0) and Sweep motions dominate Ejection motions. It should be noticed that the Sweep motion transports the momentum from the over-canopy region toward the within-canopy region. This is consistent with LDA measurements of Poggi et al. (2004). The contributions of the outward and inward interactionsRS1 and RS3 are negligibly small near the vegetation edge, which indicates that the Sweeps and Ejections are much organized motions in the Mixing-layer zone. In contrast, the Log-law zone ( y/ h  hlog/h z 2.0) is primary dominated by the Ejection (RS2 > RS4). This implies that the Ejection events are pronounced in the same manner as observed in boundary layers and open-channel flows, as pointed out by Nezu and Nakagawa (1993). The values of the interaction eventsRS1 and RS3 become larger than those in the Mixing-layer zone. For sparse canopy flow (F ¼ 0.015), the peak values of RS4 (Sweep) and RS2 (Ejection) become smaller than those for dense canopy (F ¼ 0.061). This provides more evidence that vertical momentum exchange in the Mixing-layer zone is smaller for sparse canopy. Nepf and Ghisalberti (2008) suggested that a shear layer is generated only when the canopy

291

Zh ðRS4 =RS2 Þdz

ð5Þ

hp

The values of RS/E are indicated in the legend of Fig. 4. For sparse canopy (F ¼ 0.015), the value of RS/E is 1.42, which is in good agreement with Ghisalberti and Nepf (2006)’s data, RS/E ¼ 1.43 for F ¼ ad ¼ 0.022. It is found that the value of RS/E ¼ 1.84 is larger for dense canopy flow than RS/E ¼ 1.42 for sparse canopy flow, which indicates that the contribution of sweeps becomes larger than those of ejections as the vegetation density F increases. This result is consistent with Poggi et al. (2004) and Ghisalberti and Nepf (2006). They suggested that as the vegetation density F becomes larger, a strong shear layer develops at the top of the canopy and the vertical transport of the high-speed fluid parcel toward the canopy layer is promoted more significantly. The values of RS/E are approached to a constant value for larger vegetation density (F  0.061). 3.3. Time-averaged concentration In our next stage, we investigated the influence of the vegetation density on the vertical mass transport structure on the basis of the LIF measured data. Fig. 5 shows the distributions of the time-averaged dye concentration C( y) for dense canopy (F ¼ 0.061) and sparse canopy (F ¼ 0.015). The nozzle tip positions is y0/h ¼ 1.0 (vegetation edge). The values are normalized by the concentration Cmax at the nozzle tip of dye injection. Close to the source, the distributions of C( y) for sparse canopy (F ¼ 0.015) have a local maximum near the

Fig. 4. Quadrant Reynolds stress RSi.

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= 0.061

y/h

= 0.015

y/h 3

3

x/L v = 1.0

x/L v = 1.0 x/L v = 2.0

2.5

x/L v = 2.0

2.5

x/L v = 3.0

x/L v = 3.0 2

x/L v = 4.0

2

1.5

1.5

1

1

0.5

0.5

x/L v = 4.0

0

0 0

0.05

0.1

0.15

0.2

0.25

0

0.05

0.1

0.15

0.2

0.25

C /Cmax

C /Cmax Fig. 5. Time-averaged concentration.

