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Investigation of turbulence characteristics in channel with dense vegetation
International Journal of Sediment Research 26 (2011) 269-282
Investigation of turbulence characteristics in channel with dense vegetation Hossein AFZALIMEHR1, Razieh MOGHBEL2, Jacques GALLICHAND3, and Jueyi SUI4
Abstract In this experimental study, the turbulent flow in a channel with vegetation by using sprouts of wheat on channel bed was investigated. Two different aspect ratios of channel were used. An Acoustic Doppler Velocimetry was used to measure parameters of turbulent flow over submerged sprouts of wheat, such as velocity profiles. The log law and the Reynolds shear stress distribution were applied. Results indicate that the position of the maximum turbulence intensity superposes on the inflection point situated over the top of submerged vegetation cover. Quadrant analysis shows that near the vegetation bed, the sweeps and ejections appear to be the most dominant phenomenon, while far from the vegetated bed, the outward is dominant event. Results also show that the aspect ratio plays an important role on the contribution of the different bursting events for Reynolds stress determination. Key Words: Bed vegetation, Aspect ratio, Reynolds stress, Quadrant analysis
1 Introduction Water flows in aquatic systems are rarely free of vegetative effects. Vegetation exerts a strong influence on stream-channel morphology. Based on research work in a lowland stream, Champion and Tanner (2000) pointed out that, under condition of the same water depth, flow discharge was about seven times bigger during the period of unvegetated season. Also, vegetation over the bed or channel surroundings exercises a dominant influence on capturing suspended load, production of oxygen and improvement of water quality. However, the structure of flows in channels with vegetated bed has not been well investigated, although its considerable effect of vegetation on river management, restoration, prevention of erosion and riverbank stability. In the United States, to limit the impacts of channel instability on the degradation of aquatic life habitat and water quality, one billion dollars was spent annually from 1990 to 2003 (Bernhardt et al., 2005). Up to date, studies regarding flows in vegetated channels have focused on velocity profiles, validity of the log law and turbulent characteristics (Afzalimehr and Dey, 2009; Afzalimehr et al., 2010; Guo and Julien, 2008; Guo and Julien, 2001; Jarvela, 2004; Kummu, 2002; López and García, 2001; Naot et al., 1996; Nepf, 1999; Shimizu and Tsujimoto, 1994; Stephan and Gutknecht, 2002). In the last couple of years, researchers has paid a lot of attentions to identify the coherent structures in turbulent flows over vegetated streams, due to the role played by these structures in mass and energy exchange (Yue et al., 2007). A conditional sampling and averaging technique was introduced by Wallace et al. (1972) and Willmarth and Lu (1972) to quantify the contribution to the Reynolds shear stress during the cycle of events observed in the bed region of the turbulent boundary layer. Conditional sampling techniques constitute suitable tools for identifying specific flow features that can be extracted from experimental data 1
Assoc. Prof., 2 Graduate student, Water Engineering Department, Isfahan University of Technology, Iran 84156 Prof., Département des sols et de génie agroalimentaire, Université Laval, St-Foy, QC, Canada 4 Assoc. Prof., Environmental Engineering Program, University of Northern British Columbia, Prince George, BC, Canada, V2N 4V9, E-mail: [email protected] Note: The original manuscript of this paper was received in Nov. 2010. The revised version was received in April 2011. Discussion open until Sept. 2012. 3
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(Yue et al., 2007). This technique expresses the contributions of u'w' into each quadrant of the u'- w' plane where u' and w' are the instantaneous velocities in stream-wise and vertical directions respectively. The quadrant analysis was employed to determine the frequency of occurrence of each individual event within a bursting process, i.e. outward interactions, ejections, inward interactions, and sweeps. For example, based on experimental studies, Poggi et al. (2004) and Gisalberti and Nepf (2006) found that sweeps dominate ejection within the canopy and a reversed relationship exists above the canopy. The results can be used to identify the effect of submerged vegetation and aspect ratio on the mean flow field. The quadrant analysis has not only been used to smooth bed turbulent boundary layers, but also it has been used for turbulent flows of different canopies, such as wheat (Finnigan, 1979) and corn (Shaw et al., 1983). Although quadrant analysis is traditionally performed for conditional sampling of the Reynolds shear stress and turbulent heat flux, Poggi et al. (2004); and Ghisalberti and Nepf (2006) and Zhu et al. (2007) extended the technique to include more general properties of turbulence in plant canopy flows, such as turbulent kinetic energy, vorticity, and dissipation rate. The methodology presented in this paper provides a combined analysis of the time average flow characteristics, i.e. mean velocity profiles and Reynolds shear stress components, with bursting process characteristics. The bursting process encompasses the complete sequence of outward, ejection, inward and sweep motions, and the frequency of occurrence of these events within that cycle over a vegetated cover. Kim et al. (1971) revealed that turbulent energy and Reynolds stress were generated by bursting motions, especially, ejections and sweeps. Approaches without considering frequency of occurrence and magnitude of turbulence structures appear rather incomplete (Jain, 1992; Papanicolaou et al., 2001). Lu and Willmarth (1973) introduced the quadrant analysis for studying the structure of the bursting phenomenon, and subsequent studies of others used it for interpreting the turbulence generated by fluvial bed forms (Papanicolaou et al., 2001; Mianaei and Keshavarzi, 2008; Mianaei and Keshavarzi, 2010). Sukhodolov and Sukhodolova (2010) carried out research in natural streams and claimed that “the theories advanced by laboratory studies and accomplished through systematic case studies on different plant species under different hydraulic conditions can clarify many practically important problems”. It is therefore important to understand the impact of vegetation on flow structure, including velocity and Reynolds stress distributions. Additionally, a better understanding of the interaction of flow and vegetation will help us to better understand sediment transport, and resistance to flow (Afzalimehr et al., 2010; Jarvela, 2002; Yagci and Kabdasli, 2008). In spite of effects of vegetation on ecological function of aquatic systems, the structure of densely vegetated aquatic flows has not been well studied. Also, no research work has been reported regarding the turbulence effect resulted from a dense-vegetated bed in a shear flow. In this study, the effects of submerged vegetation on turbulent flow characteristics are studied by analyzing the velocity fluctuation components (u'-w') and the quadrant analysis. The main objective is to determine the contribution of each quadrant to the Reynolds shear stress and to compute the dominant event of turbulent structure of flow in channels with densely submerged vegetation over bed for two different aspect ratios. 2 Experimental set-up Experiments were conducted in a 20-m long, 0.6-m wide and 0.6-m deep flume with glass walls. To control uniformity of flow during each experiment (or run), a limnimeter (a type of gages for measuring water levels) with an accuracy of ±1 mm was used to record the depth of water over the vegetation cover along the flume. A movable downstream weir was used to maintain uniform flow over the vegetation canopy. Graf and Altinakar (1998) pointed out that an aspect ratio of W/h=5 (W = the channel width, and h = the flow depth) is the critical value for studying flow structure in open channels. Accordingly, our experiments have been conducted in two runs with different aspect ratios: an aspect ratio of W/h=5.4 for run 1, and an aspect ratio of W/h=4 for run 2. These experimental runs have been carried out in the above mentioned flume with submerged vegetation on channel bed. The slope of the flume bed has been set to 0.5%. An electromagnetic current meter with accuracy of 3×10-4 m3/s has been used to measure discharge. Flow discharges have been selected from 0.037 m3/s to 0.055 m3/s, based on available flow discharges at the hydraulic laboratory. To obtain an aspect ratio of 5.4 for runs 1 and an aspect ratio of 4 for run 2 respectively, the water depth (h) has been 110 mm for run 1 and 150 mm for run 2 respectively. - 270 -
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Velocity measurements have been performed by using an Acoustic Doppler velocimetry (ADV). The ADV is a 10MHz Nortek Vectrino with a downward-looking probe and precision of ±0.1 mm/s. ADV signals are affected by Doppler noise, or white noise, associated with the measurement process. To remove possible aliasing effects, velocity time series have been analyzed using WinADV (Wahl, 2000), which is a windows based viewing and post-processing utility for ADV files. This software provides signal quality information in the form of a correlation coefficient (COR) and signal to noise ratio (SNR). Moreover, it has filters, such as phase-space threshold despiking and acceleration spike filter. The manufacturer suggests that when correlation coefficient does not exceed 70%, and signal to noise ratio (SNR) is less than 5 dB, the instantaneous velocity measurement is dominated by acoustic noise and, as a rule of thumb, these measurements should be discarded. To remove noise effects in this study, the data with SNR smaller than 5 dB and COR of 70% have been discarded and the velocity time series data has been passed through phase-space threshold despiking and acceleration spike filters. Almost 75% data have been considered suitable using WinADV criteria Corr>90% and SNR>20. The data of the poor quality have been easily removed from this study and have not been replaced. At each point, the flow velocity has been sampled with frequency of 200 Hz and for 120 s (experience reveals this duration for sampling is adequate for determining accurate turbulence statistics), with the lowest point for velocity measurements in each profile being 3 mm above the bed. Velocity measurements have been made along three cross sections at x=12.9 m, 13.5m and 14 m downstream of the flume entrance. At each cross section, velocity measurements have been made at different transverse-wise distances from the flume bank (D=5 cm, 12 cm and 30 cm). For each velocity profile, about 17 measurements of point-velocity have been obtained; and 7 out of these measurements of point-velocity are in the flow zone near the flume bed at a depth of Z/h <0.2 (where Z = the vertical distance from the measuring point to the top of the vegetation cover; and h = the total flow depth). Table 1 shows the hydraulic characteristics of laboratory experiments and a summary of experimental data for this study. Table 1
Hydraulic characteristics of laboratory experiments Vegetation over bed Run No. uave (m/s) h (mm) Zp (mm) Q (m3/s) 1 0.56 110 138 0.037 2 0.60 150 136 0.055 h: Water depth above the vegetation; ZP: Deflected plant height; H = h + ZP; W: channel width
W/h 5.4 4
H/Zp 1.79 2.1
There are two ways to investigate the effect of vegetation on flow structure: the first approach is the application of artificial material such as rigid and cylindrical roughness (Nepf, 1999) and the other one is to use natural vegetation directly (Sukhodolov and Sukhodolova, 2010). As reported by Maltese et al. (2007), wheat sprouts have been widely used vegetation in experimental studies. Wheat sprouts have been used in coastal engineering to protect shorelines from erosion by attenuating waves and currents, and in agricultural engineering by trapping organic and mineral particles. Thus, in our study, sprouts of wheat have been planted on flume bed along a 3-m long section. The vegetated section of flume is from x=11.5 m to 14.5 m downstream of the flume entrance, as shown in Fig. 1(a). The rest of the flume bed has been covered with gravel which has a median grain size of d50=21 mm and a standard deviation of 1.3 mm. The wheat planted over the channel bed has been long and flexible enough to result in wavy motions. The deflected plant height is 138 mm for run 1 and 136 mm for run 2 respectively. The height of submerged wheat has been kept the same during each experimental runs. The planting density of the wheat sprout has been 45,604 stems per square meter and has been longitudinally uniform over the vegetated flume section. All experiments have been carried out when water was flowing in the flume and the dense vegetation has been deflected, as shown in Fig. 1(b). Under each experimental run, no changes in the deflection height over time have been observed and the locations of h and Zp have been kept constant as indicated by Fig. 1(b). In addition, during experiment, no wheat has been detached from the channel bed which may result in water contamination. Measurements have been conducted whenever the difference in water depth between two sections of vegetated channel bed was less than 1 mm. Similar to the experimental studies of several researchers, such as Stephan and Gutkhecht (2002), Carollo et al. (2002) and Carolla et al. (2005), the vegetated International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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channel bed in our study has been also 3 m long. It is important to note that, no fundamental theory regarding the onset of fully developed flow conditions in vegetated channels has been reported. The best proof for existence of a fully developed flow is the similarity of velocity profiles at different cross sections from the starting point of bed vegetation in flume, as shown in Fig. 2. Figure 2 shows that the velocity profiles at different cross sections are similar. Very small differences in the velocity profiles should be attributed to the limitations of ADV to measure data in some height above the vegetation bed.
