The velocity patterns in rigid and mobile channels with vegetation patches ＊

Bao-liang Ren, Dan Wang, Wen-qi Li, Ke-jun Yang

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065,China

Abstract: The hydraulic characteristics in an open channel with vegetation are very important in controlling the environment pollution and restoring the river ecology.This paper studies the influence of the bed form and the vegetation patch density on the spatial velocity pattern.Rigid fiberglass circular cylinders are used to simulate the vegetation and a 3-D acoustic Doppler velocimeter(ADV) is used to measure the local flow velocities.Two types of bed forms and a series of vegetation patch densities are considered.The experimental results show that the bed form significantly influences the vertical distribution of the streamwise velocity.Besides,the velocity is affected by the bed form while the lateral distribution shape of the streamwise velocity as well as the lateral and longitudinal distribution shapes of the depth-averaged velocity is less affected.When all test conditions but the bed condition remain the same, as a result of the water energy consumption by the sediment movement, the velocity in the mobile bed case is smaller than that in the rigid bed case.The vegetation patch density has a significant effect on the flow velocity.The distributions of the flow velocity at different locations show different trends with the increase of the vegetation patch density.The upstream adjustment length is not affected by the vegetation patch density, but the steady wake length is very much affected.

Key words: Vegetation patch, density, bed form, velocity characteristics, sediment

Introduction

The aquatic vegetation widely exists in the coastal and shallow areas of natural rivers, as a basic part of the river ecosystem and an important factor in maintaining the integrity and the health of the river ecosystem.It interacts with the water flow to produce positive or negative feedbacks.As positive feedbacks,the aquatic vegetation provides the habitat for animals,and improves the water quality and clarity by taking up nutrients, by releasing oxygen to the water column and by trapping heavy metals and suspended particles[1].As the negative feedbacks, the aquatic vegetation increases the flow resistance, changes the velocity distribution, affects the discharge capacity and aggravates the flood[2].Hence, it is of great significance to study the influence of the vegetation on the flow characteristics.

The vegetation patches include trees, bushes,grass, and so on, and they commonly exist in natural river channels, influencing the flow structure, as is different from that for an individual vegetation.The aquatic vegetation greatly influences the flow resistance, the flow velocity, the turbulent structure, the transport and the settlement of the sediment, the nutrients and the pollutant, and other flow behaviors.Therefore, a large number of studies were carried out through field observations, laboratory experiments,theoretical analysis and numerical modeling for the effects of the vegetation characteristics on the flow structures.Nezuand and Onitsuka[3]conducted experiments for different vegetation densities by using different methods to study the turbulent structures.Liu et al.[4]and Shan et al.[5]proposed a model to estimate the depth-averaged 2-D flow direction (depthaveraged flow angle) along a meander in smooth and vegetated meandering compound channels.Yang et al.[6], Liu et al.[7]investigated the effects of different vegetation types on the flow characteristics.Zhang and Su[8]found that the vegetation played an important role in the flow resistance even though the density of the vegetation was low.Liu and Shan[9]proposed an analytical model to predict the longitudinal profile of depth-averaged streamwise velocities in a channel with an emergent array of rigid cylinders.Huai et al.[10]built an analytical model to predict the vertical distribution of the mean streamwise velocity in an open channel with a doublelayered rigid vegetation.Li et al.[11]proposed a model to predict the vertical distribution of the suspended sediment concentration in a flow with a submerged vegetation.Jing et al.[12]used the Reynolds stress model (RSM) to simulate the compound meandering channel flows.Guo et al.[13]found that for a given dimension of the bed roughness the relative spacing of the roughness (defined as the ratio of the center to center distance to the height of the strip) had a significant effect on the flow.Liu et al.[14]proposed a model for modeling the depth-averaged velocity and the bed shear stress in compound channels with emergent and submerged vegetations.Huai et al.[15]constructed a mathematical model for the emerged rigid vegetation, and it was pointed out that the flow could be divided into two regions: the outer region and the viscous region, and that the velocity in the outer region was a constant, mainly related to the energy slope and the vegetation density whereas the velocity in the viscous region varied.Huai et al.[16]discovered that the ejections and the sweeps are dominant at the top of the vegetation layer, and the sweep events are stronger than the ejection events inside the canopy.Huai et al.[17]investigated the effects of the turbulent structures on the momentum transfer across the outer line of the vegetation region.