vegetation edge ( y/h ¼ 1.0) with a steep gradient above and below the canopies. The time-averaged concentrations C decrease in magnitude and the distributions become more uniform with an increase of distance from the source. In contrast, the vertical turbulent diffusion becomes larger for dense canopy flow (F ¼ 0.061). The peak values of C( y) for dense canopy are smaller than those for sparse canopy. This indicates that the increased turbulence intensity near the vegetation edge enhances the vertical turbulent diffusion from the nozzle position (set at the vegetation edge) toward the free surface and the within-canopy region. Consequently, the values of C( y) become negligibly small and the vertical distribution becomes almost constant beyond x/Lv ¼ 3.0 for dense canopy flow. These results are consistent with the experiments of Rahman and Webster (2005). They revealed that the plume width increased and the time-average concentration decreased faster with downstream distance with greater bed roughness. To evaluate the vertical turbulent diffusion quantitatively, Fig. 6 compares the half-value-width by1/2þ (upper layer) and by1/2 (lower layer) at x/Lv ¼ 2.0 for F ¼ 0.0, 0.015 and 0.061. Both of by1/2þ and by1/2 become larger at y0/h ¼ 0.6 and 1.0, i.e., in the Mixing-layer zone, for F ¼ 0.015 and 0.061. The vertical turbulent diffusion is smaller at y0/h ¼ 0.2, i.e., in the Wake zone and y0/h ¼ 2.4, i.e., in the Log-law zone. In contrast, for the Smooth flat bed (no vegetation, F ¼ 0.0), the values of by1/2þ and by1/2 are negligibly small, irrespective of the nozzle tip position of y0/h. This implies that in submerged vegetation flows, a large-scale coherent vortex is generated near the vegetation edge due to the inflection point instability (Fig. 3) and the vertical turbulent exchange contributes largely to the vertical scalar transport in the Mixing-layer zone. These results are in good agreement with Nepf and Vivoni (2000) and Nezu and Sanjou (2008). It is also observed that by1/2þ and by1/2 for F ¼ 0.061 (dense canopy) are greater than those for F ¼ 0.015 (sparse canopy) and F ¼ 0.0 (smooth bed). Nezu and Sanjou (2008)

pointed out that the strong shear layer appears near the vegetation edge for dense canopies. Ghisalberti and Nepf (2005) also demonstrated that the dense canopies would generate vortices with a greater rotational speed and that the higher rates of rotation would result in a more rapid flushing in the canopy layer. Therefore, it is recognized that the large distributions of the dye concentration are mixed rapidly due to the strong shear layer for F ¼ 0.061. 3.4. Instantaneous structure ‘Flow-visualization techniques’ such as PIV and LIF have several advantages over ‘Single-point measurement technique’. Two-dimensional flow velocity data in the whole plane allow the identification of coherent structure present in the flow. Raupach et al. (1996) and Ghisalberti and Nepf (2006) revealed that there is a periodical generation mechanism of Sweeps and Ejections for submerged canopy flows and these coherent motions govern the momentum exchange between the above-canopy and within-canopy regions. x / Lv = 2.0 =0.061

3

y0 h

Log-law zone

=0.015 =0.0

Mixing-layer zone

2

1

Wake zone

0 -0.6

b y1 2− h

-0.3

0

0.3

0.6

by1 2+ h

Fig. 6. Half-width values of three sub-zones.

T.-a. Okamoto et al. / Journal of Hydro-environment Research 6 (2012) 287e297

Fig. 7 shows some examples of the instantaneous velocity vectors ð~ u; ~vÞ at y0/h ¼ 1.0 for dense canopy (F ¼ 0.061), which were obtained by PIV. The contours indicate the magnitude of turbulent fluctuations uh~ u  U for the streamwise velocity component. Fig. 8 shows the corresponding simultaneous concentration field ~cðx; y; tÞ measured by LIF. Fig. 8 reveals the high spatial variability of the instantaneous concentration field. At t ¼ 0.0(s), a Sweep motion, i.e., the downward vectors (u > 0 and v < 0), appears near the vegetation edge. It is observed that the large distribution of the instantaneous concentration is transported into the canopy layer by the Sweep motion. At t ¼ 4.8(s), an Ejection motion, i.e., the upward vectors (u < 0 and v > 0), is observed and causes the local increase of the concentration above the canopy. At t ¼ 7.5(s), the Ejection motion is transported downstream and the other Sweep motion appears at the upstream side. The individual filaments of the dye concentration are observed clearly and the highly intermittent nature of the plume is exhibited, which is consistent with Rahman and Webster (2005). These images also show that the locally-high distributions of dye concentration correspond well to these coherent structure zones. These results provide more evidence that the large-scale coherent motions dominate the vertical mass transport in vegetated flows. 3.5. Conditional analysis To evaluate the effects of the coherent motions on the vertical turbulent diffusion quantitatively, quadrant analysis was performed. Fig. 9 shows the vertical distributions of the concentration CEjection and CSweep at x/Lv ¼ 3.0 for F ¼ 0.061 (dense canopy) by using conditional sampling of the Ejection motion (u < 0, v > 0) and the Sweep motion (u > 0, v < 0), respectively. The nozzle tip positions is y0/h ¼ 1.0 (vegetation edge). To exclude the contribution of less-organized motions, a threshold level Ho, so-called the ‘hole-value’ is used. juvðtÞjiHo u0 v0