Fig. 1(a) View of vegetation over channel bed
Fig. 1(b)
A definition sketch of variables
As pointed out by Dey and Nath (2010), the bursting phenomenon are usually quantified by the conditional statistics of the velocity fluctuations (u' and w'). In this study, the quadrant analysis has been used to investigate the effect of the submerged vegetation over bed on sweep, ejection, outward and inward motions. Under the condition of the same mean flow properties, both the type and arrangement of vegetation on channel bed can play an important role on the turbulence structure (Strom and Papanicolaou, 2007). In the quadrant analysis, there are four quadrants (i = 1 to 4) in the u'-w' plane. Here, 1) i=1 represents outward motion (u'>0 and w'>0), 2); i=2 represents ejection (u'<0 and w'>0); 3) i=3 represents inward motion (u'<0 and w'<0); and 4) i=4 represents sweep (u'>0 and w'<0). The value of –u'w' < 0 corresponds to a positive Reynolds stress, whereas –u'w' > 0 represents the negative Reynolds stress. As suggested by Dey and Nath (2010), to differentiate the larger contributions to u ' w ' from each quadrant leaving the smaller u' and w' corresponding to more quiescent periods, a hole size parameter (threshold level) H is introduced in this study. In fact, the contribution of each quadrant to the Reynolds shear stress as a function of the threshold level of the hyperbolic hole region, H, has been defined as follows (Jian et al., 2009): - 272 -
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u ' w'
i, H
limt of
1 T
³0 u ' t w' t G i, H u ', w' dt T
(1)
where, T is time interval and įi,H is detection function.
Fig. 2 Verification of fully developed flow (run 1). Velocity profile at cross sections of 12.9m, 13.5m and 14 m from the entrance of the channel °1
when u ' w' t H u ' w'
°¯0
otherwise
G i , H u ' , w' ®
(2)
The fractional contribution Si,H to u ' w ' from each event is Si , H
u ' w'
i, H
u ' w'
(3)
Here, Si,H>0 is for the first and the third quadrant, and Si,H<0 is for the second and the forth quadrant. For analysis of the bursting phenomenon and for determination of the contribution of each quadrant to the Reynolds shear stress, a computer program was written in MATLAB. 3 Results 3.1 Velocity distributions Although the flow is fully developed over the gravel bed from the flume entrance along the flume section to x=11.5m (distance from the flume entrance), the change of bed roughness from gravel bed to the vegetated bed planted by wheat stems causes a new boundary layer development. Application of the empirical relations of turbulent boundary layer theory showed that the expected length of boundary layer development following a roughness transition to a vegetated bed is less than 11.5m. Therefore, along the section for velocity measurements (from x=12.9m to x=14m from the entrance), flow velocity profiles are self-similar (as shown in Fig. 2) and the flows are fully developed. Accordingly, the results at cross section x= 12.9m will be discussed in this study. Since the velocity measured by ADV within the vegetation cover shows considerable noise, measurements of flow velocity have been only conducted above the vegetation cover. Also, the ADV used in this experimental study cannot be used to measure velocity at a depth of Z/h 0.75 as Fig. 3 indicates. Therefore, a dip phenomenon has not been noticed for a water depth of 0 < Z/h 0.75. When an aspect ratio of flow is W/h5, dips in velocity profiles have been observed over smooth beds by Nezu et al. (1989) and over rough beds by Kironoto and Graf (1994), respectively. In this experimental study, when the aspect ratio of flow is W/h=5.4 (run 1), no dips in velocity profiles have been noticed, no matter where measurements for velocity profiles have been conducted (i.e., different distance from flume wall, D=5 cm, 12 cm and 30 cm). When the aspect ratio of flow is W/h=4 (run 2), even though no dips in velocity profiles have been noticed, a secondary current effect is noticeable. This obervation will be discussed in section 3.2. International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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Fig. 3
Velocity profiles of run 1-2 in channel with vegetation over bed (D=distance from the flume wall)
As claimed by Nezu and Nakagawa (1993), the occurrence of secondary currents has been mainly resulted from the anisotropy between v' (transversal velocity fluctuation component) and w' (vertical velocity fluctuation component). Such anisotropy of turbulence has been caused by a development of the complex boundary conditions at flume walls, flume bed, and the free water surface. Indeed, the secondary currents in a straight flume with fixed bed are developed as a result of the cross sectional non-homogenity of turbulence. For the case of an aspect ratio of W/h< 5, vortices are initiated at first at the corners due to existence of sidewalls and extended and then mixed in the lateral direction. For the case an aspect ratio of W/h >5, the vortices could be damped fast, while getting away from the sidewalls. Graf and Altinakar (1998) have pointed out that secondary currents cause the dip phenomenon of velocity profiles. They showed that for an aspect ratio of W/h>5, the maximum flow velocity (umax) occurs at the water surface and the influence of the secondary currents could be negligible; while for an aspect ratio of W/h<5, the effect of the secondary currents is important and umax occurs under the water surface. Secondary currents are responsible for the transport of fluids with low momentum from the near-wall zone to the corner, and the transport of fluids with high momentum from the free surface toward the channel bed. The boundary shear stress increases whenever the secondary currents flow toward the bank. On the other side, a smaller boundary shear stress appears whenever the secondary currents flow away from the bank. As shown in Fig. 4, the characteristics of the secondary currents have been affected by the magnitude of the aspect ratio (W/h=5.4 for run 1, and W/h=4 for run 2). From Fig. 4, one can also see the secondary currents 2
2
vectors, and ( v w ) . Interestingly, for run 2 (W/h = 4), the secondary current vectors have a tendency of clockwise circulation from the flume wall to the center of the flume. However, such a phenomenon has not been observed in run1 (W/h =5.4).
Fig. 4
2
2
Secondary flow velocity vectors ( v w ) in the left side of channel for both runs 1 and 2
Our findings are not identical to those of Huai et al. (2009), as shown in Fig. 4. Huai et al. (2009) carried out experimental study under condition of uniform flow over a vegetated channel bed. Their vegetated channel bed has been made of stiff and artificial vegetation cover. They found that the secondary currents cannot be created when the aspect ratio W/h is less than 5. The different types of vegetation used in the study of Huai et al. (2009) from that in our experiment may be responsible for different results. Carollo et al. (2002) observed an inflection point in velocity profile which is superposed on the maximum turbulence intensity. Nepf and Vivono (2000) declared that this superposition occurs at the top of the vegetation cover. Figure 5 shows that the turbulence intensity decreases after reaching its maximum - 274 -
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value. For dense vegetation on channel bed, the inflection point has been observed near the top of the vegetation, causing the generation of large coherent vortices via the Kelvin-Helmholtz instability, as also considered in free shear layer. These coherent vortices govern the momentum exchange between the vegetation cover and the overlying fluid. For submerged vegetation, the penetration of turbulence and momentum from the overflow plays an important role in the function of vegetation. Jarvela (2005) indicated that, based on experimental study by using a dense vegetation cover (12,000 stems/m2), the location of maximum turbulence intensity has been located above the deflected vegetation. In our experimental study, the vegetation density is larger than that of Jarvela (2005), expecting that the location maximum turbulence intensity occurs above the deflected vegetation (Z/h| 0.5).
