The role of different forms of natural riparian vegetation on turbulence and kinetic energy characteristics

Advances in Water Resources 33 (2010) 601–614

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Advances in Water Resources j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a d v wa t r e s

The role of different forms of natural riparian vegetation on turbulence and kinetic energy characteristics O. Yagci a,⁎, U. Tschiesche b, M.S. Kabdasli a a b

Istanbul Technical University, Civil Engineering Faculty, Division of Hydraulics, 34469 Maslak, Istanbul, Turkey University of Natural Resources and Applied Life Sciences, Department of Water, Atmosphere and Environment, Vienna, Austria

a r t i c l e

i n f o

Article history: Received 16 July 2009 Received in revised form 5 March 2010 Accepted 18 March 2010 Available online 24 March 2010 Keywords: Floodplain Natural vegetation Open channel flow Turbulence Vegetated channel Velocity profile

a b s t r a c t Flow measurements were conducted by ADV Vectrino to investigate the role of different forms of single natural emergent vegetation elements on kinetic energy characteristics and the flow structure in open channel flow. Experiments were carried out for both forms of “erect” and “compressed” vegetation. The findings revealed that the form of “erect” has greater retaining influence on time-averaged mean velocity characteristics than “compressed” form. Furthermore, the turbulence and kinetic energy patterns behind the single vegetation were also examined. An empirical equation giving the relationship between the kinetic energy components of flow was derived based on the data. The ratio between turbulence kinetic energy and mean kinetic energy at a certain distance downstream of vegetation element was predicted by the empirical equation depending on the vegetation characteristics. These predictions were compared with a different experimental data set and produced satisfactory results. Also, the mean flow and turbulence characteristics behind an isolated natural plant and a volumetrically equivalent rigid cylinder were also compared. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction The importance of the conservation of both aquatic and riparian vegetation is today commonly recognized by river engineers. However, it is still a complicated issue to describe quantitatively the phenomenon of “flow passing through aquatic vegetation” since in nature each species is unique in terms of biomechanical and architectural properties. The estimation of resistance due to vegetation with an acceptable precision is highly important in design of open channels as it directly affects the conveyance capacity. A number of studies in this area aimed to establish the contribution of resistance due to presence of vegetation by one dimensional approach [4,5,13,25,26,30,34,37]. Rigid stem analogy was a necessary simplification in understanding the nature of “flow through vegetation” phenomenon. This simplification was practiced in many 2D [6,12,17,18,20,21,24] and 3D studies [8,10,27,29] in the past. In all these studies, the main idea was to simulate the drag force applied by flow to the vegetation. Kouwen and Fathi-Moghadam [16], Armanini et al. [2], and Wilson et al. [38] measured instantaneous drag force directly on natural vegetation. The rigid stem analogy presents a good starting point in attempting to understand the elaborate flow structure where flowing through riparian vegetation. However, this analogy has some major drawbacks. According to the drag force equation for a rigid cylinder, the

⁎ Corresponding author. Tel.: + 90 212 2856011; fax: +90 212 2856587. E-mail address: [email protected] (O. Yagci). 0309-1708/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2010.03.008

drag is expected to increase with the square of the velocity. However, based on the drag force measurements Fathi-Maghadam et al. [7] showed that differing from the standard drag force equation, for flexible tree models, drag force appears to have a linear relationship with velocity due to deflection of the plant foliage area and reduced drag coefficient “CD” with increasing flow velocity. In fact, as a selfprotection reaction of vegetation, the plant compresses, bends and oscillates under the effect of drag force in order to decrease itself in the “frontal” (or “momentum absorbing”) area. This complex dynamic mechanism is neglected by the rigid stem analogy. Another drawback of the rigid stem analogy is that the vegetation is reduced to a stem without considering the presence of branches and foliage. According to Jarvela [13] branches contributed approximately 2/3 to the total leafless projected area for typical floodplain vegetation willows. Wilson et al. [35] showed that the bending of riparian vegetation can have a significantly greater impact on the velocity distribution compared to drag force coefficient. Although it is a known fact that while the viscous drag (i.e. skin friction) is negligibly small compared to form drag for the case of rigid cylinder [33], the role of viscous drag on flow structure where flow passes through real vegetation has not been fully understood yet. Also, Schnauder et al. [28] investigated the effect of permeability of natural vegetation on the flow. Their findings revealed that the degree of anisotropy of turbulence was significantly lower compared to the impermeable plant. Biomechanical and architectural characteristics of individual plants in a riparian forest exhibit temporal and spatial variation. This variability is higher when the plant community is composed of different species since each species has intrinsic properties. In many

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natural riparian forests light-demanding and shade-tolerant species (i.e. grasses, shrubs, and exotic species) live together Johnson and Miyanishi [14]. In order to overcome this inextricability, spatial averaging technique [39] could be applied over a vegetated region large enough to eliminate any variation due to individual vegetation elements, in addition to temporal averaging. At the beginning of this study this option was also discussed and it was decided to take one step back and the necessity of firstly understanding the physical event of “flow through isolated vegetation elements” was acknowledged. It was assumed that knowledge of the mean flow and turbulence structure where flow passes through isolated vegetation helps to give a better understanding of “flow through vegetation community.” The definition of basic natural vegetation forms (i.e., erect, compression, and bending) under the effect of drag force by flow are described in the next section. This study focuses on the case of “erect” and “compressed” forms of emergent vegetation in a flow field. All the experiments were undertaken for these two vegetation forms. The primary aim of this study is to describe quantitatively the role of single natural emergent vegetation on kinetic energy characteristics (i.e. mean kinetic energy to turbulent kinetic energy) and the turbulence structure in an open channel flow. 2. Methods 2.1. Classification of the vegetation forms under the effect of drag force In natural vegetated open channels, the emergent vegetation with large trunk exhibits three different primary motions under the impact of drag force: • Erect: The vegetation withstands flow without significant motion. The foliage of the vegetal elements gently moves dependent on its structure. • Compression: Due to the increasing speed of flow (i.e. augmented drag force), the second degree branches and foliages follow the streamlines, the permeability of the vegetation decreases; the projected area on horizontal plane diminishes. Additionally, indistinct swaying motion of the secondary degree branches and foliages are observed. But swaying motion is not observed in the plant trunk.

