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Effects of accelerating and decelerating flows in a channel with vegetated banks and gravel bed
International Journal of Sediment Research 27 (2012) 188-200
Effects of accelerating and decelerating flows in a channel with vegetated banks and gravel bed Hossein AFZALIMEHR1, Elham Fazel NAJAFABADI2, and Jacques GALLICHAND3
Abstract Experiments were conducted in an 8 m long, 40 cm wide, and 60 cm deep re-circulating flume with vegetated banks and gravel bed to study the effects of accelerating and decelerating flows on the flow structure. Significant dip phenomenon was observed in velocity profiles under decelerating flow and the velocity defect law was not suitable due to the effect of vegetated banks. Near the vegetated banks, the turbulence intensities illustrated convex distribution for both accelerating and decelerating flows. Application of quadrant analysis revealed that the effect of vegetated banks is important on the flow structure and the Reynolds stress distribution. Accelerating and decelerating flows did not show a significant difference on percentage of time occupied by each kind of turbulent event within bursting cycle, but affected the shape of joint probability distributions of turbulent intensities in the horizontal and vertical directions. Key Words: Vegetated bank, Decelerating and accelerating flows, Gravel bed, Reynolds stress
1 Introduction Knowledge of interactions of sediment on riverbed, vegetation in river banks and non-uniform flow (accelerating and decelerating flows) are crucial to study sediment transport and friction factor. In natural streams, accelerating and decelerating flows are complex phenomenons which are not fully understood although they are frequently observed in practice. From fluvial hydraulic point of view, flow over stoss and lee sides of dunes in sand-bed rivers or flow over riffles and pools of gravel-bed rivers are good examples to illustrate acceleration and deceleration flows. Studies in open channels with bare banks and coarse-bed indicate that the accelerating flow suppresses the generation of turbulence, while the decelerating flow has the opposite effect (Houra et al., 2000). Some attempts have been made to study the effect of non-uniformity on the velocity distribution and turbulence characteristics of the open channel flow with bare banks. Cardoso et al. (1991) studied gradually accelerated flows in a smooth channel and concluded that the velocity distribution cannot be represented for the total flow depth by the universal log-law except at regions very close to the bed y/h<0.2, where y is distance from the bed and h is the total flow depth. Song and Graf (1994), Kironoto and Graf (1995), Song and Chiew (2001) detected velocity profiles, turbulence intensities and Reynolds stress distributions for both accelerating and decelerating flows in gravel-bed channel and found that: 1) the maximum velocity occurs below the water surface for accelerating flow and at the water surface for decelerating flow. 2) the standard log-law velocity profile works well for y/h<0.2 for accelerating and decelerating flows. 3) Reynolds stress and turbulence intensities distributions for accelerating flow are concave and for decelerating flow are convex. 4) The wake function works well under accelerating and decelerating flows. 1
Assoc. Prof., 2 Graduate Student, Department of Water Engineering, Isfahan University of Technology, 84156-83111, Iran, E-mail: [email protected] 3 Prof., Département des sols et de génie agroalimentaire Pavillon Paul-Comtois, Université Laval, St-Foy, QC, Canada, E-mail: [email protected] Note: The original manuscript of this paper was received in July 2010. The revised version was received in Nov. 2011. Discussion open until Mar. 2013. - 188 -
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Vegetation occupies a pivotal role in river in fluvial geomorphology investigations. In last decade, many studies have been reported on the velocity profiles and the turbulent characteristics of vegetated channels (López and García, 2001; White and Nepf, 2007; White and Nepf, 2008; Afzalimehr and Dey, 2009; Nasiri et al., 2011; Afzalimehr et al., 2011). Afzalimehr and Dey (2009), Nasiri et al. (2010) found that under uniform flow conditions, vegetated banks in gravel-bed channels changes the pattern of velocity and Reynolds stress distributions. Also, Nasiri et al. (2011) found similar patterns for velocity and Reynolds stress over gravel dunes. Accordingly, the maximum velocity occurs below the water surface and the Reynolds stress distribution does not follow linear trend and its shape depends on the distance from the vegetated bank. Afzalimehr et al. (2010) investigated the accelerating flow in a channel with gravel bed, vegetated banks and found an S shape Reynolds stress distribution near the vegetated banks. They found that the occurrence umax below the water surface and nonlinear distribution of Reynolds stress is due to secondary currents and the anisotropy in turbulence in the vegetated banks channels. Also, above studies showed negative values in Reynolds stress distribution near the water surface and the zero shear stress value below the water surface. Nezu and Nakagawa (1993) showed that the negative values of Reynolds stress in near the water surface is in agreement with the fact that du/dy is also negative in this region. In addition, the negative values were likely linked to proximity to a vegetated bank. López et al. (1996) reported the connection between the sign of Reynolds shear stress and the dominant events in bursting process. Despite the importance of interaction of vegetated bank and non-uniform flow over gravel-bed channels, no comparative study has been reported to describe the effect of interaction of flow non-uniformity and vegetated banks on turbulence intensities and the Reynolds stress distributions. It is obvious that a laboratory work cannot produce a complete picture of turbulent flow characteristics in rivers because of complex interactions of many unknown factors in fluvial processes, but can improve our understanding in environmental hydraulic. Therefore, the objective of this experimental research is to investigate and compare the effects of accelerating and decelerating flows on the turbulent flow characteristics in a channel with vegetated banks and gravel bed. 2 Experimental setup Experiments have been carried out in an 8 m long, 40 cm wide, and 60 cm deep re-circulating flume at the Hydraulics Laboratory of Isfahan University of Technology, Iran. A tail gate located at the end of the flume was used to control water level during experiments. In this experimental study, the flow depth has been measured by using a point gauge with 1 mm increment. The grain size of gravel particles had a median diameter (d50) of 2 cm and the geometric standard deviation g=(d84/d16)0.5 of particle size distribution was 1.14, where d84 and d16 are 84% and 16% finer particle diameters, respectively. For flow over rough surfaces, a precise definition of the distance from the bed origin (i.e., y = 0) would be difficult. The virtual origin is a very small fraction of the roughness height (ks). Afzalimehr and Anctil (2000) and Kironoto and Graf (1994) performed their experiments on gravel beds with d50=2.54 cm and d50=2.3 cm, respectively, they applied ks=0.2d50. On the other hand, Tu and Graf (1993) and Song and Graf (1994) applied ks=0.25d50. Further, Song and Chiew (2001) found when d50=2.6 cm, ks=0.25d50. The reference level where u = 0 was obtained using a trial and error procedure based on the highest R2 between u and Ln [(y + d50)/d50], where, u was the mean-point velocity, d50 allowed for the adjustment of zero plane displacement (y = 0), y was distance from the bed and is an adjusting coefficient of median grain size. The theoretical mean bed surface was not at the upper surface of the protruding particles, but a distance d50 below it. Based on the trial and error process, the value of ks = d50 was selected for this study. Rice stems were used to illustrate the effect of vegetated banks. In order to prevent the flexibility of rice stems in water, the rice stems were stuck over a plastic carpet. In addition, to keep the stems without flexibility on the flume walls under the movement of water, rice stems were stitched by a thin cotton wire over the plastic carpet. Finally, the plastic carpet was stuck to the flume walls. The thickness of vegetation cover on flume walls was 0.5 cm. The stem density was calculated as the number of stems per unit length (400 stem m-1). The mean diameter of rice stems was d50=0.74 cm. Accelerating and decelerating flows discussed in this paper are the steady flow whose depths vary gradually along the flume. To determine if the flow is non uniform along the flume, flow depths have been measured at a distance of 5.0m, 5.50m and 6.00 m from the entrance cross section respectively. In addition, the criterion proposed by Graf and Altinakar (1993; 1998) has been used to parameterize flow International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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non-uniformity. Based on this criterion, the dimensionless longitudinal pressure gradient parameter is defined as: E
hª §
dh · º
(1)
¸» «J ¨ S 0 W ¬ © dx ¹ ¼
where, dh/dx is the longitudinal variation in water depth h, is the specific gravity of water, S0 is the bed slope and is the bed shear stress. Graf and Altinakar (1993; 1998) demonstrated that for accelerating flow < -1 and for decelerating flow > -1. As the values of in Table 1 show, to parameterize non-uniformity of flow as accelerating and decelerating flows, the Graf and Altinakar’s criterion works well for flow in channels with vegetated banks. Accordingly, the ranges of for decelerating flow is 8.99 < < 11.38 and for accelerating flow is -7.49 < < -5.69. Similar to the published work of Afzalimehr (2010) regarding flow over coarse-bed channels with bare banks, the results and the figures in this paper are presented only for the section of 6 m from the flume entrance. Table 1 Distance Distance from Non-uniform from inlet vegetation flow (m) (m) 5 0.03 0.06 0.19 5.5 0.03 Accelerating 0.06 flow 0.19 6 0.03 0.06 0.19 5 0.03 0.06 0.19 Decelerating 5.5 0.03 flow 0.06 0.19 6 0.03 0.06