Fig. 5
Turbulence intensity observed for runs 1 and 2
Song et al. (1994) had studied the flow over a gravel-bed channel with the flume width (W=0.6 m), bed slope 0.5%, flow discharge of 31 L/s to 60 L/s under subcritical and turbulent flow conditions. They showed that near the water surface, the velocity distribution approaches to vertical line for a range of an aspect ratio from 3.2 to 6.4, while Fig. 3 reveals that it moves far away from the vertical line, especially for an aspect ratio of W/h=4. In fully developed open channel flow, velocity profile can be discussed on the basis of the universal log law: u u*
1
N
ln
z C ks
(4)
where, u = mean point velocity, u* = shear velocity, z= the vertical coordinate, N = the von Karman constant, ks = roughness scale and C = constant. To describe velocity profile for flow over bed with submerged vegetation, Stephan and Gutknecht (2002) proposed a logarithmic law, with C =8.5 and N = 0.4, and which is used in our study: u u*
1
N
ln
z ZP 8. 5 ZP
(5)
where, ZP = the thickness of vegetation cover. Kummu (2002) pointed out that the vertical velocity profile above vegetated beds has logarithmical distribution only in its middle part of the velocity profile. However, Fig. 6 confirms the validity of the log law for the inner layer near the bed vegetation cover. The reason for the log-law deviation in the outer layer (Z/h>0.2) is invalidity of constant shear stress in whole flow depth and invalidity of mixing length approximation. It should be noted that the log law only approximately represents the experimental data (Barenblatt, 1982) as Fig. 6 shows for the near the bed data. 3.2 Reynolds shear stress The vertical Reynolds stress ( u ' w ' ) induces longitudinal and vertical momentum exchange as well as vertical mixing (Velasco et al., 2003). Investigations show that the Reynolds stress distribution in all channel flows is nonlinear. The linearity occurs only for low depths above the peak as stress decays from its maximum near the boundary (bed or top of vegetation) to the free surface (Nepf and Vivoni, 2000; Velasco et al., 2003 and Huai et al., 2009). Figure 7 shows that the Reynolds stress distribution is non linear, and it does decay in both experimental runs near the water surface. However, the decay phenomenon for W/h =4 is more pronounced than that for W/h=5.4 due to effects of aspect ratio and International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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stronger secondary currents. The turbulence intensity distributions in Fig. 5 further indicate the stronger decay phenomenon of W/h=4 in comparison to W/h =5.4. Furthermore, for run 2 (W/h = 4), the maximum Reynolds stress occurs above the top of vegetation at a water depth of Z/h=0.5 and reaches zero below the free surface. Accordingly, there should be a negative Reynolds stress distribution above the zero-Reynolds stress. This generates the dip phenomenon in velocity profiles because a zero-Reynolds stress corresponds to a zero-velocity gradient or the maximum velocity (Yang et al., 2006). In this study, the location of the zero-Reynolds stress coincides with the location of the last measured point. The location of dip or the maximum velocity is associated to zero shear stress location. Figure 7 reveals a strong reduction of Reynolds stress toward the water surface for the case of an aspect ratio of W/h =4, while such a tendency has not been observed for W/h =5.4. It should be noted that no measurements have been conducted within the vegetation due to very high noise in ADV data in this zone. Therefore, no velocity deflection point has been observed near the vegetated bed.
Fig. 6 Logarithmic profiles fit for flow above vegetation for different distance from the wall (D) in runs 1 and 2
The spatial inhomogeneities of Reynolds stress produce an orderly (rather than chaotic) flow pattern which is perpendicular to the main channel flow. Rectilinear turbulent flow is an instability process with the turbulent intensity being deriving force and that the transition from the rectilinear flow to instability takes place via a marginal state, exhibiting a stationary pattern of motion, i.e., at the onset of instability a stationary pattern of motions prevails (cellular secondary currents). If Reynolds shear stress can be well predicted, then the location of maximum velocity could be found from the location of zero shear stress. Therefore, if zero shear stress occurs under the water surface, the maximum velocity will occur under the water surface as well. Thus, the distribution Reynolds stress provides a suitable knowledge of understanding for maximum velocity location. Yang et al. (2006) found that nonzero bed-normal velocity was responsible for dip phenomenon in uniform flow. Figure 7 does not show a clear tendency of Reynolds stress toward the water surface for an aspect ratio of W/h =5.4, but it clearly shows a strong decay phenomenon for an aspect ratio of W/h=4. The maximum Reynolds stress approaches zero at approximately similar flow depth for different distance from the vertical walls for an aspect ratio of W/h =4. In this experimental study, each square meter of channel bed has been densely planted 45,604 wheat stems. Additionally, wheat used in our work was so dense that there was little interaction between the flow above the vegetation and the water within the vegetation, as if the vegetation has been acted as an - 276 -
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almost impermeable bed roughness of matted stems. As a consequent, this vegetation cover creates a layer of fluid above the vegetation. This layer of fluid prevents the momentum exchange and shear interaction between the inside and the outside of the vegetation cover. The drag of this layer produces additional turbulence which moves the location of maximum turbulence stress farther away from the vegetation cover. This finding is in agreement with result of Jarvela (2005) who also used wheat stems to form bed vegetation with a planting density of 12,000 stems/m2. They claimed that the maximum Reynolds stress occurs just above the top of the flexible vegetation cover.
Fig. 7 Profiles of Reynolds stress in X-Z plane ( u 'w' ) for runs 1 and 2
For uniform flow over a gravel-bed channel, Song et al. (1994) found that the distribution of u' has a weakly concave form which has been assumed linear. However, Fig. 5 reveals a convex form turbulent intensity (u') for this study. Also, according to Song et al. (1994), the maximum value of u' and u 'w' appears at the bed and minimum value of u' and u 'w' occurs at the water surface. However, for uniform flow over a vegetated-bed, as shown in Figs. 5 and 7, they occur at Z/h | 0.5. 3.3 Quadrant analysis Determination of the threshold level H is more or less arbitrary; stationary values of conditionally averaged patterns against the variation of H have not been ascertained. Indeed, the selection of an appropriate threshold parameter H has been the source of considerable ambiguity and inconsistency within published work (Papanicolaou and Hilldale, 2002). Lu and Willmarth (1973) assumed that the threshold level H of ejection ranges from 4 to 4.5. Beyond this level, the contributions of sweeps to Reynolds stress almost disappear. Also, H of sweeps ranges from 2.25 to 2.75, and beyond this level, the contribution of the interactions almost disappears. An objective selection of the threshold level is not simple. Comte-Bellot et al. (1979) carried out an extensive study on the effect of H during period between ejections and sweeps, the intermittency factor Sj and contribution of -u'w' from different quadrants. They suggested that an appropriate choice of H for events in a particular quadrant may simply be used on the percentage contribution for -u'w' from that quadrant. However, near the vegetation cover over the bed, since turbulence is generated in ejections and sweeps, the contributions of both events at H=0 are significant, especially for the sweep motion (u'>0, w'<0) which plays an important role on transferring energy toward the bed. Maltese et al. (2007) reported an ejection-dominated upper layer of the plant canopy and a sweep-dominated region around the top of the canopy with relatively fast flow (mean velocity of 5.5 cm/s). They found that in slower flow (mean velocity of 1.7 cm/ s), the plants have been quasi emergent and sweeps similarly dominated the region near the top of the canopy. Yue et al. (2007) found that significant fractions of the vertical momentum flux have been transported at high values of the International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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hole size, indicating that much of the momentum flux has been transported during periods of strong turbulent events occupying in a small fraction of time. Nezu and Nakagawa (1993) indicated that if the turbulent boundary layer is in equilibrium condition, the magnitudes of ejection and sweep motion behave in similar ways. As a consequent, their contributions are constant and irrespective of the Reynolds number. Different hole sizes (H) have been considered here including H=0, 1, 2, 3. However, H= 0 will be taken into account for further discussion in this study because it does not eliminate any value of Reynolds stress in four quadrants. Figure 8 shows the dominant turbulent event at each point over the entire flow depth at the central axis of the flume. For H=0, two zones can be distinguished over the total flow depth: the first zone has a water depth of 0
Fig. 8 Percentage of velocity fluctuation components (u' and w') from each quadrant (i=1, 2, 3 and 4) over the vertical – run 2 in center line of the channel
Figure 8 displays different trends for sweep events in H=0. However, the change of H from 0 to 3 illustrates that all events have nearly the similar trend over the entire flow depth. Moreover, an increase in the hole size causes that ejection becomes the dominant event. Accordingly, over the entire flow depth, -u'w' is negative in both quadrant 4 (sweep) and quadrant 2 (ejection). Therefore, Reynolds stress u ' w ' is positive in both quadrant 4 (sweep) and quadrant 2 (ejection), as one can see from Fig. 7. Figure 9 shows four turbulent events in four quadrants (outward interactions, ejections, inward interactions, and sweeps) that characterize the individual turbulent velocity measurements for two points at water depths of Z/h=0.29 and Z/h=0.49 respectively with H=0 at the central axis of flume. The joint frequency distribution shows that a negative correlation is associated with the boundary shear stress at the measuring point and the tilting of the joint frequency distribution into quadrants 2 and 4. Papanicolaou et al. (2001) reported no pronounced peaks or any preferential tilting toward one of the four quadrant and is rather systematic with respect to the origin, of the u'- w' plan. Typical trend for smooth boundaries (as defined by Nezu and Nakagawa, 1993) is the titling of the distribution into quadrant 2 and 4 (Papanicolaou et al., 2001). According to Papanicolaou et al. (2001) the rounder shape of the distribution, the lower packing density case is indicative of flow non-uniformity in higher packing densities the sweep and ejection are the most dominant events. The multi-peak pdf’s in Fig. 9 may be indicative of the higher vegetation density. Kaftori et al. (1998) reported that the importance of the ejection and sweep quadrants diminishes as the roughness increases, while the contribution of the outward and inward quadrants to the Reynolds stress - 278 -
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becomes more significant. Near the upper part of the vegetation layer, sweep is the most frequent event (longest time fraction) while ejection contributes most to the vertical momentum flux (largest fraction). The outward and inward events have the shortest time fraction and the smallest values of the shear stress, especially at the upper part of the vegetation layer. It means that the momentum transfer between the flow and the upper vegetation layer is mostly carried by sweep and ejection events. Using the quadrant analysis, McBride et al. (2007) claimed that, for riparian vegetation along the bank, quadrant 1 (outward) events were predominant in frequency and had a greater mean Reynolds shear stress than quadrants 2 (ejection) or 4 (sweep). On the other hand, Bennett and Best (1995) indicated through measurements over sand dunes that outward interaction events are restricted to the near bed zone. However, results of their study shows that outward and inward events have important effect on Reynolds stress in the zone far away from the vegetation bed (Z/h > 0.5).