• Bending: With the further increase of drag force on the vegetation element, the trunk of the plant cannot withstand flow and starts to bend. In this way, as a self-protection reaction the vegetal element decreases its own frontal area to decrease the drag force. In addition to these three major plant motions, a permanent oscillation occurs due to the cycle of transition between compression and bending forms. Since it is a complicated issue to describe quantitative criteria to classify the forms of vegetation under the effect of drag force, herein only some qualitative criteria were defined. Nevertheless, further studies and comprehensive data sets are necessary to improve accurate quantitative criteria for various vegetation species. In this study, experiments were undertaken in the laboratory flume in order to determine the effect of the different forms of vegetation (i.e. “erect” and “compression”) on the energy dissipation and the flow structure. The characterization of the vegetation is presented in the next section. 2.2. Characterization of the vegetation elements Throughout the experiments three different real tree saplings were utilized. These were Pinus Pinea, Thuja Orientalis, and Cupressus Macrocarpa (Fig. 1). Yagci and Kabdasli [40] classified vegetation into three groups (i.e. Type1, 2, and 3) depending on their “cumulative volume, V” versus “height, h” relationship. The main differences between these three types are the variation of gradient curves with respect to height (Eqs. (1)–(3)). 
  ð∂V = ∂hÞ = ∂h b0 for Type 1

ð1Þ


  ð∂V = ∂hÞ = ∂h ≅0 for Type 2

ð2Þ


  ð∂V = ∂hÞ = ∂h N 0 for Type 3

ð3Þ

The procedure by Wilson et al. [36] was followed to obtain variation of the cumulative volume of the plants with respect to height (Fig. 2). In this procedure, the plants were cut into parts. Then, the volume of each part was determined using a displacement technique (based on Archimedes theory) where each 50 mm

Fig. 1. Vegetation types used in the flume experiments in front of a 1 cm squared grid: (a) Pinus Pinea (scale ≈ 0.113), (b) Thuja Orientalis (scale ≈ 0.127), (c) Cupressus Macrocarpa (scale ≈ 0.067), and (d) reference square: 1 cm × 1 cm.

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2.3. Experimental set-up

Fig. 2. The variation of the cumulative volume of vegetation with respect to height of for Types 1, 2 and 3.

increment length was submerged in a measurement cylinder. Fig. 2 indicates that Pinus Pinea, Thuja Orientalis, and Cupressus Macrocarpa correspond to Types 1, 2 and 3 respectively. In order to see the role of the volume of the vegetation element on the flow domain more obviously, plants were chosen in a wider range volume. The definition of vegetation index parameter (Eq. (4)) which is firstly proposed by Yagci and Kabdasli [40] was used in the characterization of the vegetation elements. Total drag applied to an obstacle by flow is equal to the summation of form drag and skin friction (viscous drag). It is a fact that the skin friction is negligibly small compared to form drag for the case of rigid cylinder [33]. Based on this fact in many studies [8,10,12,17,18,20,21,24,25,27,29,30,36] the drag force on the elements was expressed as a function of projected area (or momentum absorbing area, MMA) in the streamwise direction. However, when real vegetation is considered, the contribution of skin friction on foliages to the total drag is not understood well yet. In this study, differing from earlier studies, the volumetric approach which was firstly proposed by Yagci and Kabdasli [40] was utilized. With this approach it was assumed that a vegetative element in a flow domain can resist flow as a function of its volume. Yagci and Kabdasli [40] described vegetation index parameter, VIP, as given in Eq. (4). VIP denotes the quantity of occupied volume by the vegetation element per unit projected volume (i.e. the product of Ahz0). In physical terms with the increasing volume of VIP, the total drag (i.e. form drag + viscous drag) on the vegetative element increases.   Vveg z0 VIP = Ah

ð4Þ

where VIP = vegetation intensity parameter; Vveg = volume occupied by vegetation for the given depth; z0 = water depth; Ah = the projected area of the vegetative element onto the horizontal plane which was calculated based on the projection diameter, Dv. The expression for the projected area is shown in Eq. (5). Vveg/z0 defines the volume occupied by vegetation for unit depth.   Vveg z0 ! VIP = 2 πDv 4

ð5Þ

where Dv = the projection diameter, which was quantified before the experiments. Dv was measured using metal wire in the shape of a circle. The diameter of the circle was fitted to the plant diameter without compressing the plant for the given water depth. The values of vegetation index parameter for the three tree saplings were VIP1 = 0.0026; VIP2 = 0.0069; VIP3 = 0. 0152 for Pinus Pinea, Thuja Orientalis, and Cupressus Macrocarpa correspond to Types 1, 2 and 3 respectively.