In natural rivers, the vegetation is commonly found in patches of finite length and width, which is a focus in the studies of the influence of the vegetation on the flow characteristics.Zong and Nepf[18]investigated the turbulent wake behind a 2-D porous circular obstructions, embodied by circular cylinders and discovered that the dimensionless length of the entire wake increases with the increase of the patch porosity.Yang et al.[19]developed a model to simulate the flow-vegetation interactions in open channels.Hu et al.[20]explored the flow structure and the pattern of the deposition directly downstream the patches of the submerged vegetation.Nicolle and Eames[21]used a group of cylinders to model a finite porous body and investigated the flow through and around the group.Liu and Nepf[22]conducted an experimental study to describe how the channel velocity and the stemgenerated turbulence influence the deposition within and around an emergent patch of vegetation.Huai et al.[23]proposed a method to predict the depth-averaged velocity effectively.

The vegetation density has significant effects on the flow structures in rivers.White and Nepf[24]observed that the mean lateral velocity profiles assume a two-layer structure in a shallow channel with a partially emergent vegetation and found that the velocity in the inner region decreases with the increase of the vegetation density whereas the velocity in the outer region is almost independent of the vegetation density.Zong and Nepf[25]studied the spatial distribution of the flow velocity for different emergent vegetation patch densities.White[26]designed an experiment with a range of different cylinder densities, as a model for the emergent vegetation in a laboratory flume to investigate the velocity characteristics and the dispersion mechanisms within the emergent vegetation.

In a word, the study of the impact of the vegetation characteristics on the flow structures has an important academic and engineering significance.However, the influence of the bed form and the vegetation patch density on the flow velocity characteristics was not adequately studied.This paper s investigates the characteristics of the flow velocity for different bed forms and various vegetation patch densities by conducting experiments in a flume.

1.Experimental arrangements

Experiments are conducted in a flume, 16.0 m long, 0.3 m wide, and 0.4 m high, at the State Key Hydraulics Laboratory (SKHL) of Sichuan University.The flow in the flume is made to be uniform by adjusting the tailgate at the downstream end of the flume.The flow depths are measured by a pointer gauge while the discharges are measured by a triangular weir, installed in front of the channel, and the velocity measurements are made by the acoustic Doppler velocimeter (ADV).

The PVC baseboard, perforated with a staggered arrangement of holes, covers the bed of the test section.A circular patch of the model vegetation is set in the center of the PVC baseboard using rigid fiberglass circular cylinders.The patch diameter (D)is 0.060 m, much smaller than the flume width(0.300 m).The cylinder diameter (d) is 0.004 m,and the cylinder length is 0.300 m.The stem density within the patch is described byn, the number of stems per bed area, and the frontal area per volume,a=nd.The solid volume fraction within the patch isφ=πad/4.The bed slope is fixed at 0.1%.The flow discharge,Q, is 18.01 L/s.U∞is the mean velocity of the cross-section.

In the rigid bed experiment, the concrete of 0.110 m thick is laid on the flume, compacted and flattened for the stability of the bed and the accuracy of the experimental results.In the mobile bed flume experiments, a uniform sediment is used with the grain diameter of 0.0015 m, the thickness of the sediment is 0.110 m, and the mobile bed length of the sediment is 10.4 m.The length of the upstream gravel transition section is 1 m.For each group of test conditions, the water runs over the bed for a while before the test.To ensure the accuracy of the test data,the measurement of the velocity begins after the bed form becomes steady.To avoid a heavy scouring, the original bed works in a slow flow, the flow backward is adopted in the mobile bed test.Firstly, the tailgate opening is minimized and the water inlet valve is turned on slowly to achieve a slow flow.When the water depth is high and the flow is stable, the opening of the tailgate and the water inlet valve is gradually increased alternately, adjusting to reach the test depth.