Fig. 9 Joint probability distributions of u'/u* and w'/u* at points with Z/h= 0.29 (b) and Z/h=0.49 (a) in run 2 in the center line of the channel (H=0)
Figure 10 shows contributions of each quadrant (Si,H) on the Reynolds stress for both runs 1 and 2 with H=0 at different distances from the flume wall. For run 1, up to a water depth of Z/h=0.55, both ejection |S2,0| and sweep |S4,0| have more contributions on the Reynolds stress, regardless of the distances from the flume wall. For run 2, the decrease in aspect ratio also results in ejection being the dominant event. However, the difference between inward S3,0 and sweep grows smaller as approaching closer to the flume wall. For run 1, the variations of values |Si,H| over the entire flow depth have a similar tendency to those of run 2, namely, a decreasing trend up to a water depth of Z/h =0.25 and then a constant value. By contrast, for run 2 (W/h =4), two zones can be observed: first up to a water depth of Z/h = 0.55 where |Si,H| diminished, and the second zone from a water depth of Z/h =0.55 toward the water surface where |Si,H| augmented. Further, in later zone (toward the water surface), the contributions of S1, 0 and S3,0 on shear stress are increasing. The positive values u ' w ' in the first and third quadrants confirm the negative sign of Reynolds stress values near the water surface. It should be noted that there is no considerable difference in the relative submergence of vegetation between two runs, as shown in Table 1, H/ZP = 1.79 and H/ZP = 2.1 for run 1 and run 2 respectively. For run 1 and run 2, the flow Froude number is 0.54 and 0.49, respectively; and the Reynolds number 264,000 and 360,000 respectively. Thus, the flow conditions encompass small relative submergence, subcritical and turbulent flows for both runs. Consequently, the differences in research results between two runs are only due to differences in flow aspect ratio regardless of the relative submergence, the Froude number and Reynolds number. 4 Conclusions This study examines the turbulence characteristics of flow over submerged vegetation in a flume. Results show that secondary currents exist in flow over vegetation with an aspect ratio of W/h= 4. The distribution of the secondary flow vectors shows that their directions change in the left side of the flume. The nonlinear distribution of the Reynolds stress indicates that it is negative in the upper layer of the uniform flow, and that the zero shear stress zone is below the free surface. Observation of smaller Reynolds stress values near the water surface (Fig. 7) confirms the presence of the secondary currents in International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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flow having an aspect ratio of W/h =4. However, there appears to be weak secondary currents in flow having an aspect ratio of W/h=5.4.
Fig. 10
Variation of S i , H
along the depth over the vegetated bed for H=0 in runs 1 and 2
The velocity profile shows an inflection point which superposes with the maximum turbulence intensity and it occurs above the vegetation cover. Also the Reynolds stress reaches its maximum value above the upper limit of the vegetation cover at a water depth of Z/h=0.5, regardless of the distance from the flume wall. Using the relationship proposed by Stephan and Gutknecht (2002), the log law is valid up to a water depth of Z/h = 0.24 for flow over submerged vegetation regardless of both the distance from the wall and the aspect ratio of flow. Results of quadrant analysis clearly demonstrate that all events within a bursting process contribute to the flow over submerged vegetation. However, near the submerged vegetation, and for H=0, sweep is the dominant event for both aspect ratios of W/h =4 and 5.4 used in this study. In addition, our findings show that for flow over a vegetation cover, the frequency of the near-bed turbulence can vary significantly with the aspect ratio. Accordingly, the frequency during which sweeps, ejections, outward, and inward interactions occur does not remain constant but vary with the aspect ratio. The accepted idea that ejections and sweeps are the most frequent events appears to be true only near the vegetation cover; however, near the water surface, the role of outward and inward events is important as well. Based on this experimental study, one can say that near the vegetation cover, the sweeps and ejections appear to be the most dominant events; while at a water depth of Z/h>0.5, the outward interaction is dominant event. References Afzalimehr H. and Dey S. 2009, Influence of bank vegetation and gravel bed on velocity and Reynolds stress distributions. International Journal of Sediment Research, Vol. 24, No. 2, pp. 236–246. Afzalimehr H., Sui J., and Moghbel R. 2010, Hydraulic parameters in channels with wall vegetation and gravel bed. International Journal of Sediment Research, Vol. 25, No. 1, pp. 81–90. Barenblatt G. I. 1982, Similarity, self-similarity and intermediate asymptotics. Consultants Bureau, New York, N. Y.
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Bennett S. J. and Best J. L. 1995, Mean flow and turbulence structure over fixed, two dimensional dunes: Implications for sediment transport and bedform stability, Sedimentology, Vol. 42, pp.491–513. Bernhardt E. S., Palmer M. A., Allan J. D., Alexander G., Barnas K., Brooks S., Carr J., Clayton S., Dahm C., Follstad-Shah J., Galat D., Gloss S., Goodwin P., Hart D., Hassett B., Jenkinson R., Katz S., Kondolf G. M., Lake P. S., Lave R., Meyer J. L., O’Donnell T. K., Pagano L., Powell B., and Sudduth E., 2005, Synthesizing U. S. river restoration efforts, Vol. 308, No. 5722, pp. 636–637. Carollo F. G., Ferro V., and Termini D. 2002, Flow velocity measurement in vegetated channels. Journal of Hydraulic engineering, Vol. 128, No. 7, pp. 664–673. Champion P. D. and Tanner C. C. 2000, Seasonality of macrophytes and interaction with flow in a New Zealand lowland stream. Hydrobiologia, Vol. 441, pp. 1–12. Comte-Bellot G., Sabot J., and Saleh I. 1979, Detection of intermittent events maintaining Reynolds stress. See Blackwelder 1979, pp. 213–29. Dey S. and Nath T. 2010, Turbulence characteristics in flows subjected to boundary injection and suction. Journal of Engineering Mechanics, Vol. 136, No. 7, pp. 877–888. Finnigan J. J. 1979, Turbulence in waving wheat: I. Mean statistics and honami. Boundary-Layer Meteorology, 16, pp. 181–211 Ghisalberti M. and Nepf H. 2006, The structure of the shear layer over rigid and flexible canopies. Environmental Fluid Mechanics, Vol. 6, No. 3, pp.277–301. Graf W. H. and Altinakar M. S. 1998, Fluvial hydraulics: Flow and transport processes in channels of simple geometry. John Willey & Sons, Chichester, England. 681 pages. ISBN 0-471-97714-4. Guo J. and Julien P. Y. 2001, Turbulent velocity profiles in sediment-laden flows. Journal of Hydraulic Research, IAHR, Vol. 39, No. 1, pp. 11–23. Guo J. and Julien P. Y. 2008, Application of the modified log-wake law in open-channels. Journal of Applied Fluid Mechanics, Vol. 1, No. 2, pp. 17–23. Huai W. X., Zeng Y. H., Xu Z. G., and Yang Z. H. 2009, Three-layer model for vertical velocity distribution in open channel flow with submerged rigid vegetation. Advances in Water Resources, Vol. 32, No. 4, pp. 487–492. Jain H., Yuichi M., and Fujio Y. 2008, Quadrant analysis of bubble induced velocity fluctuations in a transitional boundary layer. Journal of Hydrodynamics, Vol. 21, No. 1, pp. 93–99. Jain S. C. 1992, Note on lag in bed-load discharge. Journal of Hydraulic Engineering, Vol. 118, No. 6, pp. 904–917. Jarvela J. 2002, Flow resistance of flexible and stiff vegetation: A flume study with natural plants. Journal of Hydrology, Vol. 269, No. 1/2, pp. 44–54. Jarvela J. 2004, Flow resistance in environmental channels: Focus on vegetation. degree of Doctor of Science, Helsinki University of Technology. Jarvela J. 2005, Effect of submerged flexible vegetation on flow structure and resistance. Journal of Hydrology, Vol. 307, No. 1-4, pp. 233–241. Kaftori D., Hestroni G., and Banerjee S. 1998, The effect of particles on wall turbulence. International Journal of Multiphase Flow, Vol. 24, No. 3, pp. 359–386. Kim H. T., Kline S. J., and Reynolds W. C. 1971, The production of turbulence near a smooth wall in a turbulent boundary layer. Journal of Fluid Mechanics, Vol. 50, pp. 133–160. Kironoto B. A. and Graf W. H. 1994, Turbulence characteristics in rough uniform open channel flow. Proceedings of the ICE - Water Maritime and Energy, Vol. 106, pp. 333–344. Kummu M. 2002, Roughness characteristics and velocity profile in vegetated and nonvegetated channel. Master of Science thesis, Helsinki University of technology. Lu S. S. and Willmarth W. W. 1973, Measurements of the structures of the Reynolds stress in a turbulent boundary layer. Journal of Fluid Mechanics, Vol. 60, pp. 481–511. Maltese A., Cox E., Folkard A. M., Ciraolo G., Loggia G. La., and Lombardo G. 2007, Laboratory measurements of flow and turbulence in discontinuous distributions of Ligulate Seagrass. Journal of Hydraulic Engineering, Vol. 133, No. 7, pp. 750–760. McBride M., Hession W. C., Rizzo D. M., and Thompson D. M. 2007, The influence of riparian vegetation on near bank turbulence: A flume experiment. Earth and Surface Process Landforms, Vol. 32, pp. 2019–2037. Mianaei S. J. and Keshavarzi A. R. 2008, Spatio-temporal variation of transition probability of bursting events over the ripples at the bed of open channel. Stochastic Environmental Research and Risk Assessment, Vol. 22, No. 2, pp. 257–264. Mianaei S. J. and Keshavarzi A. R. 2010, Study of near bed stochastic turbulence and sediment entrainment over the ripples at the bed of open channel using image processing technique. Stochastic Environmental Research and Risk Assessment, Vol. 24, No. 5, pp. 591–598. Naot D., Nezu I., and Nakagawa H. 1996, Unstable patterns in partly vegetated channels. Journal of Hydraulic Engineering, Vol. 122, No. 11, pp. 671–673. Nepf H. M. 1999, Drag, turbulence and diffusion in flow through emergent vegetation. Water