Summary of experimental data
S0
h (m)
D50 (m)
um (m s-1)
Fr
Re (× 105)
u*Re (cm s-1)
-0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.277 0.277 0.277 0.266 0.266 0.266 0.256 0.256 0.256 0.234 0.234 0.234 0.245 0.245 0.245 0.256 0.256
0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.16 0.20 0.25 0.18 0.22 0.25 0.20 0.24 0.26 0.18 0.26 0.33 0.18 0.24 0.31 0.16 0.21
0.10 0.12 0.15 0.12 0.14 0.15 0.13 0.15 0.17 0.12 0.16 0.22 0.12 0.16 0.20 0.10 0.13
0.10 0.93 1.15 0.84 1.01 1.12 0.88 1.07 1.17 0.82 1.09 1.44 0.81 1.06 1.35 0.72 0.94
-7.45 -7.45 -7.45 -5.92 -5.92 -5.92 -5.69 -5.69 -5.69 8.99 8.99 8.99 9.57 9.57 9.57 11.38 11.38
0.98 1.25 1.64 1.41 1.39 1.64 1.33 1.24 1.61 2.12 2.37 2.26 2.02 2.50 2.24 1.68 2.12
To obtain accelerating and decelerating flows along the flow direction, the tailgate installed downstream were carefully adjusted in each experiment. For the case of accelerating flow where flow depth decreased along flow direction, an inverse bed slope (negative bed slope in flow direction) was established by gravel on the bed. To generate a decelerating flow where flow depth increased in the flow direction, a positive bed slope was created using gravel materials on the flume bed. A gravel bed slope of -%2 was used to create accelerating flow and a gravel bed slope of +%2 for decelerating flow. Figure 1 shows a schematic of accelerating and decelerating flows in the flume. The flow was allowed to stabilize for about 1 hour before an Acoustic Doppler Velocimeter (ADV) was used to measure the instantaneous velocities. The flume reach for measurement was situated between 5.0 < x (m) < 6.0, where x was the distance from the flume entrance. Within this measuring reach, the flow was considered non-uniform (Table 1). Three cross sections of 5m, 5.5m and 6m along this measuring reach were chosen for conducting measurements of hydraulic parameters. To investigate the influence of vegetated banks on flow velocity, turbulence intensities and the Reynolds stress at each cross section, flow velocities were measured at different distances from the vegetated banks (D = 0.03m, 0.06m and 0.19 m). The number of points for measuring velocity at each cross section varied from 29 to 34, depending on water depth. For each measuring point, the duration of data acquisition was 2 minutes, so that with a sampling frequency of 200 Hz, 24,000 instantaneous velocity measurements were obtained. The sampling duration was selected 2 min in order to have a statistically time independent average velocity. The adequacy of the 2 minute sample duration was confirmed by collecting data at several points for 20 min and evaluating divergence of velocity - 190 -
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statistics (mean and standard deviation). Stone and Hotchkiss (2007) showed that the ADV velocity data stabilized at sampling times of approximately 100 sec. Therefore, the 2 min ADV sampling time was considered adequate in this study.
Fig. 1 Schematic of experimental setup of accelerating and decelerating flows
The mean point velocities, the turbulence intensity, and the Reynolds stress were determined using instantaneous velocity measurements. In this study, mean flow velocity components (u, w) and velocity fluctuation components in turbulent flow (uf, wf) corresponding to the stream-wise (or longitudinal), and vertical directions, respectively. The velocity fluctuations were defined as: °u f ui u ® (2) °¯w f wi w where ui, and wi are the instantaneous velocities, and u and w are the mean-point velocities in longitudinal and vertical directions respectively. The root mean square (RMS) of velocity fluctuations (turbulence intensities) were determined as: (3) (ui u) uc ¦ N 1 2
N
i 1
(wi w)
2
N
wc
¦ i 1
(4)
N 1
where, N is the number of time series values which was 24,000 in this study. The used ADV is a 10MHz Nortek Vectrino with a downward-looking probe, precision of ±0.1 mm s-1 and a sampling volume with a height of 5.5 mm. ADV signals are affected by Doppler noise, or white noise, associated with the measurement process. To remove possible aliasing effects, velocity time series were 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 SNR. Moreover, it has filters such as phase-space threshold despiking (first described by Goring and Nikora (2002)) and acceleration spike filter. The manufacturer suggests that when COR does not exceed 70 %, and SNR is less than 5 db, the instantaneous velocity measurements are dominated by acoustic noise and, as a rule of thumb, that these measurements should be discarded. To avoid the possible aliasing effect, the data with SNR less than 15 db and COR less than 70 % were discarded and the velocity time series data was passed through these two filters. Table 1 summarizes the measured and calculated parameters in this study. This table shows that the Froude number (Fr) varies from 0.1 to 0.2 and the Reynolds number (Re) changes from 0.1× 105 to 1.44×105. Also, the shear velocity (u*Re) was calculated by the Reynolds stress method. The turbulent event within a bursting cycle are quantified by the conditional statistics of the velocity fluctuations (u' and w'). The quadrant analysis was applied to investigate the effect of the vegetated banks and gravel bed in production of negative values in the Reynolds stress distribution. According to the quadrant analysis, there are four quadrants (i = 1 to 4) in u'-w' plane: 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 quadrant analysis was discussed in details by International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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(Willmarth and Lu, 1972; Ghisalberti and Nepf, 2006; Dey and Nath, 2010; Afzalimehr et al., 2011) and will not be considered here. 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 was introduced (Willmarth and Lu, 1972). The hole size H= 0 was taken into account in this study because it did not eliminate any value of Reynolds stress in four quadrants. Table 2 presents the percentage of time occupied by each kind of turbulence event in a bursting cycle. Table 2
Percentage of time occupied by each kind of turbulence event Outward Ejection Inward (Q1) (Q2) (Q3)
Accelerating flow Near the bed and the central axis Near the water surface and the central axis Near the bed and near the vegetated bank Near the water surface and near the vegetated bank Decelerating flow Near the bed and the central axis Near the water surface and the central axis Near the bed and near the vegetated bank Near the water surface and near the vegetated bank
Sweep (Q4)
20.03 27.29 25.50
30.20 22.33 26.81
18.80 26.00 23.53
30.97 24.38 24.16
26.99
23.79
25.67
23.55
19.26 27.69 25.10
28.44 22.77 26.54
18.15 27.49 23.50
34.15 22.05 24.86
27.40
23.90
26.99
22.71
3 Results 3.1 Stream-wise velocity profile Experimental studies imply that acceleration and deceleration play an important role in respect of the position of the maximum flow velocity (Graf and Altinakar, 1998). Figure 2 shows for the central axis of flume the maximum velocity (umax) occurs at y/h=0.2 for accelerating flow and at y/h=0.4 for decelerating flow. However, near the vegetation at the distances of 3cm and 6cm from the bank, the distribution of flow velocity exhibits a wavy profile under accelerating flow, but a convex profile for decelerating flow. For the case of decelerating flow, the closer to the vegetated banks, the closer the position of umax to the bed. Also, as shown in Fig. 2, the position of umax alters from y/h=0.2 along the central axis of the flume to y/h=0.8 near the vegetated bank at a distance of D=3 cm for accelerating flow. The occurrence of the maximum velocity below the water surface is called the dip-phenomenon which is due to secondary currents effect. The secondary currents are generated by anisotropy of turbulence due to the effects of vegetated banks and small aspect ratio. Theses secondary currents alter umax position in velocity distribution. The anisotropy term (v'2–w'2)/u2* was used to represent the effect of secondary currents by the stream-wise vorticity (Nezu and Nakagawa, 1993). Studies over smooth bed reported by Nezu and Nakagawa (1993) show that (v'2–w'2)/u2* promotes the generation of secondary currents and for the aspect ratio of W/h=2, the term (v'2–w'2)/u2* increases for a relative water depth of y/h>0.6. Figure 3 shows that for accelerating flow and aspect ratio of W/h <2, the value of (v'2–w'2)/u2* decreases up to a relative water depth of y/h=0.3, and then, remains nearly constant up to the water surface. However, for decelerating flow, (v'2–w'2)/u2* decreases up to a relative water depth of y/h = 0.2, and then, presents a convex form toward the water surface. It has been revealed that for both accelerating and decelerating flows in gravel-bed channels, the velocity profile in the inner region, limited by a relative water depth of y/h < 0.20, can be expressed by the log-law (Graf and Altinakar, 1998). In addition, Afzalimehr et al. (2011), Afzalimehr and Dey (2009) found the presence of secondary currents (the dip-phenomenon) and the vegetation over the bed and banks do not influence the log-law validity. In the outer layer (y/h>0.2), the measured velocity data are deviated from the log law. The reason for deviation of the log-law in outer region (y/h>0.2) is due to invalidity of constant shear stress in whole flow depth and the mixing length approximation.