All the experiments were carried out in the Hydraulics Laboratory of Istanbul Technical University. The re-circulating flume is 0.5 m wide, 0.5 m deep and 18 m long. The flume has glass sidewalls and the bottom is made of concrete. Slope of the flume was 0.002 throughout the experiments. During the experiments the discharge was measured by a 90° V-notch weir located at the upstream of the flume. Smooth inlet conditions were achieved by a flow straightening system to diminish inlet turbulence. So as to measure the water level over notch more precisely by point gauge for the discharge calculations, the level measurements were carried out in the stilling reservoir which is adjacently connected to entrance tank. During the experiments, the point gauge which contacts the water surface in this stilling reservoir was checked to ensure the steady flow. In order to set the water depth a tailgate was used. The distance between the tailgate and the closest measurement point to tailgate was 4.75 m. Preliminary experiments were undertaken to ensure there was no flow effect from tailgate within the measurement region. The distance between the straightening system and the closest measurement point to straightening system was 5.6 m. Spatially dense and temporally high frequency velocity measurements were undertaken by a new generation 3D acoustic Doppler velocimeter (ADV) Vectrinos (NORTEK). Manually controllable traverse system which is able to move in three directions (i.e. longitudinal, vertical, and lateral) was constructed onto the channel for the positioning of the ADV. Nezu [22] proposed a criterion for the required sampling frequency for turbulence measurements. Based on that criterion, the sampling frequency was set as 200 Hz. The sampling number may also produce a great impact on the turbulence results as turbulence characteristics may be biased with small number of sampling. Hence the required minimum sampling number should be determined by preliminary tests and this number should be satisfied during the experiments [41–43]. In order to check the role of the sampling number on measured turbulence results, preliminary tests were performed in flume. For this purpose, the variation of variance values of time-averaged mean velocity, Reynolds stress and higher order statistical moments of turbulence (i.e. skewness and kurtosis) with respect to sampling number were examined. The records show that collection of data longer than 75 s (i.e. corresponding to 15,000 sampling number) does not influence the data quality. Based on this finding the sampling duration was set as 75 s and throughout the experiments this sampling value was satisfied. Special attention was given to provide particle rich environment in water to increase the data quality since it is a well-known fact that with the increasing particle ratio in water the data quality measured by ADV remarkably increases. In Fig. 3, the variation of correlation and signal-to-noise ratio (SNR) values belonging to a velocity records collected at the location of x = 110 cm, z/z0 = 0.90 are given. According to Nortek [23] “ideally, the correlation parameter should have the values between 70 and 100.” Nortek [23] also recommend SNR values to be consistently above 15 dB during a measurement. Based on these facts, the correlation and SNR values were also checked. Correlation and SNR values in Fig. 3 indicate that though the rough errors were not excluded yet, the particle rich environment provided clean velocity data. ADV records may contain rough errors and those should be used after adequate post processing. In this study, “correlation score threshold,” “velocity threshold” and “signal-to-noise ratio” methods were employed to exclude rough errors. Threshold values for those three methods were 80, 3, and 15 respectively. These values were chosen based on the recommendation of manufacturer company [23]. Additionally, a set of analyses was carried out in order to check whether the flow conditions in the flume for non-disturbed case satisfied — the logarithmic velocity distribution law. Velocity profiles that fitted logarithmic law displayed a constant gradient when plotted on semi-logarithmic paper [3,9,15,42]. In Fig. 4, for the experiment

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Fig. 3. The correlation and signal-to-noise ratio values belonging to velocity records collected by ADV at the location of x = 110 cm, z/z0 = 0.90.

no. 2, the non-disturbed velocity profile in semi-logarithmic form is illustrated. As it may be seen from Fig. 4, that the velocity profile for non-disturbed case was logarithmic and this confirmed that the flow conditions were suitable for the experiment. The experimental schedule is summarized in Table 1. As explained in the earlier section, two different discharges were applied to three vegetation species and the vegetation elements were emergent during the all experiments. The measurement locations were described in Fig. 5. All the velocity measurements were carried out along the centerline of the flume. As is seen from Figs. 5 and 16 velocity profiles were obtained, three of them were at the upstream and 13 of them were at the downstream of the vegetation element. Each vertical velocity profile was obtained based on 10 measurement points. The distance of closest measurement point to the channel bottom was 5 cm. The distances between 10 points were 1 cm for the three consecutive points which are closest to the flume bed and 3 cm for the others. Totally 160 point measurements were undertaken for each test condition. Due to the structural configuration of the channel no measurements were undertaken between the profiles with the abscissa value of x = 135 cm and x = 148 cm in Fig. 5. During the process of characterization of the non-disturbed and disturbed flow, velocity profiles with an abscissa value of x = 1 cm and x = 110 cm (according to coordinate system given in Fig. 5) respectively were used. The location of the plant was x = 82 cm throughout the experiments. It was appropriate to express the distance between the plant and disturbed velocity profile in terms of vegetation characteristics. The equivalent projection diameter of the vegetation to element on horizontal plane was employed for this goal. This distance approximately corresponds to one projection diameter Dv.

Fig. 4. The non-disturbed velocity profiles in semi-logarithmic form for the experiment no. 2, discharge value of 71 l/s.

In order to compare the flow and the turbulence characteristics behind the “vegetation element” and the “volumetrically equivalent rigid cylinder (VERC),” additional experiments were carried out. The equivalent rigid cylinder diameter which has the same volume occupied by Cupressus Macrocarpa under the water was calculated as 3.58 cm. Then the same experimental condition (i.e. exp. no.: 1, Q = 58.5 l/s, water depth = 28 cm) was applied to this volumetrically equivalent rigid cylinder. For the characterization of the nondisturbed and disturbed flow, the velocity profiles which had the abscissa value of x = 1 cm and x = 110 cm were taken into consideration respectively as was done for Cupressus Macrocarpa in the experiment no. 1. The velocity/turbulence measurements were undertaken only in the positions of x = 1 cm and x = 110 cm for volumetrically equivalent rigid cylinder case. 3. Experimental results and discussion 3.1. The effect of compression on flow 3.1.1. The effect of compression on mean flow retention So as to understand the effect of different forms of the vegetation (i.e. erect and compressed) on flow domain characteristics, the description of “retaining percentage” was used which is given below. Rp = 1−

Ud Uu

ð6Þ

Table 1 Summary of the experimental schedule. Exp. no.

Data name

Water depth (cm)

Discharge (l/s)

Reynolds number (-)

Specie

1

D28-Q1-T1

28

58.5

126953

2

D28-Q2-T1

28

71

152925

3

D28-Q1-T2

28

58.5

126953

4

D28-Q2-T2

28

70.5

152410

5 6 7

D28-Q1-T3 D28-Q2-T3 D28-Q2-VERC

28 28 28

58.5 71 58.5

126953 152925 126953

Cupresus Macrocarpa Cupresus Macrocarpa Thuja Orientalis Thuja Orientalis Pinus Pinea Pinus Pinea VERCa

a

Volumetrically equivalent rigid cylinder.