Resources Research, Vol. 35, No. 2, pp. 479–489. International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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Nepf H. M. and Vivoni E. R. 2000, Flow structure in depth-limited, vegetated flow. Journal of Geophysical Research, Vol. 150, No. 12, pp. 28547–28557. Nezu I., Nakagawa H., and Rodi W. 1989, Significant difference between secondary currents in closed channels and narrow open channel. the 23rd IAHR Congress, Ottawa, Canada, 125–132. Nezu I. and Nakagawa H. 1993, Turbulence in open channel flows. A. A. Balkema, Rotterdam, The Netherlands. Papanicolaou A., Diplas P., Dancey C., and Balakrishnan M. 2001, Surface roughness effects in near-bed turbulence: Implications to sediment entrainment. Journal of Engineering Mechanics, Vol. 127, No. 3, pp. 211–218. Papanicolaou A. N. and Hilldale R. 2002, Turbulence characteristics in gradual channel transition. Journal of Engineering Mechanics, Vol. 128, No. 9, pp. 948–960. Poggi D., Porporato A., Ridolfi L., Albertson J. D., and Katul G. G. 2004, The effect of vegetation density on canopy sub-layer turbulence. Boundary-layer Meteorol, Vol. 111, pp. 565–587. Shaw R. H., Tavangar J., and Ward D. P. 1983, Structure of the Reynolds stress in a canopy layer. Journal of Climate and Applied Meteorology, Vol. 22, pp. 1922–1931. Shimizu Y. and Tsujimoto T. 1994, Numerical analysis of turbulent open-channel flow over a vegetation layer using a k-3 turbulence model. Journal of Hydroscience and Hydraulic Engineering, Vol. 11, No. 2, pp. 57–67. Song T., Graf W. H. and Lemmin U. 1994, Uniform flow in open channels with movable gravel bed. Journal of Hydraulic Research, Vol. 32, No. 6, pp. 861–876. Stephan U. and Gutknecht D. 2002, Hydraulic resistance of submerged flexible vegetation. Journal of Hydrology, Vol. 269, pp. 27–43. Strom K. B. and Papanicolaou A. N. 2007, ADV measurement around a clustre microform in a shallow mountain stream. Journal of Hydraulic Engineering, Vol. 133, No. 12, pp. 1379–1389. Sukhodolov A. N. and Sukhodolova T. A. 2010, Case study: Effect of submerged aquatic plants on turbulence structure in a lowland river. Journal of Hydraulic Engineering, Vol. 136, No. 7, pp. 434–446. Velasco D., Bateman A., Redondo J. M., and Demedina V. 2003, An open channel flow experimental and theoretical study of resistance and turbulent characterization over flexible vegetated linings. Flow, Turbulence and Combustion, Vol. 70, pp. 69–88. Wahl T. L. 2000, Analyzing ADV data using WinADV. Proceedings of join conference on Water Resources Engineering and Water Resources Planning and Management, Minneapolis, MN, United States. pp. 1–10. Wallace J. M., Eckelmann H., and Brodkey R. S. 1972, Structure of the Reynolds stress near the wall. Journal of Fluid Mechanics, Vol. 54, pp. 65–92. Willmarth W. W and Lu S. S. 1972, Structure of Reynolds stress near the wall. Journal of Fluid Mechanics, Vol. 55, pp. 65–92. Yagci O. and Kabdasli M. S. 2008, The impact of single natural vegetation elements on flow characteristics. Hydrological processes, Vol. 22, pp. 4310–4321. Yang S. Q., Xu W. L., and Yu G. L. 2006, Velocity distribution in a gradually accelerating free surface flow. Advances in Water Resources, Vol. 29, pp. 1969-1980. Yue W., Meneveau C., Parlange M. B., Zhu W., van Hout R., and Katz J. 2007, A comparative quadrant analysis of turbulence in a plant canopy. Water Resources Research, Vol. 43, W05422, doi: 10.1029/2006WR005583. Zhu W., van Hout R., and Katz J. 2007, PIV measurements in the atmospheric boundary layer within and above a mature corn canopy. Part B: Quadrant-hole analysis. Journal of the Atmospheric Sciences, Vol. 64, pp. 2825–2838. Notation d50 = Median diameter of sediment particles; C = Constant of the log law; D = Distance from the wall; ZP = Deflected plant height; h = Water depth above the vegetation; H = h + ZP ; W = Flume width; ks =Roughness scale (Equivalent sand roughness); Q = Flow discharge; u = Mean point velocity uave = Average velocity at a section; umax = Maximum velocity; u' = Turbulence intensity in longitudinal direction; w' = Turbulence intensity in vertical direction; u* = Shear velocity; Z = The vertical distance from top of the vegetation cover; z = The vertical coordinate; N = von Karman constant.
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Investigation of turbulence characteristics in channel with dense vegetation Hossein AFZALIMEHR1, Razieh MOGHBEL2, Jacques GALLICHAND3, and Jueyi SUI4
Abstract In this experimental study, the turbulent flow in a channel with vegetation by using sprouts of wheat on channel bed was investigated. Two different aspect ratios of channel were used. An Acoustic Doppler Velocimetry was used to measure parameters of turbulent flow over submerged sprouts of wheat, such as velocity profiles. The log law and the Reynolds shear stress distribution were applied. Results indicate that the position of the maximum turbulence intensity superposes on the inflection point situated over the top of submerged vegetation cover. Quadrant analysis shows that near the vegetation bed, the sweeps and ejections appear to be the most dominant phenomenon, while far from the vegetated bed, the outward is dominant event. Results also show that the aspect ratio plays an important role on the contribution of the different bursting events for Reynolds stress determination. Key Words: Bed vegetation, Aspect ratio, Reynolds stress, Quadrant analysis
1 Introduction Water flows in aquatic systems are rarely free of vegetative effects. Vegetation exerts a strong influence on stream-channel morphology. Based on research work in a lowland stream, Champion and Tanner (2000) pointed out that, under condition of the same water depth, flow discharge was about seven times bigger during the period of unvegetated season. Also, vegetation over the bed or channel surroundings exercises a dominant influence on capturing suspended load, production of oxygen and improvement of water quality. However, the structure of flows in channels with vegetated bed has not been well investigated, although its considerable effect of vegetation on river management, restoration, prevention of erosion and riverbank stability. In the United States, to limit the impacts of channel instability on the degradation of aquatic life habitat and water quality, one billion dollars was spent annually from 1990 to 2003 (Bernhardt et al., 2005). Up to date, studies regarding flows in vegetated channels have focused on velocity profiles, validity of the log law and turbulent characteristics (Afzalimehr and Dey, 2009; Afzalimehr et al., 2010; Guo and Julien, 2008; Guo and Julien, 2001; Jarvela, 2004; Kummu, 2002; López and García, 2001; Naot et al., 1996; Nepf, 1999; Shimizu and Tsujimoto, 1994; Stephan and Gutknecht, 2002). In the last couple of years, researchers has paid a lot of attentions to identify the coherent structures in turbulent flows over vegetated streams, due to the role played by these structures in mass and energy exchange (Yue et al., 2007). A conditional sampling and averaging technique was introduced by Wallace et al. (1972) and Willmarth and Lu (1972) to quantify the contribution to the Reynolds shear stress during the cycle of events observed in the bed region of the turbulent boundary layer. Conditional sampling techniques constitute suitable tools for identifying specific flow features that can be extracted from experimental data 1
Assoc. Prof., 2 Graduate student, Water Engineering Department, Isfahan University of Technology, Iran 84156 Prof., Département des sols et de génie agroalimentaire, Université Laval, St-Foy, QC, Canada 4 Assoc. Prof., Environmental Engineering Program, University of Northern British Columbia, Prince George, BC, Canada, V2N 4V9, E-mail: [email protected] Note: The original manuscript of this paper was received in Nov. 2010. The revised version was received in April 2011. Discussion open until Sept. 2012. 3
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(Yue et al., 2007). This technique expresses the contributions of u'w' into each quadrant of the u'- w' plane where u' and w' are the instantaneous velocities in stream-wise and vertical directions respectively. The quadrant analysis was employed to determine the frequency of occurrence of each individual event within a bursting process, i.e. outward interactions, ejections, inward interactions, and sweeps. For example, based on experimental studies, Poggi et al. (2004) and Gisalberti and Nepf (2006) found that sweeps dominate ejection within the canopy and a reversed relationship exists above the canopy. The results can be used to identify the effect of submerged vegetation and aspect ratio on the mean flow field. The quadrant analysis has not only been used to smooth bed turbulent boundary layers, but also it has been used for turbulent flows of different canopies, such as wheat (Finnigan, 1979) and corn (Shaw et al., 1983). Although quadrant analysis is traditionally performed for conditional sampling of the Reynolds shear stress and turbulent heat flux, Poggi et al. (2004); and Ghisalberti and Nepf (2006) and Zhu et al. (2007) extended the technique to include more general properties of turbulence in plant canopy flows, such as turbulent kinetic energy, vorticity, and dissipation rate. The methodology presented in this paper provides a combined analysis of the time average flow characteristics, i.e. mean velocity profiles and Reynolds shear stress components, with bursting process characteristics. The bursting process encompasses the complete sequence of outward, ejection, inward and sweep motions, and the frequency of occurrence of these events within that cycle over a vegetated cover. Kim et al. (1971) revealed that turbulent energy and Reynolds stress were generated by bursting motions, especially, ejections and sweeps. Approaches without considering frequency of occurrence and magnitude of turbulence structures appear rather incomplete (Jain, 1992; Papanicolaou et al., 2001). Lu and Willmarth (1973) introduced the quadrant analysis for studying the