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Fig. 2 Comparison of dimensionless streamwise velocity distribution in accelerating and decelerating flows
Fig. 3 Comparison of dimensionless profiles of vorticity production term ( (v' 2 w' 2 ) / u*2 for accelerating and decelerating flows
3.2 Velocity defect law Kármán revealed that the difference between the velocity in the outer layer and the velocity at the edge of the shear layer is independent of viscosity but is related to shear layer thickness (Schlichting, 1979). Accordingly, a velocity defect law was presented by Coles (White, 1994; Graf and Altinakar, 1998) as fellow: International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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u max u u
1
N
ln
§ y· y 2 ¸¸ cos 2 ¨¨ N © 2 ¹
(5)
The deviation of the measured velocity from the log-law in the outer layer of flow (0.2
Fig. 4 Comparison of dimensionless velocity-defect law distribution in accelerating and decelerating flows
3.3 Turbulence intensities distributions Results of the present study showed that for both accelerating and decelerating flows, the distribution of u c 2 u at the central axis of channel has concave shape. However, more data scatter is noticed for accelerating flow. Also, different distribution profiles of w c 2 u were observed under both accelerating and decorating flows at the central axis of flume. Song and Graf (1994), Kironoto and Graf (1995) and Song and Chiew (2001) demonstrated that turbulence intensities profiles have concave and - 194 -
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convex forms for accelerating and decelerating flows respectively. The distributions of
u c 2
u
and
along the central axis of the flume with vegetated banks are similar to those reported by Graf and Altinakar (1998) for bare banks. However, the generation of strong secondary currents by the joint effects of aspect ratio and vegetation causes a convex distribution for u c 2 u and w c 2 u under accelerating and decelerating flows near the banks (D= 3cm and D=6cm). Along the central axis of flume, and at D= 6 cm, the turbulence intensities were greater for accelerating flow near the bed; and away from the bed the turbulence intensities are nearly the same. However, at D= 3cm the turbulence intensities for decelerating flow are greater than those for accelerating flow (Fig. 5). Song and Graf (1994), Kironoto and Graf (1995) and Song and Chiew (2001) also showed that in decelerating flow, u c 2 u is larger than that in accelerating flow. w c 2
u
Fig. 5 Comparison of normalized streamwise ( u ' / u* ) and normalized vertical ( w' / u* ) turbulence intensities in accelerating and decelerating flows
3.4 Reynolds stress distribution The present study confirmed the results of Kironoto and Graf (1995) and Song and Chiew (2001) regarding the Reynolds stress distribution for both accelerating and decelerating flows at the center line of the flume where the effect of vegetated banks is weakest. Accordingly, the maximum Reynolds stress occurs at the bed for accelerating flow and at y/h =0.2 for decelerating flow for the central axis. The presence of vegetated banks caused considerable deviation of Reynolds shear stress from either the concave or convex shapes observed at the center line of flume and the reported studies in literature. Figure 6 shows a wavy distribution for Reynolds stress at distances of 3cm and 6cm from the vegetated banks for accelerating flow. On the other hand, for decelerating flow, a concave distribution of Reynolds stress is observed at the distances of 3 cm and 6 cm from the vegetated bank. It should be noted that based on momentum equation, the vertical distribution of Reynolds stress near channel bed should increase for decelerating flow. However, Fig. 6 shows that distribution of Reynolds stress has an opposite trend near International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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the vegetated banks (D= 3cm and D= 6 cm). In addition, for accelerating flow near the vegetated bank, a wavy distribution is observed for profiles of Reynolds stress.