ð6Þ

u0 and v0 is the RMS values of the streamwise velocity and the vertical velocity, respectively. The time-averaged concentration C (Non-conditional) is also included for comparison in

293

Fig. 9. It is evident from Fig. 9 that CEjection has the peak value above the vegetation edge and the values of CEjection are larger than C (Non-conditional) in the over-canopy region. This implies that the vertical diffusion of the high concentration value toward the free surface is enhanced by the Ejection motion, which is consistent with Figs. 7and 8. Whereas, CSweep becomes larger than C below the vegetation edge ( y/ h ¼ 1.0) and the Sweep motion transports the dye concentration into the within-canopy layer. It is also observed the distribution of the concentration CEjection(Ho ¼ 1) and CSweep(Ho ¼ 1) are greater than those of CEjection(Ho ¼ 0) and CSweep(Ho ¼ 0). This indicates that much organized Sweep and Ejection motions would transport larger-values of the dye concentration. Using mean scalar concentration within the canopy, we can compare the rate of mass flux into the canopy layer quantitatively (see Reidenbach et al. (2006, 2007)). The transport rate into the canopy layer of CSweep(Ho ¼ 0) is 44% and CSweep(Ho ¼ 1) is 109% larger than that of C (Nonconditional). 3.6. Turbulent scalar flux Of particular significance in this study is that the turbulent scalar flux measurements present a detailed picture of how and where mass is transferred to the vegetation layer. The PIV-LIF measurements afford us to calculate the local covariance between the concentration and velocity fluctuations, vc. Fig. 10 shows the turbulent scalar flux vc for dense (F ¼ 0.061) and sparse (F ¼ 0.015) canopies. The nozzle tip positions is y0/h ¼ 1.0 (vegetation edge). The RMS values of the vertical velocity v0 and the concentration, c0 , are used to normalize the flux quantities. The magnitude of the normalized scalar flux vc appears to lie between 0.25 and 0.25. These values are in good agreement with Crimaldi et al. (2007)’s LIF measured data. It is also apparent that the contours of turbulent scalar flux vc are almost symmetric about the vegetation edge, i.e., the turbulent flux vc has the positive values above the vegetation edge ( y/h > 1.0). The positive flux vc > 0 (c > 0, v > 0) means dye diffusion toward the free surface by the Ejection motion (u < 0, v > 0). In contrast, the contours of vc have negative values within the canopy layer,

Fig. 7. Instantaneous velocity vectors (F ¼ 0.061).

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T.-a. Okamoto et al. / Journal of Hydro-environment Research 6 (2012) 287e297

Fig. 8. Instantaneous dye concentration field corresponding to Fig. 8.

which implies that the Sweep motion (u > 0, v < 0) transports the dye concentration into the canopy layer (c > 0). It should be noticed that the contour values of the turbulent scalar flux vc are greater for dense canopy than those for sparse canopy. These results reveal that mass is actively transported by organized momentum structures in the presence of the strong shear layer for dense canopy flow, which is consistent with Figs. 4 and 6. The PIV-LIF measured data provides instantaneous velocity and concentration in a plane at the same time. This technique is capable of calculating the vertical turbulent diffusivity Dy directly. Fig. 11 shows the distribution of the vertical turbulent diffusivity Dy and eddy viscosity nt for dense (F ¼ 0.061) and sparse canopy (F ¼ 0.015). The nozzle tip position is at y0/ h ¼ 1.0. Experimental values of Dy and nt are evaluated by following equations. vc ¼ Dy

vC vy

ð7Þ

Fig. 9. Distribution of conditional sampling concentration (F ¼ 0.061).