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Fig. 5. Coordinates of the ADV measurement points (in cm) and the vegetation in the side view (no scale for the vegetation element).

where the U are time-averaged streamwise velocities in the locations upstream (non-disturbed) (subscript u) and downstream (disturbed) (subscript d) of the vegetation element. The positive values of Rp show Uu N Ud which means that due to the presence of vegetation the downstream velocity has lower value compared to upstream velocity for a given water level. In order to understand which form of the plant (i.e. erect or compressed) has greater retaining influence on the flow field, the term “comparative retaining percentage” CRp was described (Eq. (7)) and used in the analysis of the data. CRp compares the retaining performance of two forms (i.e. erect and compressed) of the vegetation element. Positive values of CRp indicate that the erect form of the plant has greater retaining performance compared to the compressed form. h  i = CRp Rp − Rp e

c

ð7Þ

where the Rp are the retaining percentages for the forms of the plant “erect” (subscript e) and “compressed” (subscript c). In Fig. 6, the variation of CRp versus relative depth is illustrated. Unexpectedly, along the vegetation trunk the CRp has positive values except top of the vegetation elements. Especially, in the region close to the bottom, the positive values of the CRp denote that the form of “erect” has greater retaining influence on the flow domain compared to “compressed” form. In other words, even though the permeability of the vegetation decreases due to compression with the increasing velocity, the retaining performance of the vegetation diminishes. The lower retaining performance of the compressed form could be explained by the movement of the foliages under the effect of flow. Within the plant, with the movement of the foliages narrow gaps occur in the direction of flow. Due to these gaps where the water passes through, the effective flow area in vegetation increases and the flow passes through vegetation meeting with less resistance.

Fig. 6. The variations of CRp with respect to relative depth.

3.1.2. The effect of compression on Reynolds stresses In this section the effect of the different forms of the vegetation elements on the Reynolds stresses are discussed. In Figs. 7 and 8, the variations of horizontal and lateral Reynolds stress with respect to relative depth were given respectively for the “erect” and “compressed” forms of the three species at the locations of x = 110. According to Fig. 7, the differences between the horizontal Reynolds stresses belonging to erect and compressed forms of vegetation are almost identical probably due to the fact that the mean flow patterns vegetation element are not dramatically different for erect and compressed forms (Fig. 9). In Fig. 8, when the absolute values of lateral Reynolds stresses were considered it can be seen that the compression of the plant led to increase the magnitude of the lateral Reynolds stresses. Additionally, each species (herein Types 1, 2, and 3) induces a Reynolds stress with intrinsic pattern though their magnitudes are quite close to each other. In Figs. 7c and 8c, the vertical distributions of Reynolds Stresses are given for the volumetrically equivalent rigid cylinder for the comparison as well. The analysis of those data was made in Section 5 below. When comparing Figs. 7 and 8, it can be noticed that the lateral Reynolds stress values are generally slightly higher than those horizontal Reynolds Stress. This could be explained by the velocity distribution around the vegetation elements. In the vertical XZ plane (shown in Fig. 5) which is neighbor to the location of the plant (i.e. between the plant and the glass wall), the velocity values are higher due to the obstruction of the flow by the vegetation element. Hence, a strong lateral momentum transfer occurs from this plane to the plane where the vegetation is located. For a velocity profile which follows logarithmic law, Reynolds stresses −u′ w′ always take positive values. However, Fig. 7 indicates that negative Reynolds stress values are observed behind the different isolated vegetation elements. In this paragraph, the aim was to understand the negative Reynolds stresses based on the data belonging to Type 3 since only the contour plots of U was given for this species (i.e. Cupressus Macrocarpa). As seen from Fig. 9 where x = 110, the contour plots of U denote that velocity profile behind the vegetation (i.e. Cupressus Macrocarpa) did not fit the logarithmic law. In the flow field, when two different levels parallel to bed are considered it could be said that there is a mutual momentum transfer between those levels due to the fluctuation effect. According to Tennekes and Lumley [31] “a molecule coming from another reference level adjusts its momentum in the flow direction to that of its new environment.” In Fig. 9 where x = 110 and z/z0 b 0.5–0.6, at the upper level (any level closer to the water surface) the timeaveraged mean velocity value is smaller than those at the lower level (closer to the bottom). When a molecule from upper level reaches the lower level with a vertical velocity of w b 0 (herein the negative values of w denotes downward direction) it has to adjust its momentum in

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Fig. 7. The variations of horizontal Reynolds stress −u′ w′ (cm2 s− 2) with respect to relative depth z/z0 (-) at the locations of x = 110 cm for the “erect” and “compressed” forms of the three species (a) Pinus Pinea; (b) Thuja Orientalis; and (c) Cupressus Macrocarpa (E: Erect form of the plant; C: Compressed form of the plant; VERC: Volumetrically equivalent rigid cylinder).

the x direction according to its new environment. In this case, it has to absorb an amount of momentum. When a downward travelling molecule collides with another molecule at the lower level, it leads to decrease in fluctuation velocity (negative fluctuation component) at the lower level hence the −u′ w′ takes negative values. Similarly, when a molecule from lower level arrives at upper level with a vertical velocity of w N 0 it adjusts its momentum in the x direction according to its new environment. The upward travelling molecule collides with another molecule at the upper level. This increases the fluctuation velocity (positive fluctuation component) at the higher level thus −u′ w′ takes negative values again. 3.2. Patterns of mean flow and turbulence characteristics As explained in the earlier section successive velocity profiles were measured for three types of vegetation. Based on those measurements, velocity and turbulence contours were obtained in order to examine the influence of two different forms of the plant on flow pattern behind the vegetation element. The flow patterns were similar for three species. However, the variability was observed more clearly for Type 3 since the VIP value belonging to this species (Cupressus Macrocarpa) was the highest. Hence, herein only the

results belonging to Type 3 are presented due to space limitations. However, considering it might be useful, also the ranges of the values of mean flow and turbulence characteristics for all the experiments were given in Table 2. What should be noted is that the comments on the patterns presented in this section are valid for the other types as well though the magnitudes of the examined parameters were slightly different from each other. 3.2.1. Time-averaged mean velocity characteristics 3.2.1.1. Streamwise velocity. In Fig. 9, the streamwise time-averaged mean velocity contours were illustrated for the forms of the plant “erect” and “compressed” for Type 3. According to Fig. 9, the influence of the plant forms on flow pattern is not distinctive. As may be seen from Fig. 9, the presence of vegetation creates stream variability in flow domain and generates a “dead zone” behind the plant in the region close to water surface. However, interestingly the “dead zone” is not just behind the vegetation element. It is located at approximately 60 cm further downstream from the vegetation. This value corresponds to approximately 2 projection diameter of the plant on the horizontal plane. Similarly, severe “sub-canopy flow region” (velocity field with the highest values) is also not located just below