Fig. 6 Comparison of the Reynolds shear stress distribution in accelerating and decelerating flows
4 Discussion The results of present study reveal that the vegetated banks and non-uniform flows have significant role on the distribution of velocity. Some studies over gravel bed with bare banks reveal that the dip-phenomenon can never be considered in decelerating flows (Kironoto and Graf, 1995; Song and Chiew, 2001). However, Fig. 3 shows that the vegetated banks enhance anisotropy in turbulence in v'-w' to generates strong secondary currents, leading to the occurrence of a dip-phenomenon for decelerating flow. Figure 6 shows that for both accelerating and decelerating flows at the central axis of flume the Reynolds stress values are positive near the bed but negative near the water surface. Table 2 and Fig. 7 show that for positive values of Reynolds stress near the bed in the central axis of the flume, the sweep and ejection on the average, occupy the higher percentage of time within a bursting cycle. However, near the water surface where Reynolds stress values are negative, the outward and inward occupy higher percentage of time in a bursting cycle. López et al. (1996) also found the connection between the sign of Reynolds shear stress and the dominant quadrants. They reported that the effects of sweep and ejection are dominant when Reynolds stress values are positive and the effects of the outward and inward are dominant when the Reynolds stress values are negative. - 196 -
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Fig. 7 Joint probability distributions of u ' / u* and w' / u* at the central axis of flume and near the vegetated banks: D = 3cm; (a) for accelerating flow (b) for decelerating flow International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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The idea that sweep and ejection are the most frequent events appears to be true only near the bed at the central axis of the flume. Figure 7 indicates that the distribution of (u/u*)-(w/w*) is tilted toward the second and fourth for the central axis of the flume, but no tilting is observed near the vegetated banks. Also, Fig.7 illustrates that close the vegetated bank and near the bed the distribution of (u/u*)-(w/w*) for accelerating and decelerating flows are flat, showing a light dominance of the outward and ejection. The negative sign of Reynolds stress near the bed and close the vegetated bank can be attributed to the superiority of ejection and the outward contribution. On the other hand, near the water surface and close the vegetated bank, although the outward and inward contributions are dominant, no negative sign is observed in the Reynolds stress distribution (Fig. 6). This may attribute to interaction of accelerating or decelerating flows with vegetated banks and secondary currents. Finally, Table 2 shows that accelerating and decelerating flows at the same locations (near the bed or near the water surface) have not significant difference on percentage of time occupied by each kind of turbulent event within a bursting cycle. For example, comparison of the first row in accelerating flow with the same row in decelerating flow in Table 2 demonstrates similar percentages of time occupied by each event. However, accelerating and decelerating flows affect the shape of joint probability distributions of u'/u* and w'/u* (Fig. 7). 5 Conclusions The following results can be drawn from this experimental study: (1) Graf and Altinakar’s criterion works well in gravel-bed channel with the vegetated banks to parameterize non-uniformity of flow as both accelerating and decelerating flows. (2) Near the vegetated banks at the distances of 3cm and 6cm, velocity distribution exhibits a wavy shape under accelerating flow and a convex shape for decelerating flow. Significant dip phenomenon is observed in velocity profiles under decelerating flow, while such a phenomenon has not been reported in literature for flow over gravel bed and bare banks with small aspect ratio (W/h<5). The present study reveals that the position of umax for decelerating flow is lower than that for accelerating flow. (3) Application of the anisotropy generation term (v'2–w'2)/u2* reveals that for accelerating flow with an aspect ratio of W/h <2, this term increases up to a relative water depth of y/h=0.3, and then remains nearly constant up to the water surface. However, for decelerating flow, this term increases up to a relative water depth of y/h = 0.2, and then shows a convex shape toward the water surface. (4) The velocity-defect law cannot be applied for flow over gravel bed with the vegetated banks under accelerating and decelerating flows. (5) Near the vegetated banks, the turbulence intensities (u'/u* and w'/u*) display convex distribution for both accelerating and decelerating flows. (6) Accelerating and decelerating flows do not reveal a significant difference on percentages of time occupied by each kind of turbulent event within bursting cycle. (7) The results of this study can be applied for channels with small aspect ratio where the effect of secondary currents is significant. The future work should be developed in natural channels to explore the interaction of large aspect ratio and the vegetated banks on the turbulence structure under non-uniform flow conditions. References Afzalimehr H. Moghbel R., Ghalichand J., and Sui J. 2011, Investigation of turbulence characteristics in channel with dense vegetation over bed. International Journal of Sediment Research, Vol. 26, No. 3, In press. Afzalimehr H. 2010, Effect of flow non-uniformity on velocity and turbulence intensities in flow over a cobble-bed. Hydrological Process Journal, Vol. 24, No. 3, pp. 331–341. Afzalimehr H., Fazel E., and Singh V. J. 2010, Effect of vegetation on banks on distributions of velocity and Reynolds stress under accelerating flow. Journal of Hydrologic Engineering American Society of Civil Engineers (ASCE), Vol. 15, No. 9, pp. 708–713. 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. and Anctil F. 2000, Accelerating shear velocity in gravel bed channels. Hydrological Science Journal, IAHR, Vol. 45, No. 1, pp. 113–124. Cardoso A. H., Graf W. H., and Gust G. 1991, Steady gradually accelerating flow in a smooth open channel. Hydraulic Research Journal, Delft, The Netherlands, Vol. 29, No. 4, pp. 525–543.
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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. 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. Goring D. G. and Nikora V. I. 2002, Despiking acoustic Doppler velocimeter data. Journal of Hydraulic Engineering (ASCE ), Vol. 128, No. 1, pp. 117–126. Graf W. H. and Altinakar M. S. 1993, Hydraulique fluvial. Tome 1, Presses Polytechniques et Univ. Romandes, Lausanne, CH. Graf W. H. and Altinakar M. S. 1998, Fluvial Hydraulics, Flow and transport processes in channels of simple geometry. John Wiley and Sons, New York, p. 681. Houra T., Tsuji T., and Nagano Y. 2000, Effects of adverse pressure gradient on quasi-coherent structures in turbulent boundary layer. International Journal of Heat and Fluid Flow, Vol. 21, pp. 304–311. Kironoto B. and Graf W. H. 1994, Turbulence characteristics in rough uniform open-channel flow. Proceedings of the Institution of Civil Engineers - Water Maritime and Energy, Vol. 106, pp. 333–344. Kironoto B. and Graf W. H. 1995, Turbulence characteristics in rough nonuniform open-channel flow. Proceedings of the Institution of Civil Engineers - Water Maritime and Energy, Vol. 112, pp. 316–348. López F., Niño Y., and García M. H. 1996, Turbulent coherent structures in open-channel flows with smooth beds. Hydraulic Engineering in Mexico, Vol. 11, No. 1, pp. 5–13. López F. and García M. H. 2001, Mean flow and turbulence structure of open channel flow through non-emergent vegetation. Journal of Hydraulic Engineering (ASCE), Vol. 127, No. 5, pp. 392–402. Nasiri E., Afzalimehr H., and Singh V. P. 2011, Effect of bed forms and vegetated banks on velocity distributions and turbulent flow structure. Journal Hydrologic Engineering, ASCE, Vol. 16, No. 6, pp. 495–507. Nezu I. and Nakagawa H. 1993, Turbulence in Open-Channel Flows. IAHR-Monograph, Balkema Netherlands. Schlichting, H. _1979_. Boundary layer theory, 7th Ed., McGraw-Hill, New York. Song T. and Chiew Y. M. 2001, Turbulence measurement in non uniform open channel flow using Acoustic Doppler Velocimeter (ADV). Journal of Engineering Mechanics (ASCE), Vol. 127, No. 3, pp. 219–232. Song T. and Graf W. H. 1994, Nonuniform open-channel flow over a rough bed. Journal of Hydroscience and Hydraulic Engineering, Vol. 12, No. 1, pp. 1–25. Stone M. C. and Hotchkiss R. H., 2007, Evaluating velocity measurement techniques in shallow streams. Journal of Hydraulic Research, Vol. 45, No. 6, pp. 752–762. Tu H. and Graf W. H. 1993, Friction velocity in unsteady open-channel flow over gravel beds. Journal of Hydraulic Research, Vol. 31, No. 1, pp. 99–110. Wahl T. L. 2000, Analyzing ADV Data Using Win ADV. Joint Conference on Water Resources Engineering and Water Resources Planning and Management, Minneapolis, MN, United States. pp. 1–10. White F. M. 1974, Viscous Fluid Flow. McGraw-Hill, New York. White B. and Nepf H. 2007, Shear instability and coherent structures in a flow adjacent to a porous layer. Journal of Fluid Mechanics, Vol. 593, pp. 1–32. White B. L. and Nepf H. 2008, A vortex-based model of velocity and shear stress in a partially vegetated shallow channel. Water Resources Research, Vol. 44, No. 1, pp. W01412. Willmarth W. W. and Lu S. S. 1972, Structure of Reynolds stress near the wall. Journal of Fluid Mechanics, Vol. 55, pp. 65–92. Notation D = Distances from the vegetation bank; d50 = Median diameter of sediment particles; d84 = 84% finer particle diameters; d16 = 16% finer particle diameters; h = Flow depth; ks = Nikuradse’s equivalent roughness; N = Number of time series values; S0 = Bed slope; u = Stream-wise component of mean flow velocity; uf = Stream-wise component of velocity fluctuation; ui = Stream-wise component of instantaneous velocity; u ' = Stream-wise component of turbulence intensity; umax = Maximum velocity observed over a velocity profile; u* = Shear velocity; v' = Lateral component of turbulence intensity; W = Width of channel; International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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w wf wi w' x y N g
= Vertical component of mean flow velocity; = Vertical component of velocity fluctuation; = Vertical component of instantaneous velocity; = Vertical component of turbulence intensity; = Distance from the flume entrance; = Distance from the bed; = Dimensionless longitudinal pressure gradient parameter; = Thickness of boundary-layer; = Von Karman’s constant; = Coles' parameter; = Geometric standard deviation; = Shear stress; = An adjusting coefficient of median grain size.