uv ¼ nt

vU vy

ð8Þ

The distributions of eddy viscosity nt and turbulent diffusivity Dy have larger-values in the Mixing-layer zone than those in the Wake zone and Log-law zone. The averaged turbulent diffusivity Dy for F ¼ 0.061 in the Mixing-layer zone is 310% larger than Dy for F ¼ 0.015. This strongly suggests that the vertical turbulent diffusion is enhanced by strong shear layer for dense canopy flow. This result is consistent with Fig. 5. The averaged turbulent Schmit number Sct ¼ ðnt =Dy Þ in the Mixing-layer zone is 0.59 (for dense canopy) and 1.08 (for sparse canopy). The value of Sct ¼ 0:59 for dense canopy is of the same order of magnitude as Sct ¼ 0:5 of Raupach et al. (1996) and Sct ¼ 0:47 of Ghisalberti and Nepf (2005). This indicates that the transport of mass is twice as efficient as the transport of momentum in Mixing-layer zone. Fig. 12 shows the distribution of turbulent scalar flux vcEjection and vcSweep at x/Lv ¼ 3.0. vcEjection and vcSweep are the vertical scalar flux by using conditional sampling of the Ejection motion (u < 0, v > 0) and the Sweep motion (u > 0, v < 0), respectively. The nozzle tip positions is y0/h ¼ 1.0 (vegetation edge). The bulk mean velocity Um and the timeaveraged concentration Cmax are used to normalize the flux quantities. The distribution of turbulent scalar flux vc (Nonconditional) is also indicated for comparison. It is evident from Fig. 12 that the values of vcEjection and vcSweep are much larger than those of vcNonconditional . The negative peak value of the turbulent scalar flux vcSweep is 300% larger than that of vcNonconditional . This provides more evidence that the Sweep motion (u > 0, v < 0) contributes to the vertical turbulent diffusion into the canopy layer more significantly, which is consistent with Fig. 9. It is also observed that vcSweep has the positive values ðvcSweep > 0Þ near the vegetation edge. This is because the contribution of Sweep motion to scalar transport is larger than that of Ejection motion even in the over-canopy region ( y/h ¼ 1.2e1.5, see Fig. 4). However, in the present study, the dye concentration is injected at the vegetation edge ( y/h ¼ 1.0) and the time-averaged concentration is negligibly small in the over-canopy region ( y/h ¼ 1.2e1.5). Consequently, the lower distribution of concentration (c < 0) is transported to the within-canopy region from the over-canopy

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295

Fig. 10. Turbulent scalar flux vc ( y0/h ¼ 1.0).

region by the Sweep motion (u > 0, v < 0) and vcSweep has the positive values ðvcSweep > 0Þ near the vegetation edge. In contrast, the distribution of vcEjection has the positive peak value above the vegetation edge ( y/h ¼ 1.2e2.0) and this value is 336% larger than that of vcNonconditional . The values of vcSweep and vcEjection are negligibly small in the Wake region. On the basis of PIV & LIF measured data, the present study tried to compare the contributions of Sweep and Ejection to the vertical mass transport. Vertical penetration of turbulent scalar flux into the canopy is a measure of a region within the canopy, which actively exchanges mass. The extent of this region ( y ¼ hdc) can be defined as the point within the canopy at which the turbulent scalar flux vc becomes negligibly small. In Fig. 13, dc (Non-conditional) is the penetration thickness of turbulent scalar flux vc for dense canopy (F ¼ 0.061). The nozzle tip positions is y0/h ¼ 1.0 (vegetation edge). dc (Sweep) and dc (Ejection) are the penetration

thickness of vertical scalar flux vcSweep and vcEjection , respectively. dc increases as the plume evolves downstream and become almost constant (dc/h ¼ 0.8) at x/Lv  4.5. It should be noticed that the penetration thickness of the Reynolds stress uv is duv ¼ 1  hp ¼ 0:75 for F ¼ 0.061 (see Fig. 3) and the values of dc (Non-conditional) become larger than duv at x/ Lv ¼ 4.0. This implies that the vertical exchange rate of mass is larger than that of momentum. These results are in good agreement with Fig. 11. It is also observed that the values of dc (Sweep) are significantly larger than those of dc (Non-conditional) and the Sweep motions dominate the vertical penetration of scalar flux into the canopy. dc (Sweep) is larger than the largest value dc (Non-conditional)/h ¼ 0.8. This indicates that supply of mass to the regions below y/h ¼ 0.2 from the overcanopy region would need to rely on the large-scale Sweep motions. This conclusion is supported by the conditional sampling analysis (Fig. 9).