Fig. 8. The variations of lateral Reynolds stress −u′ w′ (cm2 s− 2) with respect to relative depth z/z0 (-) at the locations of x = 110 cm for the “erect” and “compressed” forms of the three species (a) Pinus Pinea; (b) Thuja Orientalis; and (c) Cupressus Macrocarpa (E: Erect form of the plant; C: Compressed form of the plant; VERC: Volumetrically equivalent rigid cylinder).

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Fig. 9. The contours of dimensionless streamwise time-averaged mean velocity (U/Umax) for the forms of the plant (a) “erect” and (b) “compressed” forms of Cupressus Macrocarpa (the location of the plant is x = 82 cm).

the plant. It is even further downstream from the vegetation. Furthermore in “erect” form the centers of the contours belonging to both “dead zone” and “sub-canopy flow zone” are slightly at further downstream. During the experiments differing from the rigid body, multiple wakes behind the vegetation element were also clearly observed. 3.2.1.2. Vertical time-averaged mean velocity. The vertical timeaveraged mean velocity, W, field behind the vegetal element was also examined for the form of erect for Type 3 (Fig. 10). In Fig. 10, positive values denote upward direction of the vertical velocity component. Fig. 10 indicates that there is a strong vertical velocity component in the direction of upward just between these two zones. The presence of two field zones (i.e. dead zone and sub-canopy flow) with different flow characteristics (i.e. different kinetic energy levels) behind the vegetation lead to momentum exchange. Also, it is seen that at just upstream of the vegetation element there is a high value downward vertical velocity component.

3.2.2. Turbulence characteristics 3.2.2.1. Normalized turbulent kinetic energy (NTKE). In this study, in addition to mean velocity characteristics, turbulence structure was also examined. In textbooks, instantaneous velocity “u” described as given in Eq. (8). Eq. (9) is used to define the violence or intensity of the turbulence. The intensity of turbulence may be influenced by the magnitude of the velocity or the external effect [i.e. presence of an obstacle in a flow field, channel form, bed roughness etc.] in an open channel. According to T'joen et al. [32] as the Reynolds number increases the flow becomes more turbulent (promoting mixture of the bulk flow with the boundary layers). Hence it is a good way to examine the ratio between turbulent kinetic energy per unit mass “k” (Eq. (10)) and time-averaged mean velocity at that measurement point “U” to understand the source of turbulence better. Hereafter this ratio is called normalized turbulent kinetic energy “NTKE” (Eq. (11)). When two values of NTKE are considered the higher one indicates obstacle induced (herein vegetation) turbulence is more dominant. ′

u=U+u Table 2 The ranges of the values belonging to mean flow and turbulence characteristics. Exp. no.

Ud (cm/s)

Wd (cm/s)

NTKE (-)

DTKE (-)

Ω (-)

1 2 3 4 5 6

3.96–50.21 0.05–58.39 0.01–41.38 4.55–50.58 − 0.01 to 44.12 2.78–52.6

− 3.77 to 5.53 − 4.95 to 8.96 − 3.02 to 1.93 − 4.63 to 0.65 − 3.15 to 2.34 − 4.44 to 2.1

0.12–0.82 0.12–0.77 0.11–0.72 0.09–0.81 0.09–0.79 0.09–0.72

0.06–0.27 0.02–0.26 0.01–0.38 0.01–0.20 0.01–0.29 0.01–0.20

0.03–0.81 0.03–0.82 0.03–0.65 0.02–0.82 0.02–0.80 0.02–0.67

σu =

k=

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi varðuÞ = u′ 2 = urms

1 2 2 2 σu + σv + σw 2

NTKE =

k0:5 U

ð8Þ ð9Þ ð10Þ

ð11Þ

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Fig. 10. The vertical time-averaged mean velocity contours for the form of “erect” of Cupressus Macrocarpa (the location of the plant is x = 82 cm).

where u = instantaneous velocity, u′ = fluctuation velocity, σ = standard deviation. In Fig. 11, the spatial variation of NTKE is presented for erect form of Type 3. As seen from Fig. 11, behind the vegetation element the values of NTKE vary in a wide range and have a clear pattern. Hence the plot is given in black and white form. The maximum NTKE values are around 50–60% and those were observed near the region of “dead zone” close to water surface where the U values are minimal behind the plant. Conversely, within the region where heavy sub-canopy flow is observed the NTKE values are relatively lower compared to “dead zone” and their values are around 15%. 3.2.2.2. Dimensionless turbulent kinetic energy (DTKE). The pattern of NTKE is analyzed above. “TKE” is divided by time-averaged mean velocity “U” and NTKE is obtained. What should be noted is that the value of “U” is different for each measurement point illustrated in Fig. 5. Hence the contour pattern of TKE (k) is not identical with k0.5/U. In order to see the contour pattern of TKE clearly in dimensionless form, “dimensionless turbulent kinetic energy ratio” DTKE is described below. 0:5