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Effects of accelerating and decelerating flows in a channel with vegetated banks and gravel bed Hossein AFZALIMEHR1, Elham Fazel NAJAFABADI2, and Jacques GALLICHAND3
Abstract Experiments were conducted in an 8 m long, 40 cm wide, and 60 cm deep re-circulating flume with vegetated banks and gravel bed to study the effects of accelerating and decelerating flows on the flow structure. Significant dip phenomenon was observed in velocity profiles under decelerating flow and the velocity defect law was not suitable due to the effect of vegetated banks. Near the vegetated banks, the turbulence intensities illustrated convex distribution for both accelerating and decelerating flows. Application of quadrant analysis revealed that the effect of vegetated banks is important on the flow structure and the Reynolds stress distribution. Accelerating and decelerating flows did not show a significant difference on percentage of time occupied by each kind of turbulent event within bursting cycle, but affected the shape of joint probability distributions of turbulent intensities in the horizontal and vertical directions. Key Words: Vegetated bank, Decelerating and accelerating flows, Gravel bed, Reynolds stress
1 Introduction Knowledge of interactions of sediment on riverbed, vegetation in river banks and non-uniform flow (accelerating and decelerating flows) are crucial to study sediment transport and friction factor. In natural streams, accelerating and decelerating flows are complex phenomenons which are not fully understood although they are frequently observed in practice. From fluvial hydraulic point of view, flow over stoss and lee sides of dunes in sand-bed rivers or flow over riffles and pools of gravel-bed rivers are good examples to illustrate acceleration and deceleration flows. Studies in open channels with bare banks and coarse-bed indicate that the accelerating flow suppresses the generation of turbulence, while the decelerating flow has the opposite effect (Houra et al., 2000). Some attempts have been made to study the effect of non-uniformity on the velocity distribution and turbulence characteristics of the open channel flow with bare banks. Cardoso et al. (1991) studied gradually accelerated flows in a smooth channel and concluded that the velocity distribution cannot be represented for the total flow depth by the universal log-law except at regions very close to the bed y/h<0.2, where y is distance from the bed and h is the total flow depth. Song and Graf (1994), Kironoto and Graf (1995), Song and Chiew (2001) detected velocity profiles, turbulence intensities and Reynolds stress distributions for both accelerating and decelerating flows in gravel-bed channel and found that: 1) the maximum velocity occurs below the water surface for accelerating flow and at the water surface for decelerating flow. 2) the standard log-law velocity profile works well for y/h<0.2 for accelerating and decelerating flows. 3) Reynolds stress and turbulence intensities distributions for accelerating flow are concave and for decelerating flow are convex. 4) The wake function works well under accelerating and decelerating flows. 1
Assoc. Prof., 2 Graduate Student, Department of Water Engineering, Isfahan University of Technology, 84156-83111, Iran, E-mail: [email protected] 3 Prof., Département des sols et de génie agroalimentaire Pavillon Paul-Comtois, Université Laval, St-Foy, QC, Canada, E-mail: [email protected] Note: The original manuscript of this paper was received in July 2010. The revised version was received in Nov. 2011. Discussion open until Mar. 2013. - 188 -
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Vegetation occupies a pivotal role in river in fluvial geomorphology investigations. In last decade, many studies have been reported on the velocity profiles and the turbulent characteristics of vegetated channels (López and García, 2001; White and Nepf, 2007; White and Nepf, 2008; Afzalimehr and Dey, 2009; Nasiri et al., 2011; Afzalimehr et al., 2011). Afzalimehr and Dey (2009), Nasiri et al. (2010) found that under uniform flow conditions, vegetated banks in gravel-bed channels changes the pattern of velocity and Reynolds stress distributions. Also, Nasiri et al. (2011) found similar patterns for velocity and Reynolds stress over gravel dunes. Accordingly, the maximum velocity occurs below the water surface and the Reynolds stress distribution does not follow linear trend and its shape depends on the distance from the vegetated bank. Afzalimehr et al. (2010) investigated the accelerating flow in a channel with gravel bed, vegetated banks and found an S shape Reynolds stress distribution near the vegetated banks. They found that the occurrence umax below the water surface and nonlinear distribution of Reynolds stress is due to secondary currents and the anisotropy in turbulence in the vegetated banks channels. Also, above studies showed negative values in Reynolds stress distribution near the water surface and the zero shear stress value below the water surface. Nezu and Nakagawa (1993) showed that the negative values of Reynolds stress in near the water surface is in agreement with the fact that du/dy is also negative in this region. In addition, the negative values were likely linked to proximity to a vegetated bank. López et al. (1996) reported the connection between the sign of Reynolds shear stress and the dominant events in bursting process. Despite the importance of interaction of vegetated bank and non-uniform flow over gravel-bed channels, no comparative study has been reported to describe the effect of interaction of flow non-uniformity and vegetated banks on turbulence intensities and the Reynolds stress distributions. It is obvious that a laboratory work cannot produce a complete picture of turbulent flow characteristics in rivers because of complex interactions of many unknown factors in fluvial processes, but can improve our understanding in environmental hydraulic. Therefore, the objective of this experimental research is to investigate and compare the effects of accelerating and decelerating flows on the turbulent flow characteristics in a channel with vegetated banks and gravel bed. 2 Experimental setup Experiments have been carried out in an 8 m long, 40 cm wide, and 60 cm deep re-circulating flume at the Hydraulics Laboratory of Isfahan University of Technology, Iran. A tail gate located at the end of the flume was used to control water level during experiments. In this experimental study, the flow depth has been measured by using a point gauge with 1 mm increment. The grain size of gravel particles had a median diameter (d50) of 2 cm and the geometric standard deviation g=(d84/d16)0.5 of particle size distribution was 1.14, where d84 and d16 are 84% and 16% finer particle diameters, respectively. For flow over rough surfaces, a precise definition of the distance from the bed origin (i.e., y = 0) would be difficult. The virtual origin is a very small fraction of the roughness height (ks). Afzalimehr and Anctil (2000) and Kironoto and Graf (1994) performed their experiments on gravel beds with d50=2.54 cm and d50=2.3 cm, respectively, they applied ks=0.2d50. On the other hand, Tu and Graf (1993) and Song and Graf (1994) applied ks=0.25d50. Further, Song and Chiew (2001) found when d50=2.6 cm, ks=0.25d50. The reference level where u = 0 was obtained using a trial and error procedure based on the highest R2 between u and Ln [(y + d50)/d50], where, u was the mean-point velocity, d50 allowed for the adjustment of zero plane displacement (y = 0), y was distance from the bed and is an adjusting coefficient of median grain size. The theoretical mean bed surface was not at the upper surface of the protruding particles, but a distance d50 below it. Based on the trial and error process, the value of ks = d50 was selected for this study. Rice stems were used to illustrate the effect of vegetated banks. In order to prevent the flexibility of rice stems in water, the rice stems were stuck over a plastic carpet. In addition, to keep the stems without flexibility on the flume walls under the movement of water, rice stems were stitched by a thin cotton wire over the plastic carpet. Finally, the plastic carpet was stuck to the flume walls. The thickness of vegetation cover on flume walls was 0.5 cm. The stem density was calculated as the number of stems per unit length (400 stem m-1). The mean diameter of rice stems was d50=0.74 cm. Accelerating and decelerating flows discussed in this paper are the steady flow whose depths vary gradually along the flume. To determine if the flow is non uniform along the flume, flow depths have been measured at a distance of 5.0m, 5.50m and 6.00 m from the entrance cross section respectively. In addition, the criterion proposed by Graf and Altinakar (1993; 1998) has been used to parameterize flow International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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non-uniformity. Based on this criterion, the dimensionless longitudinal pressure gradient parameter is defined as: E
hª §
dh · º
(1)
¸» «J ¨ S 0 W ¬ © dx ¹ ¼
where, dh/dx is the longitudinal variation in water depth h, is the specific gravity of water, S0 is the bed slope and is the bed shear stress. Graf and Altinakar (1993; 1998) demonstrated that for accelerating flow < -1 and for decelerating flow > -1. As the values of in Table 1 show, to parameterize non-uniformity of flow as accelerating and decelerating flows, the Graf and Altinakar’s criterion works well for flow in channels with vegetated banks. Accordingly, the ranges of for decelerating flow is 8.99 < < 11.38 and for accelerating flow is -7.49 < < -5.69. Similar to the published work of Afzalimehr (2010) regarding flow over coarse-bed channels with bare banks, the results and the figures in this paper are presented only for the section of 6 m from the flume entrance. Table 1 Distance Distance from Non-uniform from inlet vegetation flow (m) (m) 5 0.03 0.06 0.19 5.5 0.03 Accelerating 0.06 flow 0.19 6 0.03 0.06 0.19 5 0.03 0.06 0.19 Decelerating 5.5 0.03 flow 0.06 0.19 6 0.03 0.06