structure of the bursting phenomenon, and subsequent studies of others used it for interpreting the turbulence generated by fluvial bed forms (Papanicolaou et al., 2001; Mianaei and Keshavarzi, 2008; Mianaei and Keshavarzi, 2010). Sukhodolov and Sukhodolova (2010) carried out research in natural streams and claimed that “the theories advanced by laboratory studies and accomplished through systematic case studies on different plant species under different hydraulic conditions can clarify many practically important problems”. It is therefore important to understand the impact of vegetation on flow structure, including velocity and Reynolds stress distributions. Additionally, a better understanding of the interaction of flow and vegetation will help us to better understand sediment transport, and resistance to flow (Afzalimehr et al., 2010; Jarvela, 2002; Yagci and Kabdasli, 2008). In spite of effects of vegetation on ecological function of aquatic systems, the structure of densely vegetated aquatic flows has not been well studied. Also, no research work has been reported regarding the turbulence effect resulted from a dense-vegetated bed in a shear flow. In this study, the effects of submerged vegetation on turbulent flow characteristics are studied by analyzing the velocity fluctuation components (u'-w') and the quadrant analysis. The main objective is to determine the contribution of each quadrant to the Reynolds shear stress and to compute the dominant event of turbulent structure of flow in channels with densely submerged vegetation over bed for two different aspect ratios. 2 Experimental set-up Experiments were conducted in a 20-m long, 0.6-m wide and 0.6-m deep flume with glass walls. To control uniformity of flow during each experiment (or run), a limnimeter (a type of gages for measuring water levels) with an accuracy of ±1 mm was used to record the depth of water over the vegetation cover along the flume. A movable downstream weir was used to maintain uniform flow over the vegetation canopy. Graf and Altinakar (1998) pointed out that an aspect ratio of W/h=5 (W = the channel width, and h = the flow depth) is the critical value for studying flow structure in open channels. Accordingly, our experiments have been conducted in two runs with different aspect ratios: an aspect ratio of W/h=5.4 for run 1, and an aspect ratio of W/h=4 for run 2. These experimental runs have been carried out in the above mentioned flume with submerged vegetation on channel bed. The slope of the flume bed has been set to 0.5%. An electromagnetic current meter with accuracy of 3×10-4 m3/s has been used to measure discharge. Flow discharges have been selected from 0.037 m3/s to 0.055 m3/s, based on available flow discharges at the hydraulic laboratory. To obtain an aspect ratio of 5.4 for runs 1 and an aspect ratio of 4 for run 2 respectively, the water depth (h) has been 110 mm for run 1 and 150 mm for run 2 respectively. - 270 -
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Velocity measurements have been performed by using an Acoustic Doppler velocimetry (ADV). The ADV is a 10MHz Nortek Vectrino with a downward-looking probe and precision of ±0.1 mm/s. ADV signals are affected by Doppler noise, or white noise, associated with the measurement process. To remove possible aliasing effects, velocity time series have been analyzed using WinADV (Wahl, 2000), which is a windows based viewing and post-processing utility for ADV files. This software provides signal quality information in the form of a correlation coefficient (COR) and signal to noise ratio (SNR). Moreover, it has filters, such as phase-space threshold despiking and acceleration spike filter. The manufacturer suggests that when correlation coefficient does not exceed 70%, and signal to noise ratio (SNR) is less than 5 dB, the instantaneous velocity measurement is dominated by acoustic noise and, as a rule of thumb, these measurements should be discarded. To remove noise effects in this study, the data with SNR smaller than 5 dB and COR of 70% have been discarded and the velocity time series data has been passed through phase-space threshold despiking and acceleration spike filters. Almost 75% data have been considered suitable using WinADV criteria Corr>90% and SNR>20. The data of the poor quality have been easily removed from this study and have not been replaced. At each point, the flow velocity has been sampled with frequency of 200 Hz and for 120 s (experience reveals this duration for sampling is adequate for determining accurate turbulence statistics), with the lowest point for velocity measurements in each profile being 3 mm above the bed. Velocity measurements have been made along three cross sections at x=12.9 m, 13.5m and 14 m downstream of the flume entrance. At each cross section, velocity measurements have been made at different transverse-wise distances from the flume bank (D=5 cm, 12 cm and 30 cm). For each velocity profile, about 17 measurements of point-velocity have been obtained; and 7 out of these measurements of point-velocity are in the flow zone near the flume bed at a depth of Z/h <0.2 (where Z = the vertical distance from the measuring point to the top of the vegetation cover; and h = the total flow depth). Table 1 shows the hydraulic characteristics of laboratory experiments and a summary of experimental data for this study. Table 1
Hydraulic characteristics of laboratory experiments Vegetation over bed Run No. uave (m/s) h (mm) Zp (mm) Q (m3/s) 1 0.56 110 138 0.037 2 0.60 150 136 0.055 h: Water depth above the vegetation; ZP: Deflected plant height; H = h + ZP; W: channel width
W/h 5.4 4
H/Zp 1.79 2.1
There are two ways to investigate the effect of vegetation on flow structure: the first approach is the application of artificial material such as rigid and cylindrical roughness (Nepf, 1999) and the other one is to use natural vegetation directly (Sukhodolov and Sukhodolova, 2010). As reported by Maltese et al. (2007), wheat sprouts have been widely used vegetation in experimental studies. Wheat sprouts have been used in coastal engineering to protect shorelines from erosion by attenuating waves and currents, and in agricultural engineering by trapping organic and mineral particles. Thus, in our study, sprouts of wheat have been planted on flume bed along a 3-m long section. The vegetated section of flume is from x=11.5 m to 14.5 m downstream of the flume entrance, as shown in Fig. 1(a). The rest of the flume bed has been covered with gravel which has a median grain size of d50=21 mm and a standard deviation of 1.3 mm. The wheat planted over the channel bed has been long and flexible enough to result in wavy motions. The deflected plant height is 138 mm for run 1 and 136 mm for run 2 respectively. The height of submerged wheat has been kept the same during each experimental runs. The planting density of the wheat sprout has been 45,604 stems per square meter and has been longitudinally uniform over the vegetated flume section. All experiments have been carried out when water was flowing in the flume and the dense vegetation has been deflected, as shown in Fig. 1(b). Under each experimental run, no changes in the deflection height over time have been observed and the locations of h and Zp have been kept constant as indicated by Fig. 1(b). In addition, during experiment, no wheat has been detached from the channel bed which may result in water contamination. Measurements have been conducted whenever the difference in water depth between two sections of vegetated channel bed was less than 1 mm. Similar to the experimental studies of several researchers, such as Stephan and Gutkhecht (2002), Carollo et al. (2002) and Carolla et al. (2005), the vegetated International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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channel bed in our study has been also 3 m long. It is important to note that, no fundamental theory regarding the onset of fully developed flow conditions in vegetated channels has been reported. The best proof for existence of a fully developed flow is the similarity of velocity profiles at different cross sections from the starting point of bed vegetation in flume, as shown in Fig. 2. Figure 2 shows that the velocity profiles at different cross sections are similar. Very small differences in the velocity profiles should be attributed to the limitations of ADV to measure data in some height above the vegetation bed.
Fig. 1(a) View of vegetation over channel bed
Fig. 1(b)
A definition sketch of variables
As pointed out by Dey and Nath (2010), the bursting phenomenon are usually quantified by the conditional statistics of the velocity fluctuations (u' and w'). In this study, the quadrant analysis has been used to investigate the effect of the submerged vegetation over bed on sweep, ejection, outward and inward motions. Under the condition of the same mean flow properties, both the type and arrangement of vegetation on channel bed can play an important role on the turbulence structure (Strom and Papanicolaou, 2007). In the quadrant analysis, there are four quadrants (i = 1 to 4) in the u'-w' plane. Here, 1) i=1 represents outward motion (u'>0 and w'>0), 2); i=2 represents ejection (u'<0 and w'>0); 3) i=3 represents inward motion (u'<0 and w'<0); and 4) i=4 represents sweep (u'>0 and w'<0). The value of –u'w' < 0 corresponds to a positive Reynolds stress, whereas –u'w' > 0 represents the negative Reynolds stress. As suggested by Dey and Nath (2010), to differentiate the larger contributions to u ' w ' from each quadrant leaving the smaller u' and w' corresponding to more quiescent periods, a hole size parameter (threshold level) H is introduced in this study. In fact, the contribution of each quadrant to the Reynolds shear stress as a function of the threshold level of the hyperbolic hole region, H, has been defined as follows (Jian et al., 2009): - 272 -
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u ' w'
i, H
limt of
1 T
³0 u ' t w' t G i, H u ', w' dt T
(1)
where, T is time interval and įi,H is detection function.