DTKE =

k Vm

ð12Þ

where Vm is the mean flow velocity which is equal to ratio of Q/A, where “Q” denotes discharge, “A” denotes wetted area. The presented DTKE values are obtained by the ratio of k0.5 to constant value of Vm (e.g. for the experiment no.: 1, the value of Vm is equal to 41.94 cm/s). Thus the contour pattern of DTKE and “k” is entirely identical to each other though their magnitudes are different. In Fig. 12, the spatial variation of DTKE is presented in the form of contour plot for erect form of Type 3. As seen from Fig. 12, the DTKE takes the minimum values behind the vegetation element. The DTKE values are slightly higher where sub-canopy flow occurs. Owing to the strong momen-

tum transfer between the region of “dead zone” and “sub-canopy flow” the DTKE values takes highest values between these two zones. 3.2.2.3. Spatial variation of TKE/MKE ratio. The description of the mean kinetic energy per unit mass is defined as K=

1 2 2 2 U +V +W 2

ð13Þ

where U, V, and W are time-averaged mean velocity of flow in the longitudinal, transverse, and vertical directions, respectively. The ratio between MKE and TKE was denoted with the notation of “Ω” as seen in Eq. (14). Ω=

TKE k = MKE K

ð14Þ

In Fig. 13, the spatial variation of “Ω” for the erect form of Cupressus Macrocarpa is illustrated. “Ω” values at the upstream of the vegetation element are around 0.02–0.04. In the region of “sub-canopy flow” this value does not change dramatically and it is around 6%. On the other hand, a sudden increment of the values belonging to “Ω” is observed at the downstream of the “dead zone.” The value of “Ω” reaches 0.70– 0.80 in this zone. This means that the significant part of the total kinetic energy is composed of turbulent kinetic energy in “dead zone.” 3.2.2.4. Turbulence intensity. Three turbulence intensity components (i.e. streamwise u′, transverse v′, vertical w′) were also examined to discuss the turbulence characteristics further. The intensities are obtained by calculating the root mean square (RMS) of the fluctuating velocities for each direction. Fig. 14 gives the contours of turbulence intensity components. As may be concluded from Fig. 14 the turbulence is non-isotropic though the turbulence intensity patterns in three directions closely resemble each other. While the magnitude

Fig. 11. The spatial variation of NTKE for the erect form of Cupressus Macrocarpa (the location of the plant is x = 82 cm).

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609

Fig. 12. The spatial variation of DTKE for erect form of Cupressus Macrocarpa (the location of the plant is x = 82 cm).

of lateral and streamwise turbulence intensities are quite close to each other, the vertical turbulence intensity is relatively lower compared to the other two components. The patterns indicate that there are two primary regions behind the vegetation element for all three directions. One region has relatively lower intensity values which are located at the upper part behind the vegetation element and this region extends and narrows towards downstream. The other region has comparatively higher intensity values which are positioned at the lower part behind the vegetal element and this region extends and expands towards downstream. 4. Theory and analysis 4.1. An empirical equation for the prediction of TKE/MKE ratio in a vegetated channel One of the primary objectives of the current study is to understand the effect of vegetation on conversion of mean kinetic energy to turbulent kinetic energy since this process plays an important role on turbulent structure where flow passes through vegetation. Given the diffusion of fluid particles depends on the degree of their kinetic energy [11], better understanding the turbulent kinetic energy will improve our ability to understand the turbulent diffusivity and dissipation rate since those parameters are function of TKE parameter. With this in mind, it was aimed to develop a formula giving the relationship between the kinetic energy components of flow (i.e. MKE and TKE) belonging to upstream and downstream of vegetation as a function of vegetation characteristics. In other words, vegetation induced turbulence was formulated as a function of plant characteristics. To do this firstly the relative energy conversion parameter “RΩ” was described as given in Eq. (15). The subscripts “u” and “d” denote “non-disturbed upstream” and “disturbed downstream” flow, respec-

tively. As stated above, during the characterization of the nondisturbed upstream and disturbed downstream flow, the velocity profiles which have the abscissa value of x = 1 cm and x = 110 cm were taken into consideration respectively. RΩ =

Ωd −1 Ωu

ð15Þ

In physical terms, RΩ makes a comparison between the parameters of Ω belonging to upstream and downstream of the vegetation element. It gives variation of Ω in terms of percentage. The positive value of RΩ indicates that Ωd N Ωu which means the TKE/MKE ratio is greater (see Eq. (14)) for the downstream of the vegetation element compared to upstream. In order to express the role of vegetation on kinetic energy budget the value of RΩ was divided by VIP for Type1, 2 and 3 respectively. In this way the influence of unit VIP on energy conversion was characterized. In the present study tree-like vegetation was classified into three different distinct types. On the other hand, in reality there are large numbers of species which have unique biomechanical and architectural characteristics. Considering this may cause difficulty for practitioners in matching the types described here, it was assumed that it would be better to define a single equation. Based on this idea, the variation of all the experimentally obtained (i.e. exp. nos.: 1 to 6) RΩ/VIP ratios were marked on the same graph (Fig. 15). Based on the data, a power curve was generated using best curve fitting method. The correlation coefficient of the curve was 0.71. The equation of the power curve is given in Eq. (16):  1 = 0:456 z R = 0:043 Ω VIP z0

Fig. 13. The spatial variation of Ω for erect form of Cupressus Macrocarpa (the location of the plant is x = 82 cm).

ð16Þ

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Fig. 14. The spatial variation of three turbulence intensity (a) u′, (b) v′, and (c) w′, for erect form of Cupressus Macrocarpa (the location of the plant is x = 82 cm).

Leaving RΩ alone on the other side of the equation:  1 z =z0 ð =0:456 Þ RΩ = VIP 0:043

ð17Þ

Substituting the expanded form of the RΩ in the Eq. (17)

Fig. 15. The variation of RΩ/VIP ratios with respect to relative depth.