The coordinate system is defined asxin the streamwise direction, withx=0 at the center of the patch, as shown in Fig.1,yin the lateral direction,withy=0 at the center of the patch and the flume,andzin the vertical direction, withz=0 at the bed.The velocity measurements are made from a distance 4Dupstream the patch to a distance 23Ddownstream the patch using an ADV.At each point,the velocity is measured for 30 s with a sampling frequency of 50 Hz.

Twenty-nine measuring sections are arranged, as shown in Fig.1.Seven verticals are arranged where the lateral values of y from the far left vertical to the far right one are 1.75D, 1.17D, 0.58D, 0D,-0.58D, -1.17Dand -1.75D.Eight measuring points are arranged on each vertical.When the vertical distance from the measurement point to the bed is less than 0.005 m, the measurement interval is reduced to 0.001 m, in order to capture small changes of the velocity,and when the distance is larger than 0.005 m, the measurement intervals are 0.005 m and 0.010 m,according to the particular flow depth.A summary of experimental conditions is given in Table 1.

2.Vertical distribution of streamwise velocity along the centerline of the flume for different bed forms and vegetation patch densities

In this and subsequent sections,zis the distance from the measurement point to the bed anduis the streamwise point velocity.As is shown in Fig.2, the bed form has apparent effects on the vertical distribution of the streamwise velocity along the centerline of the flume.In the mobile bed case, the streamwise velocity is smaller than that in the rigid bed case.Besides, the streamwise velocity at the sectionx/D=23 returns to be in line with the upstream streamwise velocity in the mobile bed case while that at the sectionx/D=19 is consistent with the upstream streamwise velocity in the rigid bed case.Due to the energy consumption of the water caused by scouring and deposition of the sediment in the mobile bed, the velocity declines and a longer distance is required to eliminate the effects of the vegetation patch on the velocity.For both the rigid and the mobile beds, the streamwise velocity in the centerline generally remains unchanged firstly, then decreases and increases, and tends to a steady value eventually.Before the vegetation patch, the streamwise velocity generally distributes logarithmically.From the end of the patch to a certain downstream section, the stream-wise velocity appears to be in an S-shaped distribution,after which it is basically in a logarithmic distribution.The vegetation density affects the vertical distribution of the streamwise velocity along the centerline of the flume.Before the sectionx/D=1, the streamwise velocity declines gradually with the increase of the surging density, and a denser vegetation witnesses a faster reduction of the streamwise velocity, which reflects the fact that a denser vegetation means a larger flow resistance.After the sectionx/D=1, the denser the vegetation is, the higher the recovery rate of the streamwise velocity is, which can be explained by the fact that the shear layers accelerate the energy exchange and promote the recovery of the velocity.

Fig.1 Layout of the measuring lines, measuring points and model patch (10-2 m)

3.Lateral distribution of velocity

3.1 Lateral distribution of depth-averaged velocity for different bed forms and vegetation patch densities

The depth-averaged velocity,U, can be computed through the integration of the streamwise point velocity (u) along the depth of the water.From Fig.3, it can be seen the bed form influences the depth-averaged velocity while having little influence on its lateral distribution shape.Owing to the energy consumption of the water caused by the sediment incipient motion, the saltation, the rolling and the collision, the depth-averaged velocity in the mobile bed is less than that in the rigid bed.The vegetation patch has a less effect on the lateral distribution of the upstream (for example on the sectionx/D=-1)depth-averaged velocity, which appears to be in an approximately horizontal line.A marked impact is seen of the vegetation patch on the lateral distribution of the downstream (for example the sectionx/D=1)depth-averaged velocity, and the lateral distribution appears to take a trough shape, which can be described in a way that the depth-averaged velocity increases symmetrically on the two sides with the minimum value taking at the centerline, which declines as the density increases.