Fig. 2 Verification of fully developed flow (run 1). Velocity profile at cross sections of 12.9m, 13.5m and 14 m from the entrance of the channel °1
when u ' w' t H u ' w'
°¯0
otherwise
G i , H u ' , w' ®
(2)
The fractional contribution Si,H to u ' w ' from each event is Si , H
u ' w'
i, H
u ' w'
(3)
Here, Si,H>0 is for the first and the third quadrant, and Si,H<0 is for the second and the forth quadrant. For analysis of the bursting phenomenon and for determination of the contribution of each quadrant to the Reynolds shear stress, a computer program was written in MATLAB. 3 Results 3.1 Velocity distributions Although the flow is fully developed over the gravel bed from the flume entrance along the flume section to x=11.5m (distance from the flume entrance), the change of bed roughness from gravel bed to the vegetated bed planted by wheat stems causes a new boundary layer development. Application of the empirical relations of turbulent boundary layer theory showed that the expected length of boundary layer development following a roughness transition to a vegetated bed is less than 11.5m. Therefore, along the section for velocity measurements (from x=12.9m to x=14m from the entrance), flow velocity profiles are self-similar (as shown in Fig. 2) and the flows are fully developed. Accordingly, the results at cross section x= 12.9m will be discussed in this study. Since the velocity measured by ADV within the vegetation cover shows considerable noise, measurements of flow velocity have been only conducted above the vegetation cover. Also, the ADV used in this experimental study cannot be used to measure velocity at a depth of Z/h 0.75 as Fig. 3 indicates. Therefore, a dip phenomenon has not been noticed for a water depth of 0 < Z/h 0.75. When an aspect ratio of flow is W/h5, dips in velocity profiles have been observed over smooth beds by Nezu et al. (1989) and over rough beds by Kironoto and Graf (1994), respectively. In this experimental study, when the aspect ratio of flow is W/h=5.4 (run 1), no dips in velocity profiles have been noticed, no matter where measurements for velocity profiles have been conducted (i.e., different distance from flume wall, D=5 cm, 12 cm and 30 cm). When the aspect ratio of flow is W/h=4 (run 2), even though no dips in velocity profiles have been noticed, a secondary current effect is noticeable. This obervation will be discussed in section 3.2. International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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Fig. 3
Velocity profiles of run 1-2 in channel with vegetation over bed (D=distance from the flume wall)
As claimed by Nezu and Nakagawa (1993), the occurrence of secondary currents has been mainly resulted from the anisotropy between v' (transversal velocity fluctuation component) and w' (vertical velocity fluctuation component). Such anisotropy of turbulence has been caused by a development of the complex boundary conditions at flume walls, flume bed, and the free water surface. Indeed, the secondary currents in a straight flume with fixed bed are developed as a result of the cross sectional non-homogenity of turbulence. For the case of an aspect ratio of W/h< 5, vortices are initiated at first at the corners due to existence of sidewalls and extended and then mixed in the lateral direction. For the case an aspect ratio of W/h >5, the vortices could be damped fast, while getting away from the sidewalls. Graf and Altinakar (1998) have pointed out that secondary currents cause the dip phenomenon of velocity profiles. They showed that for an aspect ratio of W/h>5, the maximum flow velocity (umax) occurs at the water surface and the influence of the secondary currents could be negligible; while for an aspect ratio of W/h<5, the effect of the secondary currents is important and umax occurs under the water surface. Secondary currents are responsible for the transport of fluids with low momentum from the near-wall zone to the corner, and the transport of fluids with high momentum from the free surface toward the channel bed. The boundary shear stress increases whenever the secondary currents flow toward the bank. On the other side, a smaller boundary shear stress appears whenever the secondary currents flow away from the bank. As shown in Fig. 4, the characteristics of the secondary currents have been affected by the magnitude of the aspect ratio (W/h=5.4 for run 1, and W/h=4 for run 2). From Fig. 4, one can also see the secondary currents 2
2
vectors, and ( v w ) . Interestingly, for run 2 (W/h = 4), the secondary current vectors have a tendency of clockwise circulation from the flume wall to the center of the flume. However, such a phenomenon has not been observed in run1 (W/h =5.4).
Fig. 4
2
2
Secondary flow velocity vectors ( v w ) in the left side of channel for both runs 1 and 2
Our findings are not identical to those of Huai et al. (2009), as shown in Fig. 4. Huai et al. (2009) carried out experimental study under condition of uniform flow over a vegetated channel bed. Their vegetated channel bed has been made of stiff and artificial vegetation cover. They found that the secondary currents cannot be created when the aspect ratio W/h is less than 5. The different types of vegetation used in the study of Huai et al. (2009) from that in our experiment may be responsible for different results. Carollo et al. (2002) observed an inflection point in velocity profile which is superposed on the maximum turbulence intensity. Nepf and Vivono (2000) declared that this superposition occurs at the top of the vegetation cover. Figure 5 shows that the turbulence intensity decreases after reaching its maximum - 274 -
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value. For dense vegetation on channel bed, the inflection point has been observed near the top of the vegetation, causing the generation of large coherent vortices via the Kelvin-Helmholtz instability, as also considered in free shear layer. These coherent vortices govern the momentum exchange between the vegetation cover and the overlying fluid. For submerged vegetation, the penetration of turbulence and momentum from the overflow plays an important role in the function of vegetation. Jarvela (2005) indicated that, based on experimental study by using a dense vegetation cover (12,000 stems/m2), the location of maximum turbulence intensity has been located above the deflected vegetation. In our experimental study, the vegetation density is larger than that of Jarvela (2005), expecting that the location maximum turbulence intensity occurs above the deflected vegetation (Z/h| 0.5).
Fig. 5
Turbulence intensity observed for runs 1 and 2
Song et al. (1994) had studied the flow over a gravel-bed channel with the flume width (W=0.6 m), bed slope 0.5%, flow discharge of 31 L/s to 60 L/s under subcritical and turbulent flow conditions. They showed that near the water surface, the velocity distribution approaches to vertical line for a range of an aspect ratio from 3.2 to 6.4, while Fig. 3 reveals that it moves far away from the vertical line, especially for an aspect ratio of W/h=4. In fully developed open channel flow, velocity profile can be discussed on the basis of the universal log law: u u*
1
N
ln
z C ks
(4)
where, u = mean point velocity, u* = shear velocity, z= the vertical coordinate, N = the von Karman constant, ks = roughness scale and C = constant. To describe velocity profile for flow over bed with submerged vegetation, Stephan and Gutknecht (2002) proposed a logarithmic law, with C =8.5 and N = 0.4, and which is used in our study: u u*
1
N
ln
z ZP 8. 5 ZP
(5)
where, ZP = the thickness of vegetation cover. Kummu (2002) pointed out that the vertical velocity profile above vegetated beds has logarithmical distribution only in its middle part of the velocity profile. However, Fig. 6 confirms the validity of the log law for the inner layer near the bed vegetation cover. The reason for the log-law deviation in the outer layer (Z/h>0.2) is invalidity of constant shear stress in whole flow depth and invalidity of mixing length approximation. It should be noted that the log law only approximately represents the experimental data (Barenblatt, 1982) as Fig. 6 shows for the near the bed data. 3.2 Reynolds shear stress The vertical Reynolds stress ( u ' w ' ) induces longitudinal and vertical momentum exchange as well as vertical mixing (Velasco et al., 2003). Investigations show that the Reynolds stress distribution in all channel flows is nonlinear. The linearity occurs only for low depths above the peak as stress decays from its maximum near the boundary (bed or top of vegetation) to the free surface (Nepf and Vivoni, 2000; Velasco et al., 2003 and Huai et al., 2009). Figure 7 shows that the Reynolds stress distribution is non linear, and it does decay in both experimental runs near the water surface. However, the decay phenomenon for W/h =4 is more pronounced than that for W/h=5.4 due to effects of aspect ratio and International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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stronger secondary currents. The turbulence intensity distributions in Fig. 5 further indicate the stronger decay phenomenon of W/h=4 in comparison to W/h =5.4. Furthermore, for run 2 (W/h = 4), the maximum Reynolds stress occurs above the top of vegetation at a water depth of Z/h=0.5 and reaches zero below the free surface. Accordingly, there should be a negative Reynolds stress distribution above the zero-Reynolds stress. This generates the dip phenomenon in velocity profiles because a zero-Reynolds stress corresponds to a zero-velocity gradient or the maximum velocity (Yang et al., 2006). In this study, the location of the zero-Reynolds stress coincides with the location of the last measured point. The location of dip or the maximum velocity is associated to zero shear stress location. Figure 7 reveals a strong reduction of Reynolds stress toward the water surface for the case of an aspect ratio of W/h =4, while such a tendency has not been observed for W/h =5.4. It should be noted that no measurements have been conducted within the vegetation due to very high noise in ADV data in this zone. Therefore, no velocity deflection point has been observed near the vegetated bed.
Fig. 6 Logarithmic profiles fit for flow above vegetation for different distance from the wall (D) in runs 1 and 2
The spatial inhomogeneities of Reynolds stress produce an orderly (rather than chaotic) flow pattern which is perpendicular to the main channel flow. Rectilinear turbulent flow is an instability process with the turbulent intensity being deriving force and that the transition from the rectilinear flow to instability takes place via a marginal state, exhibiting a stationary pattern of motion, i.e., at the onset of instability a stationary pattern of motions prevails (cellular secondary currents). If Reynolds shear stress can be well predicted, then the location of maximum velocity could be found from the location of zero shear stress. Therefore, if zero shear stress occurs under the water surface, the maximum velocity will occur under the water surface as well. Thus, the distribution Reynolds stress provides a suitable knowledge of understanding for maximum velocity location. Yang et al. (2006) found that nonzero bed-normal velocity was responsible for dip phenomenon in uniform flow. Figure 7 does not show a clear tendency of Reynolds stress toward the water surface for an aspect ratio of W/h =5.4, but it clearly shows a strong decay phenomenon for an aspect ratio of W/h=4. The maximum Reynolds stress approaches zero at approximately similar flow depth for different distance from the vertical walls for an aspect ratio of W/h =4. In this experimental study, each square meter of channel bed has been densely planted 45,604 wheat stems. Additionally, wheat used in our work was so dense that there was little interaction between the flow above the vegetation and the water within the vegetation, as if the vegetation has been acted as an - 276 -
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almost impermeable bed roughness of matted stems. As a consequent, this vegetation cover creates a layer of fluid above the vegetation. This layer of fluid prevents the momentum exchange and shear interaction between the inside and the outside of the vegetation cover. The drag of this layer produces additional turbulence which moves the location of maximum turbulence stress farther away from the vegetation cover. This finding is in agreement with result of Jarvela (2005) who also used wheat stems to form bed vegetation with a planting density of 12,000 stems/m2. They claimed that the maximum Reynolds stress occurs just above the top of the flexible vegetation cover.