 1 Ωd z =z0 ð =0:456 Þ −1 = VIP Ωu 0:043

ð18Þ

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same conclusion can be drawn for the species of Pinus Pinea based on Fig. 16a and b. In summary, though the proposed empirical equation gives acceptable results for some species (herein for Pinus Pinea and Thuja Orientalis) it may also yield underestimated values for different species. This can be explained by the biomechanical (i.e. flexural rigidity) and architectural (i.e. branching pattern, volume of plant in cubic meter, volumetric ratio between foliage and main branches, main stem diameter, leaf structure etc.) properties. For example the needle foliage structure of Pinus Pinea is extremely convenient to follow the streamlines. On the other hand the foliage structure of Thuja Orientalis is more sheet like (the third dimension of the foliage is negligibly small) and depending on the angle with flow direction the foliages may easily adapt themselves to streamlines. However, the situation is different due to the three dimensional foliage structure of Cupressus Macrocarpa. In the light of these arguments, it was assumed that it would be appropriate to insert a coefficient “Cva” into Eq. (20) to characterize the vegetation architecture. After the modification, the final form of the proposed empirical equation is obtained below.

Table 3 The summary of the experimental set-up applied by Yagci and Kabdasli [40]. Channel dimensions Measurement equipment Sampling frequency Sampling duration Methods for editing time series

26 m (length) × 0.98 m (width) × 0.85 m (depth) ADV Vectrino (Nortek) 200 Hz 60 s SNR ≥ 15 dB, Correlation score ≥ 80% Velocity threshold (clean up if Vx,y,z ≥ 3σx,y,z)

Leaving alone the parameter Ωd on the one side of the Eq. (18):

Ωd =

!  1 z= z0 ð =0:456 Þ VIP + 1 Ωu 0:043

ð19Þ

Inserting the expanded form of the Ωd and Ωu into Eq. (19):   k = K d

!   1 z =z0 ð =0:456 Þ k VIP +1 0:043 K u

611

ð20Þ

!   1   k z= z0 ð =0:456 Þ k = Cva VIP +1 0:043 K d K u

Eq. (20) gives the TKE/MKE (k/K) ratio at a certain distance (1Dv) downstream of vegetation in terms of the vegetation and nondisturbed flow characteristics. Once the vegetation and non-disturbed flow characteristics are (i.e. TKE and MKE) determined with an acceptable accuracy, the ratio of TKE/MKE belonging to certain distance downstream of the vegetation is then calculated by Eq. (20).

ð21Þ

In Fig. 16, the variation of k/K values with respect to relative depth are given for the calibrated Cva values. What should be noted is that these proposed Cva coefficients were species specific and those should be further investigated for the different hydraulic conditions as well as the scale effect. For the practical use of Eq. (21), the determination of the term (k/ K)u in Eq. (21) with an adequate precision is needed. Better understanding the magnitude of ratios “k/K” for non-disturbed upstream flow will improve the ability of practitioners to use Eq. (21). From this motivation, in Fig. 17 the statistical distribution of “k/K” was depicted based on the 60 experimental data in the format of box plot for non-disturbed upstream flow. The central mark on this box plot indicates the median value which is equal to 0.025. The edges of the box denote 25th and 75th percentiles and their values are 0.021 and 0.032 respectively. These values of box plot indicate that the ratio of k/K distributed in an extremely narrow range and the shape of box plot denotes positively skewed distribution. Upper and lower adjacent values are 0.041 and 0.016 respectively. The outliers are seen individually by the sign of “+.” Herein an outlier is described as the value which is more than 1.5 times the interquartile range away from the bottom and top of the box. It should be borne in mind that these k/ K ratios are valid for these experimental flume conditions. For any natural river these ratios may take dramatically different values.

4.2. Testing the validity of the empirical equation In order to test the validation of the introduced empirical equation, the experimental results obtained by Yagci and Kabdasli [40] in a different experimental set-up were employed. The summaries of those experimental set-up and the test conditions were given in Tables 3 and 4 respectively. Based on the proposed empirical equation (Eq. 20) the TKE/MKE (k/K) ratios at one Dv distance downstream of vegetation element were predicted. Then these predicted values were compared with the data measured by Yagci and Kabdasli [40]. The variations of predicted TKE/MKE ratios are given in Fig. 16 together with the measured data by Yagci and Kabdasli [40] for the different species. As seen from Fig. 16a and b, for the species of Pinus Pinea, the variations of the predicted percentage of “k/K” by Eq. (20) along the depth accord with those measured values. For the species Thuja Orientalis Eq. (20) resulted in an underestimation of “k/K” ratios in the areas close to the bottom and the water surface (Fig. 16c). On the other hand, for this species the “k/K” ratio values accord well with the measured values in the vicinity of the middle part of the water depth. When the predicted results are considered for the species of Cupressus Macrocarpa, it was seen that the Eq. (20) yields relatively underestimated “k/K” values for both shallow (Fig. 16d) and deep case (Fig. 16e). According to Fig. 16d and e, with the increasing water depth the difference between predicted by Eq. (20) and measured values of k/K becomes more significant for the species Cupressus Macrocarpa. Though it is not as obvious as Cupressus Macrocarpa, the

5. How much is rigid stem analogy successful in representing a real plant? The physical/numerical modelers who study on “flow-vegetation interaction” used the rigid stem analogy commonly so far. However, unless the difference between the physical events of “flow through vegetation” and “flow around rigid cylinder” are understood well, the

Table 4 The summary of the test conditions of Yagci and Kabdasli [40]. Test condition

Specie

VIP (-)

Situation of veg. under the flow condition

Water depth (cm)

Number of applied discharge for this test condition

Number of measured velocity profile for each discharge condition

C1 C2 C3 C4 C5

Pinus Pinea Pinus Pinea Thuja Orientalis Cupressus Macrocarpa Cupressus Macrocarpa

0.0040 0.0032 0.0041 0.0049 0.0048

Emerged Emerged Emerged Emerged Emerged

25 40 25 25 40

5 4 3 4 4

15 15 10 17 17

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Fig. 16. The variations of predicted and measured TKE/MKE ratios with respect to relative depth according to Table 3. (a) Case 1, (b) case 2, (c) case 3, (d) case 4, and (e) case 5.