3.2 Lateral distribution of streamwise velocity for different bed forms and vegetation patch densities

As is shown in Fig.4, the bed form has a less effect on the lateral distribution shape of the streamwise velocity than the effect on its value.In the mobile bed case, the streamwise velocity at the middle of the section is a little less than that in the rigid bed while the streamwise velocity on both sides is significantly less than that in the rigid bed.Moreover,the streamwise velocity at the middle of the section decreases as the vegetation density rises, and on both sides it increases as the vegetation density increases,with the value at the middle point much smaller than that on both sides.The high flow resistance within the vegetation patch, as a result of the denser vegetation,makes the upstream flow deflect to both sides of the patch with a higher velocity on sides and a lower velocity in the middle.These results are in line with the analysis given above.The larger the velocity is,the more intense the sediment movement is, and the more energy will be consumed, with a more obvious difference of the streamwise velocity value on sides between mobile and rigid bed cases.From the mobile bed test, it can be seen that with the increase of the vegetation density, the degree of the water erosion of the sediment increases and the bed elevation decreases gradually, much more in the middle than on both sides.This observation supports the above explanation.Besides, the streamwise velocity on both sides is approximately in a logarithmic distribution for a denser vegetation patch while in other cases it appears to be S-shaped.

Fig.3 Lateral distribution of depth-averaged velocity for different bed forms and vegetation patch densities.Velocity is normalized by the mean velocity at the crosssection, U∞, and the distance, y, is normalized by the vegetation patch diameter, D

4.Longitudinal distribution of depth-averaged velocity for different bed forms and vegetation patch densities

Fig.4 Lateral distribution of streamwise velocity at the cross section x/ D=1 for different bed forms and vegetation patch densities

The scouring and the deposition of the sediment has a close relation with the longitudinal distribution of the velocity.Therefore, it is desirable to study the longitudinal distribution of the depth-averaged velocity theoretically and practically.As is shown in Fig.5, the bed form has a much less effect on the longitudinal distribution shape of the depth-averaged velocity than on its value.For a given vegetation patch density, on the one hand, the movement and the saltation of the sediment as well as the collision and the friction between sediments involve the energy consumption of the water.On the other hand, the sediment starts to move under the action of the water flow, scouring the bed surface.Thus the bed elevation is lowered, with an increasing relative depth of the cross-section.Under the combined action of these factors, the depth-averaged velocity at the same location in the mobile bed case is smaller than that in the rigid bed case.In addition, it can be concluded from the discussions in previous sections that the vegetation patch affects little the upstream water flow but significantly the downstream water flow in a certain area.Compared to the upstream reach of the vegetation patch, the downstream reach witnesses severer sediment movement with larger turbulent intensity of the water flow.With the interaction of the two facts, the decreasing rate of the velocity in the mobile bed case is much larger than that in the rigid bed case, with a much steeper longitudinal distribution shape of the depth-averaged velocity.The vegetation density affects little the longitudinal distribution shape of the depth-averaged velocity while affects its value significantly.As the vegetation density increases, the minimum value of the depth-averaged velocity behind the patch decreases and the maximum value increases.In front of the downstream minimum velocity section,the denser the vegetation patch, the larger the water flow resistance and the more intense the scour of the sediment.Consequently, more energy is consumed and the cross-section depth increases, resulting in a smaller velocity.Behind the downstream minimum velocity section, the denser the vegetation patch, the stronger the shear action of the water and the more intense the exchanges of mass and momentum.As a result, the disturbance by von Karman vortex street in the water becomes stronger, promoting the velocity recovery.

Fig.5 Longitudinal distribution of depth-averaged velocity for different bed forms and vegetation patch densities. The distance,x,is normalized by the vegetation patch diameter, D.Two vertical solid lines indicate the position of patch between x/ D =-0.5 and x/ D =0.5

5.The upstream adjustment length and the steady wake length for different bed forms and vegetation patch densities

From the discussions in the previous section, it can be found that the depth-averaged velocity begins to decline at a certain section of upper reaches of the vegetation patch.The upstream adjustment length,expressed byL0in Fig.6, is the distance from the leading edge of the patch (x=-0.5D) to the section where the depth-averaged velocity begins to decrease.As the water flows through the porous obstruction, a wake structure is formed.The length scaleL1in Fig.6 is estimated from the longitudinal velocity transect as the distance from the downstream edge of the patch(x=0.5D) to the last point before the velocity begins to increase, marking the beginning of the wake-scale mixing associated with the von Karman vortex street.