Fig. 7 Profiles of Reynolds stress in X-Z plane ( u 'w' ) for runs 1 and 2
For uniform flow over a gravel-bed channel, Song et al. (1994) found that the distribution of u' has a weakly concave form which has been assumed linear. However, Fig. 5 reveals a convex form turbulent intensity (u') for this study. Also, according to Song et al. (1994), the maximum value of u' and u 'w' appears at the bed and minimum value of u' and u 'w' occurs at the water surface. However, for uniform flow over a vegetated-bed, as shown in Figs. 5 and 7, they occur at Z/h | 0.5. 3.3 Quadrant analysis Determination of the threshold level H is more or less arbitrary; stationary values of conditionally averaged patterns against the variation of H have not been ascertained. Indeed, the selection of an appropriate threshold parameter H has been the source of considerable ambiguity and inconsistency within published work (Papanicolaou and Hilldale, 2002). Lu and Willmarth (1973) assumed that the threshold level H of ejection ranges from 4 to 4.5. Beyond this level, the contributions of sweeps to Reynolds stress almost disappear. Also, H of sweeps ranges from 2.25 to 2.75, and beyond this level, the contribution of the interactions almost disappears. An objective selection of the threshold level is not simple. Comte-Bellot et al. (1979) carried out an extensive study on the effect of H during period between ejections and sweeps, the intermittency factor Sj and contribution of -u'w' from different quadrants. They suggested that an appropriate choice of H for events in a particular quadrant may simply be used on the percentage contribution for -u'w' from that quadrant. However, near the vegetation cover over the bed, since turbulence is generated in ejections and sweeps, the contributions of both events at H=0 are significant, especially for the sweep motion (u'>0, w'<0) which plays an important role on transferring energy toward the bed. Maltese et al. (2007) reported an ejection-dominated upper layer of the plant canopy and a sweep-dominated region around the top of the canopy with relatively fast flow (mean velocity of 5.5 cm/s). They found that in slower flow (mean velocity of 1.7 cm/ s), the plants have been quasi emergent and sweeps similarly dominated the region near the top of the canopy. Yue et al. (2007) found that significant fractions of the vertical momentum flux have been transported at high values of the International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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hole size, indicating that much of the momentum flux has been transported during periods of strong turbulent events occupying in a small fraction of time. Nezu and Nakagawa (1993) indicated that if the turbulent boundary layer is in equilibrium condition, the magnitudes of ejection and sweep motion behave in similar ways. As a consequent, their contributions are constant and irrespective of the Reynolds number. Different hole sizes (H) have been considered here including H=0, 1, 2, 3. However, H= 0 will be taken into account for further discussion in this study because it does not eliminate any value of Reynolds stress in four quadrants. Figure 8 shows the dominant turbulent event at each point over the entire flow depth at the central axis of the flume. For H=0, two zones can be distinguished over the total flow depth: the first zone has a water depth of 0
Fig. 8 Percentage of velocity fluctuation components (u' and w') from each quadrant (i=1, 2, 3 and 4) over the vertical – run 2 in center line of the channel
Figure 8 displays different trends for sweep events in H=0. However, the change of H from 0 to 3 illustrates that all events have nearly the similar trend over the entire flow depth. Moreover, an increase in the hole size causes that ejection becomes the dominant event. Accordingly, over the entire flow depth, -u'w' is negative in both quadrant 4 (sweep) and quadrant 2 (ejection). Therefore, Reynolds stress u ' w ' is positive in both quadrant 4 (sweep) and quadrant 2 (ejection), as one can see from Fig. 7. Figure 9 shows four turbulent events in four quadrants (outward interactions, ejections, inward interactions, and sweeps) that characterize the individual turbulent velocity measurements for two points at water depths of Z/h=0.29 and Z/h=0.49 respectively with H=0 at the central axis of flume. The joint frequency distribution shows that a negative correlation is associated with the boundary shear stress at the measuring point and the tilting of the joint frequency distribution into quadrants 2 and 4. Papanicolaou et al. (2001) reported no pronounced peaks or any preferential tilting toward one of the four quadrant and is rather systematic with respect to the origin, of the u'- w' plan. Typical trend for smooth boundaries (as defined by Nezu and Nakagawa, 1993) is the titling of the distribution into quadrant 2 and 4 (Papanicolaou et al., 2001). According to Papanicolaou et al. (2001) the rounder shape of the distribution, the lower packing density case is indicative of flow non-uniformity in higher packing densities the sweep and ejection are the most dominant events. The multi-peak pdf’s in Fig. 9 may be indicative of the higher vegetation density. Kaftori et al. (1998) reported that the importance of the ejection and sweep quadrants diminishes as the roughness increases, while the contribution of the outward and inward quadrants to the Reynolds stress - 278 -
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becomes more significant. Near the upper part of the vegetation layer, sweep is the most frequent event (longest time fraction) while ejection contributes most to the vertical momentum flux (largest fraction). The outward and inward events have the shortest time fraction and the smallest values of the shear stress, especially at the upper part of the vegetation layer. It means that the momentum transfer between the flow and the upper vegetation layer is mostly carried by sweep and ejection events. Using the quadrant analysis, McBride et al. (2007) claimed that, for riparian vegetation along the bank, quadrant 1 (outward) events were predominant in frequency and had a greater mean Reynolds shear stress than quadrants 2 (ejection) or 4 (sweep). On the other hand, Bennett and Best (1995) indicated through measurements over sand dunes that outward interaction events are restricted to the near bed zone. However, results of their study shows that outward and inward events have important effect on Reynolds stress in the zone far away from the vegetation bed (Z/h > 0.5).
Fig. 9 Joint probability distributions of u'/u* and w'/u* at points with Z/h= 0.29 (b) and Z/h=0.49 (a) in run 2 in the center line of the channel (H=0)
Figure 10 shows contributions of each quadrant (Si,H) on the Reynolds stress for both runs 1 and 2 with H=0 at different distances from the flume wall. For run 1, up to a water depth of Z/h=0.55, both ejection |S2,0| and sweep |S4,0| have more contributions on the Reynolds stress, regardless of the distances from the flume wall. For run 2, the decrease in aspect ratio also results in ejection being the dominant event. However, the difference between inward S3,0 and sweep grows smaller as approaching closer to the flume wall. For run 1, the variations of values |Si,H| over the entire flow depth have a similar tendency to those of run 2, namely, a decreasing trend up to a water depth of Z/h =0.25 and then a constant value. By contrast, for run 2 (W/h =4), two zones can be observed: first up to a water depth of Z/h = 0.55 where |Si,H| diminished, and the second zone from a water depth of Z/h =0.55 toward the water surface where |Si,H| augmented. Further, in later zone (toward the water surface), the contributions of S1, 0 and S3,0 on shear stress are increasing. The positive values u ' w ' in the first and third quadrants confirm the negative sign of Reynolds stress values near the water surface. It should be noted that there is no considerable difference in the relative submergence of vegetation between two runs, as shown in Table 1, H/ZP = 1.79 and H/ZP = 2.1 for run 1 and run 2 respectively. For run 1 and run 2, the flow Froude number is 0.54 and 0.49, respectively; and the Reynolds number 264,000 and 360,000 respectively. Thus, the flow conditions encompass small relative submergence, subcritical and turbulent flows for both runs. Consequently, the differences in research results between two runs are only due to differences in flow aspect ratio regardless of the relative submergence, the Froude number and Reynolds number. 4 Conclusions This study examines the turbulence characteristics of flow over submerged vegetation in a flume. Results show that secondary currents exist in flow over vegetation with an aspect ratio of W/h= 4. The distribution of the secondary flow vectors shows that their directions change in the left side of the flume. The nonlinear distribution of the Reynolds stress indicates that it is negative in the upper layer of the uniform flow, and that the zero shear stress zone is below the free surface. Observation of smaller Reynolds stress values near the water surface (Fig. 7) confirms the presence of the secondary currents in International Journal of Sediment Research, Vol. 26, No. 3, 2011, pp. 269–282
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flow having an aspect ratio of W/h =4. However, there appears to be weak secondary currents in flow having an aspect ratio of W/h=5.4.
Fig. 10
Variation of S i , H
along the depth over the vegetated bed for H=0 in runs 1 and 2
The velocity profile shows an inflection point which superposes with the maximum turbulence intensity and it occurs above the vegetation cover. Also the Reynolds stress reaches its maximum value above the upper limit of the vegetation cover at a water depth of Z/h=0.5, regardless of the distance from the flume wall. Using the relationship proposed by Stephan and Gutknecht (2002), the log law is valid up to a water depth of Z/h = 0.24 for flow over submerged vegetation regardless of both the distance from the wall and the aspect ratio of flow. Results of quadrant analysis clearly demonstrate that all events within a bursting process contribute to the flow over submerged vegetation. However, near the submerged vegetation, and for H=0, sweep is the dominant event for both aspect ratios of W/h =4 and 5.4 used in this study. In addition, our findings show that for flow over a vegetation cover, the frequency of the near-bed turbulence can vary significantly with the aspect ratio. Accordingly, the frequency during which sweeps, ejections, outward, and inward interactions occur does not remain constant but vary with the aspect ratio. The accepted idea that ejections and sweeps are the most frequent events appears to be true only near the vegetation cover; however, near the water surface, the role of outward and inward events is important as well. Based on this experimental study, one can say that near the vegetation cover, the sweeps and ejections appear to be the most dominant events; while at a water depth of Z/h>0.5, the outward interaction is dominant event. References Afzalimehr H. and Dey S. 2009, Influence of bank vegetation and gravel bed on velocity and Reynolds stress distributions. International Journal of Sediment Research, Vol. 24, No. 2, pp. 236–246. Afzalimehr H., Sui J., and Moghbel R. 2010, Hydraulic parameters in channels with wall vegetation and gravel bed. International Journal of Sediment Research, Vol. 25, No. 1, pp. 81–90. Barenblatt G. I. 1982, Similarity, self-similarity and intermediate asymptotics. Consultants Bureau, New York, N. Y.
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