obtained results are disputable. In this section, it was aimed to compare flow structures behind the obstructive elements, i.e. vegetation and rigid stem. In this context, the parameters Rp and RΩ emerged as important parameters in achieving this objective. The

Fig. 17. The box plot graph of the ratio “k/K” belonging to non-disturbed upstream flow 25%–75% (0.021 , 0.032); min–max (0.016, 0.061); number of outliers: 2.

descriptions of the Rp and RΩ are given above. Briefly, the parameter Rp was utilized in the characterization of retaining performance of the obstructive element (i.e. vegetation or rigid stem) comparatively. Similarly, the parameter RΩ was employed in the quantifying of conversion of mean kinetic energy to turbulent kinetic energy due to obstructive element. In physical terms, the positive elevated value of Rp indicates higher retaining impact of the obstacle (i.e. herein the plant or the cylinder) on the flow field. On the basis of the definition of Rp, lower velocity values are expected at the downstream of the obstacle where the retaining percentage, Rp, is higher. In Fig. 18a the variation of retaining percentage, Rp, with respect to relative depth for the plant and the volumetrically equivalent rigid cylinder is presented. According to Fig. 18a, equivalent cylinder resulted in an underestimation of the retaining effect where z/z0 ≥ 0.46, hence overestimation of velocity values. When two RΩ values are taken into consideration, comparatively

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613

Fig. 18. The variation of (a) Rp and (b) RΩ values with respect to relative depth for the plant (Cupressus Macrocarpa) and the volumetrically equivalent rigid cylinder (the flow conditions in flume: Q = 58.5 l/s, water depth = 28 cm).

higher value of RΩ denotes the obstacle induced turbulence is higher at the downstream of that obstructive element. According to Fig 18b, rigid equivalent cylinder generates significantly more turbulence compared to real plant along the depth except the region where z/z0 ≥ 0.84. The distribution of Rp and RΩ is solely a result of the plant morphology. In nature, riparian woodland trees have a characteristic shape. They have significantly lower density close to the bed [1,19,37,38], which causes the water to flow under the plant instead of through it. Hence, though the values of the Rp and RΩ along the depth may vary depending on the species, but the distribution of these two parameters along the depth kept its characteristic form. In Figs. 7c and 8c, the vertical distributions of horizontal and lateral Reynolds stresses behind the volumetrically equivalent rigid cylinder (VERC) are presented for the comparison. As may be seen from Figs. 7c and 8c, the magnitudes of both horizontal and lateral Reynolds stress behind the VERC are considerably lower than those for the real plant. The lower values of horizontal Reynolds stress can be explained by the unvarying velocity distribution in most of the depth behind the rigid cylinder (Fig. 18a). More specifically, for VERC case mean velocity differences between the layers are not as significant as real plant, In other words, (∂U/∂(z/z0)) does not have variable character along the depth for VERC compared to real vegetation. For this reason the vertical momentum transfers between the layers are relatively weaker in VERC case. Due to the weaker momentum transfer the horizontal Reynolds stresses take lower values. Also, the values of both horizontal and lateral Reynolds stresses behind the VERC are positive differing from the natural vegetative element. When the magnitudes of horizontal and lateral Reynolds stress are compared it may be stated that the lateral Reynolds stress is higher than horizontal one. 6. Conclusions Laboratory experiments were undertaken to explore the effect of different forms of single natural emergent vegetation elements on turbulence and kinetic energy characteristics. The following conclusions were drawn based on the experimental data. The vegetation form of “erect” unexpectedly exhibited more retaining influence over time-averaged mean velocity compared to “compressed” form. This may be explained by the streamlining effect. When the foliages of the plant adapt streamlines of the flow effective area for the water passing through vegetation increases. For both forms of the plant, the velocity profile behind the vegetation element no longer follows a logarithmic law. The data also revealed that

Reynolds stresses are not dramatically different from each other for the forms of “erect” and “compressed.” It was also seen that the variations of Reynolds stress with respect to relative depth for each considered species (i.e. Pinus Pinea, Thuja Orientalis, and Cupressus Macrocarpa) has unique profile though their magnitudes are close to each other . Based on the experimental data the flow and turbulence patterns behind the vegetation element were determined for the erect form of “Type 3.” Similar patterns were acquired for the other types (i.e. Types 1 and 2) although their magnitudes are slightly different from each other. The flow patterns indicated that there are two major zones at the upstream of vegetation. Those are “dead zone” and “sub-canopy flow zone.” The highest vertical velocity component is observed between these two zones in the upward direction, due to the strong momentum transfer. Also relatively elevated vertical velocity values were recorded at just downstream of the vegetation element and where it goes downwards. The NTKE pattern behind the vegetation element showed that the values of NTKE vary in a wide range and their values are around 50– 60% and 15% for “dead zone” and “sub-canopy flow zone” respectively. The highest DTKE ratios were located just between “dead zone” and “sub-canopy flow zone” because of the heavy momentum transfer. The TKE/MKE ratios are around 0.04–0.08 just behind the vegetation and the maximum TKE/MKE ratios were seen at the slightly further downstream of the “dead zone.” Based on the experimental data, an empirical equation was derived. The equation gives the ratios of “TKE/MKE” at a certain distance downstream of vegetation element in terms of vegetation characteristics. The validity of the proposed model was checked by a different data set. It was seen that the proposed empirical equation gives reasonable results. However, the coefficient of vegetation architecture in empirical equation should be investigated further for the other species. The experimental findings revealed that the rigid cylinder analogy resulted in overestimation of velocity where z/z0 ≥ 0.46 and underestimation of velocity where z/z0 ≤ 0.46. Also, the data indicated that rigid cylinder generates dramatically extra turbulence compared to real plant along the depth except the region where z/z0 ≥ 0.84. In experimental and numerical studies the rigid stem analogy was practiced by many researchers in the representation of vegetation community so far. It is hoped that this study will adequately stress the differences between the physical events of “flow through vegetation” and “flow around rigid cylinder.”

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