Fig.6 Schematic diagram of velocity adjustment near a circular patch.Two vertical solid lines indicate the position of the patch between x/ D =-0.5 and x/ D =0.5

Rominger and Nepf[2]suggested that for a vegetation patch of finite width,L0is related to the half width of the patch, and for a circular patch,L0is related to the diameterD.Values ofL0under various conditions are listed in Table 2.

Fine particle depositions can be found in the steady wake, which would influence the growth of plants and animals in the water, but not all vegetation patches produce a steady wake.Thus this paper investigates the effect of the vegetation density on the steady wake.

According to previous studies, for the low density vegetation patches, such asa=0.20× 10-2m-1anda=0.25× 10-2m-1in this paper, von Karman vortex street will not be formed, andL1is not relevant.For the vegetation patch of the largest density, such asa=0.70× 10-2m-1anda=0.80×10-2m-1, the wake structure is similar to that for abluff body, with no steady wake, and a recirculation zone occurs directly behind the patch, and thusL1is not relevant.Values ofL1under various conditions are listed in Table 3.

Table 2 The values of L0/D under different conditions

Table 3 Summary of values of L1/D under different conditions

Fig.7 The upstream adjustment length and the steady wake length for different bed forms and vegetation patch densities.Length is normalized by vegetation patch diameter,D

Based on the above analysis, the trend chart ofL0/Dagainstais drawn using the data in Table 2 and that ofL1/Dis drawn using the data in Table 3 likewise.With the analysis of these charts, the influences of the bed form and the vegetation patch density onL0andL1can be seen as shown in Fig.7.

In Fig.7, it is shown that the bed form has less significant effect on the upstream adjustment length and the steady wake length.The vegetation patch density hardly affectsL0whileL1declines as the density goes up.L0remains in a value around 2.6Din the mobile bed case and around 2.9Din the rigid bed case.The water energy is consumed by the sediment movement in the mobile bed case, and the velocity decreases near the leading edge of the patch, with the reduction ofL0.As the vegetation density increases, the action of the water flow shear layer becomes stronger and von Karman vortex street can be formed in a shorter distance, with the reduction ofL1.

6.Conclusions

This paper investigates the effects of the bed form and the vegetation patch density on the flow velocity patterns by conducting laboratory experiments in a flume.The conclusions are as follows:

(1) The bed form affects the distribution of the streamwise velocity along the centerline of the flume.Due to the energy consumption by the sediment movement, the streamwise velocity in the mobile bed case is smaller than that in the rigid bed case.The vegetation patch density has relatively little effect on the upstream flow but a greater impact on the downstream flow in certain area.From the end of the vegetation patch to a certain downstream section, the streamwise velocity is in an S-shaped distribution, and it approximately distributes logarithmically at other locations.

(2) The lateral distribution shapes of the depthaveraged velocity and the streamwise velocity are less affected by the bed form while their values are influenced significantly.The velocity in the mobile bed case is smaller than that in the rigid bed case.The lateral distribution of the depth-averaged velocity appears to take a trough shape and the minimum value of the depth-averaged velocity decreases as the vegetation patch density increases.The vegetation patch density has an apparent effect on the lateral distribution of the streamwise velocity.For a denser vegetation patch, the streamwise velocity on both sides of the section is generally in a logarithmic distribution while its distribution is S-shaped in other cases.

(3) As for the longitudinal distribution of the depth-averaged velocity, the value in the mobile bed is smaller than that in the rigid bed.As the vegetation patch density increases, the minimum value of the depth-averaged velocity at the trailing edge of the patch declines while the maximum value increases.

(4) The upstream adjustment length and the steady wake length are less affected by the bed form.The upstream adjustment length is not affected by the vegetation patch density while the steady wake length declines as the vegetation patch density increases.