Summary of experimental data
S0
h (m)
D50 (m)
um (m s-1)
Fr
Re (× 105)
u*Re (cm s-1)
-0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.277 0.277 0.277 0.266 0.266 0.266 0.256 0.256 0.256 0.234 0.234 0.234 0.245 0.245 0.245 0.256 0.256
0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.16 0.20 0.25 0.18 0.22 0.25 0.20 0.24 0.26 0.18 0.26 0.33 0.18 0.24 0.31 0.16 0.21
0.10 0.12 0.15 0.12 0.14 0.15 0.13 0.15 0.17 0.12 0.16 0.22 0.12 0.16 0.20 0.10 0.13
0.10 0.93 1.15 0.84 1.01 1.12 0.88 1.07 1.17 0.82 1.09 1.44 0.81 1.06 1.35 0.72 0.94
-7.45 -7.45 -7.45 -5.92 -5.92 -5.92 -5.69 -5.69 -5.69 8.99 8.99 8.99 9.57 9.57 9.57 11.38 11.38
0.98 1.25 1.64 1.41 1.39 1.64 1.33 1.24 1.61 2.12 2.37 2.26 2.02 2.50 2.24 1.68 2.12
To obtain accelerating and decelerating flows along the flow direction, the tailgate installed downstream were carefully adjusted in each experiment. For the case of accelerating flow where flow depth decreased along flow direction, an inverse bed slope (negative bed slope in flow direction) was established by gravel on the bed. To generate a decelerating flow where flow depth increased in the flow direction, a positive bed slope was created using gravel materials on the flume bed. A gravel bed slope of -%2 was used to create accelerating flow and a gravel bed slope of +%2 for decelerating flow. Figure 1 shows a schematic of accelerating and decelerating flows in the flume. The flow was allowed to stabilize for about 1 hour before an Acoustic Doppler Velocimeter (ADV) was used to measure the instantaneous velocities. The flume reach for measurement was situated between 5.0 < x (m) < 6.0, where x was the distance from the flume entrance. Within this measuring reach, the flow was considered non-uniform (Table 1). Three cross sections of 5m, 5.5m and 6m along this measuring reach were chosen for conducting measurements of hydraulic parameters. To investigate the influence of vegetated banks on flow velocity, turbulence intensities and the Reynolds stress at each cross section, flow velocities were measured at different distances from the vegetated banks (D = 0.03m, 0.06m and 0.19 m). The number of points for measuring velocity at each cross section varied from 29 to 34, depending on water depth. For each measuring point, the duration of data acquisition was 2 minutes, so that with a sampling frequency of 200 Hz, 24,000 instantaneous velocity measurements were obtained. The sampling duration was selected 2 min in order to have a statistically time independent average velocity. The adequacy of the 2 minute sample duration was confirmed by collecting data at several points for 20 min and evaluating divergence of velocity - 190 -
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statistics (mean and standard deviation). Stone and Hotchkiss (2007) showed that the ADV velocity data stabilized at sampling times of approximately 100 sec. Therefore, the 2 min ADV sampling time was considered adequate in this study.
Fig. 1 Schematic of experimental setup of accelerating and decelerating flows
The mean point velocities, the turbulence intensity, and the Reynolds stress were determined using instantaneous velocity measurements. In this study, mean flow velocity components (u, w) and velocity fluctuation components in turbulent flow (uf, wf) corresponding to the stream-wise (or longitudinal), and vertical directions, respectively. The velocity fluctuations were defined as: °u f ui u ® (2) °¯w f wi w where ui, and wi are the instantaneous velocities, and u and w are the mean-point velocities in longitudinal and vertical directions respectively. The root mean square (RMS) of velocity fluctuations (turbulence intensities) were determined as: (3) (ui u) uc ¦ N 1 2
N
i 1
(wi w)
2
N
wc
¦ i 1
(4)
N 1
where, N is the number of time series values which was 24,000 in this study. The used ADV is a 10MHz Nortek Vectrino with a downward-looking probe, precision of ±0.1 mm s-1 and a sampling volume with a height of 5.5 mm. ADV signals are affected by Doppler noise, or white noise, associated with the measurement process. To remove possible aliasing effects, velocity time series were 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 SNR. Moreover, it has filters such as phase-space threshold despiking (first described by Goring and Nikora (2002)) and acceleration spike filter. The manufacturer suggests that when COR does not exceed 70 %, and SNR is less than 5 db, the instantaneous velocity measurements are dominated by acoustic noise and, as a rule of thumb, that these measurements should be discarded. To avoid the possible aliasing effect, the data with SNR less than 15 db and COR less than 70 % were discarded and the velocity time series data was passed through these two filters. Table 1 summarizes the measured and calculated parameters in this study. This table shows that the Froude number (Fr) varies from 0.1 to 0.2 and the Reynolds number (Re) changes from 0.1× 105 to 1.44×105. Also, the shear velocity (u*Re) was calculated by the Reynolds stress method. The turbulent event within a bursting cycle are quantified by the conditional statistics of the velocity fluctuations (u' and w'). The quadrant analysis was applied to investigate the effect of the vegetated banks and gravel bed in production of negative values in the Reynolds stress distribution. According to the quadrant analysis, there are four quadrants (i = 1 to 4) in u'-w' plane: 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 quadrant analysis was discussed in details by International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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(Willmarth and Lu, 1972; Ghisalberti and Nepf, 2006; Dey and Nath, 2010; Afzalimehr et al., 2011) and will not be considered here. 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 was introduced (Willmarth and Lu, 1972). The hole size H= 0 was taken into account in this study because it did not eliminate any value of Reynolds stress in four quadrants. Table 2 presents the percentage of time occupied by each kind of turbulence event in a bursting cycle. Table 2
Percentage of time occupied by each kind of turbulence event Outward Ejection Inward (Q1) (Q2) (Q3)
Accelerating flow Near the bed and the central axis Near the water surface and the central axis Near the bed and near the vegetated bank Near the water surface and near the vegetated bank Decelerating flow Near the bed and the central axis Near the water surface and the central axis Near the bed and near the vegetated bank Near the water surface and near the vegetated bank
Sweep (Q4)
20.03 27.29 25.50
30.20 22.33 26.81
18.80 26.00 23.53
30.97 24.38 24.16
26.99
23.79
25.67
23.55
19.26 27.69 25.10
28.44 22.77 26.54
18.15 27.49 23.50
34.15 22.05 24.86
27.40
23.90
26.99
22.71
3 Results 3.1 Stream-wise velocity profile Experimental studies imply that acceleration and deceleration play an important role in respect of the position of the maximum flow velocity (Graf and Altinakar, 1998). Figure 2 shows for the central axis of flume the maximum velocity (umax) occurs at y/h=0.2 for accelerating flow and at y/h=0.4 for decelerating flow. However, near the vegetation at the distances of 3cm and 6cm from the bank, the distribution of flow velocity exhibits a wavy profile under accelerating flow, but a convex profile for decelerating flow. For the case of decelerating flow, the closer to the vegetated banks, the closer the position of umax to the bed. Also, as shown in Fig. 2, the position of umax alters from y/h=0.2 along the central axis of the flume to y/h=0.8 near the vegetated bank at a distance of D=3 cm for accelerating flow. The occurrence of the maximum velocity below the water surface is called the dip-phenomenon which is due to secondary currents effect. The secondary currents are generated by anisotropy of turbulence due to the effects of vegetated banks and small aspect ratio. Theses secondary currents alter umax position in velocity distribution. The anisotropy term (v'2–w'2)/u2* was used to represent the effect of secondary currents by the stream-wise vorticity (Nezu and Nakagawa, 1993). Studies over smooth bed reported by Nezu and Nakagawa (1993) show that (v'2–w'2)/u2* promotes the generation of secondary currents and for the aspect ratio of W/h=2, the term (v'2–w'2)/u2* increases for a relative water depth of y/h>0.6. Figure 3 shows that for accelerating flow and aspect ratio of W/h <2, the value of (v'2–w'2)/u2* decreases up to a relative water depth of y/h=0.3, and then, remains nearly constant up to the water surface. However, for decelerating flow, (v'2–w'2)/u2* decreases up to a relative water depth of y/h = 0.2, and then, presents a convex form toward the water surface. It has been revealed that for both accelerating and decelerating flows in gravel-bed channels, the velocity profile in the inner region, limited by a relative water depth of y/h < 0.20, can be expressed by the log-law (Graf and Altinakar, 1998). In addition, Afzalimehr et al. (2011), Afzalimehr and Dey (2009) found the presence of secondary currents (the dip-phenomenon) and the vegetation over the bed and banks do not influence the log-law validity. In the outer layer (y/h>0.2), the measured velocity data are deviated from the log law. The reason for deviation of the log-law in outer region (y/h>0.2) is due to invalidity of constant shear stress in whole flow depth and the mixing length approximation.