Fig. 11. Turbulent diffusivity and Eddy viscosity.

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2.

3.

Fig. 12. Vertical distribution of conditional sampling scalar flux vcEjection and vcSweep (F ¼ 0.061).

4.

5.

the within-canopy region. The quadrant analysis of the instantaneous Reynolds stress revealed that the contribution of Sweep to vertical momentum transport becomes larger as the vegetation density increases. Distributions of the time-averaged concentration for dense canopy decrease more rapidly than those for sparse canopy. This indicates that as the vegetation density increases, the increased turbulence intensity near the vegetation edge enhances the vertical turbulent diffusion from the nozzle position (set at the vegetation edge) toward the free surface and the within-canopy region. On the basis of LIF& PIV data, we revealed that the largescale Sweep and Ejection motions dominate the vertical mass transport in vegetated flows. Using mean scalar concentration within the canopy, we evaluated the rate of mass flux into the canopy layer quantitatively. Mass transfer rate of large-scale Sweep motion is 109% larger than that of Non-conditional case. We calculated the turbulent scalar flux and the vertical turbulent diffusivity from LIF& PIV measured data. The values of the turbulent diffusivity become larger in the Mixing-layer zone and the vertical diffusion is smaller in the Wake zone and in the Log-law zone. This implies that a large-scale coherent vortex is generated near the vegetation edge and the vertical turbulent exchange contributes largely to the vertical turbulent diffusion in the Mixinglayer zone. The averaged vertical turbulent diffusivity for dense canopy in the Mixing-layer zone is 310% larger than that for sparse canopy. These results reveal that mass is actively transported by organized momentum structures in the presence of the strong shear layer for dense canopy flow.

Notation Fig. 13. Penetration thickness of vertical scalar flux (F ¼ 0.061).

4. Conclusions In the present study, continuous dye injection experiments were conducted to evaluate the vertical turbulent diffusion in open-channel flow with rigid vegetation models by changing the vegetation density. A combination technique between PIV and LIF was developed by using two sets of high-speed CCD cameras to measure the instantaneous velocity and concentration field simultaneously. The technique is capable of determining the vertical scalar flux and turbulent diffusivity. Consequently, the effects of the vegetation density on vertical mass transport structure were examined in detail. The significant results obtained in this study are as follows: 1. In submerged vegetation flow, the Sweep motion transports the momentum from the over-canopy region toward

b by1/2þ, C CD Dy Fr H h hp hlog Ho I Lv, Bv Re Sct th

¼ vegetation-element width by1/2 ¼ half-value-width ¼ time-averaged concentration ¼ canopy drag coefficient ¼ vertical turbulent diffusivity ¼ Um/( gH )1/2, Froude number ¼ flow depth ¼ vegetation-element height ¼ penetration height of Reynolds stress ¼ lower limit position of log-law zone ¼ hole value ¼ light intensity ¼ neighboring vegetation spacings in streamwise and spanwise directions, respectively ¼ HUm/n, Reynolds number ¼ turbulent Schmit number ¼ vegetation element thickness

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U, V, W ¼ double-averaged streamwise, vertical and spanwise velocity ¼ streamwise mean velocity at vegetation edge Uh ¼ bulk mean velocity Um ¼ friction velocity U* Vo ¼ vegetation zone volume x, y, z ¼ streamwise, vertical and spanwise coordinates ¼ nozzle tip position y0 F ¼ vegetation density ¼ eddy viscosity nt ¼ penetration depth of the vertical scalar flux dc ¼ penetration depth of the Reynolds stress duv ¼ wavelength lw

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