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Fig. 2 Comparison of dimensionless streamwise velocity distribution in accelerating and decelerating flows
Fig. 3 Comparison of dimensionless profiles of vorticity production term ( (v' 2 w' 2 ) / u*2 for accelerating and decelerating flows
3.2 Velocity defect law Kármán revealed that the difference between the velocity in the outer layer and the velocity at the edge of the shear layer is independent of viscosity but is related to shear layer thickness (Schlichting, 1979). Accordingly, a velocity defect law was presented by Coles (White, 1994; Graf and Altinakar, 1998) as fellow: International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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u max u u
1
N
ln
§ y· y 2 ¸¸ cos 2 ¨¨ N © 2 ¹
(5)
The deviation of the measured velocity from the log-law in the outer layer of flow (0.2
Fig. 4 Comparison of dimensionless velocity-defect law distribution in accelerating and decelerating flows
3.3 Turbulence intensities distributions Results of the present study showed that for both accelerating and decelerating flows, the distribution of u c 2 u at the central axis of channel has concave shape. However, more data scatter is noticed for accelerating flow. Also, different distribution profiles of w c 2 u were observed under both accelerating and decorating flows at the central axis of flume. Song and Graf (1994), Kironoto and Graf (1995) and Song and Chiew (2001) demonstrated that turbulence intensities profiles have concave and - 194 -
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convex forms for accelerating and decelerating flows respectively. The distributions of
u c 2
u
and
along the central axis of the flume with vegetated banks are similar to those reported by Graf and Altinakar (1998) for bare banks. However, the generation of strong secondary currents by the joint effects of aspect ratio and vegetation causes a convex distribution for u c 2 u and w c 2 u under accelerating and decelerating flows near the banks (D= 3cm and D=6cm). Along the central axis of flume, and at D= 6 cm, the turbulence intensities were greater for accelerating flow near the bed; and away from the bed the turbulence intensities are nearly the same. However, at D= 3cm the turbulence intensities for decelerating flow are greater than those for accelerating flow (Fig. 5). Song and Graf (1994), Kironoto and Graf (1995) and Song and Chiew (2001) also showed that in decelerating flow, u c 2 u is larger than that in accelerating flow. w c 2
u
Fig. 5 Comparison of normalized streamwise ( u ' / u* ) and normalized vertical ( w' / u* ) turbulence intensities in accelerating and decelerating flows
3.4 Reynolds stress distribution The present study confirmed the results of Kironoto and Graf (1995) and Song and Chiew (2001) regarding the Reynolds stress distribution for both accelerating and decelerating flows at the center line of the flume where the effect of vegetated banks is weakest. Accordingly, the maximum Reynolds stress occurs at the bed for accelerating flow and at y/h =0.2 for decelerating flow for the central axis. The presence of vegetated banks caused considerable deviation of Reynolds shear stress from either the concave or convex shapes observed at the center line of flume and the reported studies in literature. Figure 6 shows a wavy distribution for Reynolds stress at distances of 3cm and 6cm from the vegetated banks for accelerating flow. On the other hand, for decelerating flow, a concave distribution of Reynolds stress is observed at the distances of 3 cm and 6 cm from the vegetated bank. It should be noted that based on momentum equation, the vertical distribution of Reynolds stress near channel bed should increase for decelerating flow. However, Fig. 6 shows that distribution of Reynolds stress has an opposite trend near International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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the vegetated banks (D= 3cm and D= 6 cm). In addition, for accelerating flow near the vegetated bank, a wavy distribution is observed for profiles of Reynolds stress.
Fig. 6 Comparison of the Reynolds shear stress distribution in accelerating and decelerating flows
4 Discussion The results of present study reveal that the vegetated banks and non-uniform flows have significant role on the distribution of velocity. Some studies over gravel bed with bare banks reveal that the dip-phenomenon can never be considered in decelerating flows (Kironoto and Graf, 1995; Song and Chiew, 2001). However, Fig. 3 shows that the vegetated banks enhance anisotropy in turbulence in v'-w' to generates strong secondary currents, leading to the occurrence of a dip-phenomenon for decelerating flow. Figure 6 shows that for both accelerating and decelerating flows at the central axis of flume the Reynolds stress values are positive near the bed but negative near the water surface. Table 2 and Fig. 7 show that for positive values of Reynolds stress near the bed in the central axis of the flume, the sweep and ejection on the average, occupy the higher percentage of time within a bursting cycle. However, near the water surface where Reynolds stress values are negative, the outward and inward occupy higher percentage of time in a bursting cycle. López et al. (1996) also found the connection between the sign of Reynolds shear stress and the dominant quadrants. They reported that the effects of sweep and ejection are dominant when Reynolds stress values are positive and the effects of the outward and inward are dominant when the Reynolds stress values are negative. - 196 -
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Fig. 7 Joint probability distributions of u ' / u* and w' / u* at the central axis of flume and near the vegetated banks: D = 3cm; (a) for accelerating flow (b) for decelerating flow International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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The idea that sweep and ejection are the most frequent events appears to be true only near the bed at the central axis of the flume. Figure 7 indicates that the distribution of (u/u*)-(w/w*) is tilted toward the second and fourth for the central axis of the flume, but no tilting is observed near the vegetated banks. Also, Fig.7 illustrates that close the vegetated bank and near the bed the distribution of (u/u*)-(w/w*) for accelerating and decelerating flows are flat, showing a light dominance of the outward and ejection. The negative sign of Reynolds stress near the bed and close the vegetated bank can be attributed to the superiority of ejection and the outward contribution. On the other hand, near the water surface and close the vegetated bank, although the outward and inward contributions are dominant, no negative sign is observed in the Reynolds stress distribution (Fig. 6). This may attribute to interaction of accelerating or decelerating flows with vegetated banks and secondary currents. Finally, Table 2 shows that accelerating and decelerating flows at the same locations (near the bed or near the water surface) have not significant difference on percentage of time occupied by each kind of turbulent event within a bursting cycle. For example, comparison of the first row in accelerating flow with the same row in decelerating flow in Table 2 demonstrates similar percentages of time occupied by each event. However, accelerating and decelerating flows affect the shape of joint probability distributions of u'/u* and w'/u* (Fig. 7). 5 Conclusions The following results can be drawn from this experimental study: (1) Graf and Altinakar’s criterion works well in gravel-bed channel with the vegetated banks to parameterize non-uniformity of flow as both accelerating and decelerating flows. (2) Near the vegetated banks at the distances of 3cm and 6cm, velocity distribution exhibits a wavy shape under accelerating flow and a convex shape for decelerating flow. Significant dip phenomenon is observed in velocity profiles under decelerating flow, while such a phenomenon has not been reported in literature for flow over gravel bed and bare banks with small aspect ratio (W/h<5). The present study reveals that the position of umax for decelerating flow is lower than that for accelerating flow. (3) Application of the anisotropy generation term (v'2–w'2)/u2* reveals that for accelerating flow with an aspect ratio of W/h <2, this term increases up to a relative water depth of y/h=0.3, and then remains nearly constant up to the water surface. However, for decelerating flow, this term increases up to a relative water depth of y/h = 0.2, and then shows a convex shape toward the water surface. (4) The velocity-defect law cannot be applied for flow over gravel bed with the vegetated banks under accelerating and decelerating flows. (5) Near the vegetated banks, the turbulence intensities (u'/u* and w'/u*) display convex distribution for both accelerating and decelerating flows. (6) Accelerating and decelerating flows do not reveal a significant difference on percentages of time occupied by each kind of turbulent event within bursting cycle. (7) The results of this study can be applied for channels with small aspect ratio where the effect of secondary currents is significant. The future work should be developed in natural channels to explore the interaction of large aspect ratio and the vegetated banks on the turbulence structure under non-uniform flow conditions. References Afzalimehr H. Moghbel R., Ghalichand J., and Sui J. 2011, Investigation of turbulence characteristics in channel with dense vegetation over bed. International Journal of Sediment Research, Vol. 26, No. 3, In press. Afzalimehr H. 2010, Effect of flow non-uniformity on velocity and turbulence intensities in flow over a cobble-bed. Hydrological Process Journal, Vol. 24, No. 3, pp. 331–341. Afzalimehr H., Fazel E., and Singh V. J. 2010, Effect of vegetation on banks on distributions of velocity and Reynolds stress under accelerating flow. Journal of Hydrologic Engineering American Society of Civil Engineers (ASCE), Vol. 15, No. 9, pp. 708–713. 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. and Anctil F. 2000, Accelerating shear velocity in gravel bed channels. Hydrological Science Journal, IAHR, Vol. 45, No. 1, pp. 113–124. Cardoso A. H., Graf W. H., and Gust G. 1991, Steady gradually accelerating flow in a smooth open channel. Hydraulic Research Journal, Delft, The Netherlands, Vol. 29, No. 4, pp. 525–543.
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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. 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. Goring D. G. and Nikora V. I. 2002, Despiking acoustic Doppler velocimeter data. Journal of Hydraulic Engineering (ASCE ), Vol. 128, No. 1, pp. 117–126. Graf W. H. and Altinakar M. S. 1993, Hydraulique fluvial. Tome 1, Presses Polytechniques et Univ. Romandes, Lausanne, CH. Graf W. H. and Altinakar M. S. 1998, Fluvial Hydraulics, Flow and transport processes in channels of simple geometry. John Wiley and Sons, New York, p. 681. Houra T., Tsuji T., and Nagano Y. 2000, Effects of adverse pressure gradient on quasi-coherent structures in turbulent boundary layer. International Journal of Heat and Fluid Flow, Vol. 21, pp. 304–311. Kironoto B. and Graf W. H. 1994, Turbulence characteristics in rough uniform open-channel flow. Proceedings of the Institution of Civil Engineers - Water Maritime and Energy, Vol. 106, pp. 333–344. Kironoto B. and Graf W. H. 1995, Turbulence characteristics in rough nonuniform open-channel flow. Proceedings of the Institution of Civil Engineers - Water Maritime and Energy, Vol. 112, pp. 316–348. López F., Niño Y., and García M. H. 1996, Turbulent coherent structures in open-channel flows with smooth beds. Hydraulic Engineering in Mexico, Vol. 11, No. 1, pp. 5–13. López F. and García M. H. 2001, Mean flow and turbulence structure of open channel flow through non-emergent vegetation. Journal of Hydraulic Engineering (ASCE), Vol. 127, No. 5, pp. 392–402. Nasiri E., Afzalimehr H., and Singh V. P. 2011, Effect of bed forms and vegetated banks on velocity distributions and turbulent flow structure. Journal Hydrologic Engineering, ASCE, Vol. 16, No. 6, pp. 495–507. Nezu I. and Nakagawa H. 1993, Turbulence in Open-Channel Flows. IAHR-Monograph, Balkema Netherlands. Schlichting, H. _1979_. Boundary layer theory, 7th Ed., McGraw-Hill, New York. Song T. and Chiew Y. M. 2001, Turbulence measurement in non uniform open channel flow using Acoustic Doppler Velocimeter (ADV). Journal of Engineering Mechanics (ASCE), Vol. 127, No. 3, pp. 219–232. Song T. and Graf W. H. 1994, Nonuniform open-channel flow over a rough bed. Journal of Hydroscience and Hydraulic Engineering, Vol. 12, No. 1, pp. 1–25. Stone M. C. and Hotchkiss R. H., 2007, Evaluating velocity measurement techniques in shallow streams. Journal of Hydraulic Research, Vol. 45, No. 6, pp. 752–762. Tu H. and Graf W. H. 1993, Friction velocity in unsteady open-channel flow over gravel beds. Journal of Hydraulic Research, Vol. 31, No. 1, pp. 99–110. Wahl T. L. 2000, Analyzing ADV Data Using Win ADV. Joint Conference on Water Resources Engineering and Water Resources Planning and Management, Minneapolis, MN, United States. pp. 1–10. White F. M. 1974, Viscous Fluid Flow. McGraw-Hill, New York. White B. and Nepf H. 2007, Shear instability and coherent structures in a flow adjacent to a porous layer. Journal of Fluid Mechanics, Vol. 593, pp. 1–32. White B. L. and Nepf H. 2008, A vortex-based model of velocity and shear stress in a partially vegetated shallow channel. Water Resources Research, Vol. 44, No. 1, pp. W01412. Willmarth W. W. and Lu S. S. 1972, Structure of Reynolds stress near the wall. Journal of Fluid Mechanics, Vol. 55, pp. 65–92. Notation D = Distances from the vegetation bank; d50 = Median diameter of sediment particles; d84 = 84% finer particle diameters; d16 = 16% finer particle diameters; h = Flow depth; ks = Nikuradse’s equivalent roughness; N = Number of time series values; S0 = Bed slope; u = Stream-wise component of mean flow velocity; uf = Stream-wise component of velocity fluctuation; ui = Stream-wise component of instantaneous velocity; u ' = Stream-wise component of turbulence intensity; umax = Maximum velocity observed over a velocity profile; u* = Shear velocity; v' = Lateral component of turbulence intensity; W = Width of channel; International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200
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w wf wi w' x y N g
= Vertical component of mean flow velocity; = Vertical component of velocity fluctuation; = Vertical component of instantaneous velocity; = Vertical component of turbulence intensity; = Distance from the flume entrance; = Distance from the bed; = Dimensionless longitudinal pressure gradient parameter; = Thickness of boundary-layer; = Von Karman’s constant; = Coles' parameter; = Geometric standard deviation; = Shear stress; = An adjusting coefficient of median grain size.
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International Journal of Sediment Research, Vol. 27, No. 2, 2012, pp. 188–200