Experimental and numerical study on hydrodynamics of riparian vegetation*

UOTANI Takuya

Kobe City Bureau, Kobe, Japan, E-mail: takuya_uotani@office.city.kobe.lg.jp

KANDA Keiichi

Department of Civil Engineering, Akashi National College of Technology, Akashi, Japan

MICHIOKU Kohji

Department of Civil and Environmental Engineering, Hosei University, Shinjuku, Tokyo, Japan

Experimental and numerical study on hydrodynamics of riparian vegetation*

UOTANI Takuya

Kobe City Bureau, Kobe, Japan, E-mail: takuya_uotani@office.city.kobe.lg.jp

KANDA Keiichi

Department of Civil Engineering, Akashi National College of Technology, Akashi, Japan

MICHIOKU Kohji

Department of Civil and Environmental Engineering, Hosei University, Shinjuku, Tokyo, Japan

(Received March 25, 2014, Revised May 5, 2014)

Recently, many channelized rivers tend to be heavily vegetated due to regime shifts in hydrological, fluvial and ecological processes. Dense vegetation in a river frequently obstructs a flood flow and reduces conveyance capacity of channels. On the other hand, river vegetation provides various ecological services such as habitats for various species and life, natural cycle of organic and inorganic substances, etc.. It is of engineering importance to understand vegetation hydrodynamics in order to preserve vegetation nature and keep a certain level of flow conveyance capacity. In view that willows tend to be densely vegetated along the shoreline of floodplains or sandbars, a field measurement, a physical model experiment and a numerical analysis were carried out for investigating hydrodynamics in an open channel with riparian vegetation. Discussion was made focusing on flow and shear layer structures developed around the vegetation canopy.

open channel, riparian vegetation, drag force, velocity profile, laboratory experiment, hydrodynamic model

Introduction

Vegetation on flood plains is a world-wide engineering issue in most channelized rivers, which brings forth not only degradation of flow conveyance capacity but also irreversible changes in the ecological system of rivers. In the old days before the modern ages, the natural vegetation such as bamboo and pine trees was nation-widely used as construction materials for riparian works. Considering that the river restoration paradigm is now shifting toward a direction of nearnature river work, a proper management and wise use of vegetation would provide us a new strategy of sustainable flood protection. Our field measurement in a densely vegetated river reach suggests that most of willows tend to be vegetated along shorelines of main channel. Trees vegetated in rivers have two distinctly opposite functions from viewpoints of river morphodynamics and flood control. They reduce flow, regulate streamlines and protect shoreline against erosion. On the other hand, the decelerated stream on the vegetated floodplain eventually promotes sedimentation and leads to overgrowth of vegetation. In this study, hydrodynamics of riparian vegetation was experimentally and theoretically investigated and their potential performance as a natural structure for protecting the main channelʼs revetment is discussed.

Due to differences in water depth and bed roughness, a spanwise shear layer and an organized vortex street are generated along the boundary between the floodplain and the main channel. The bank vegetation must play a role as an additional driving force to furthermore intensify the shear-dominant flow structure. Zong and Nepf[1,2]and Rominger and Nepf[3]investigated a streamwise development and turbulent dynamics of the shear layer in emergent canopies of finite width. White and Nepf[4]proposed a formula giving the shear layer thickness as a function of vegetation parameters such as the frontal area, the drag coefficient and width of vegetation. The key issue in flow modelling of the vegetated channels is how to properly evaluate a roughness or a drag flow coefficient ofvegetation. Researches such as Nikora and Nikora[5]contributed to finding a functional dependency of the drag flow coefficient on vegetation density and stem diameter.

Besides the experimental studies, various hydraulic models were proposed to describe velocity profile and to evaluate flow conveyance in vegetated channels[6-8]. They are 1-D or quasi-2-D models focusing on the spanwise shear-layer structure, which provides a solution of the depth-averaged velocity profile. Although understanding of the vegetation hydrodynamics has extensively been promoted by these studies, discussion was limited within the case of emergent canopies. The vegetation tends to be submerged when the water level is high or the vegetation is small. In this regime of flow and vegetation, a significant shear layer is additionally generated at the top of the vegetation canopy, which is another mechanism in reducing flow conveyance capacity. Considering the turbulent characteristics of the vertical shear layer, field survey, laboratory experiments and flow modeling were extensively performed regarding to this issue[9-11]. Flow models were furthermore developed to a 3-D analysis by using the RANS and LES[12,13]. Flow configurations in most of the studies, however, are still limited to rather simple morphological and vegetational configurations such as laboratory test flumes. In order to perform a flood flow analysis in prototype vegetated channels with the minimum computer resources, a quasi 3-D or a layer-averaged 2-D models is required. The authors have developed a 2-D two-layer model, mentioned as “2D2L model” hereafter, which could simulate flows not only through but also around the vegetation. The water was vertically separated into two layers above and through the vegetation by an interface horizontally encompassing through the vegetation canopy top. The vegetation drag was considered by using a conventional formula used in many studies. The model was successfully applied to several flood events occurring in a vegetated river reach and a good agreement of time-dependent velocity profiles was obtained between the analysis and the field data[14,15].

In this study, a laboratory experiment was carried out in an open channel with a compound cross section and riparian vegetation. Discharge was varied in a wide range from the emerged vegetation to submerged vegetation. The velocity was measured by a micropropeller velocimeter and a PIV technique. Both the one-dimensional single layer model (1D1L model) and the 2D2L model were applied in order to discuss the riparian vegetation dynamics.

1. Field survey of vegetation

1.1Study site

In order to learn a structure of willow vegetation, a field measurement was carried out focusing on the riparian vegetation. The study site is a reach in the Kako River between 23.15 km-24.3 km distances from the river mouth. The Kako River is a first class river stretching in the southern region in Hyogo Prefecture, Japan. Its total length and catchment area are 96 km and 1 730 km2, respectively. The locations of stream and rain gauging stations and the field study site are shown in Fig.1.

Fig.1 Kako River system with the field site and major gauging stations

Fig.2 Distribution of vegetation in test reach. A milestone of 23.6 km distance from the river mouth is denoted in a white square. A water level gauge and an H-ADCP transducer were equipped in the span-wise cross section shown in a black line

1.2Summary of field survey

A plane view of the study area is shown in Fig.2. In the last few decades, the river landscape has been tremendously changed from sand bars mostly covered by sand and gravel into green floodplains densely vegetated with willows. Twenty two times field surveys were carried out focusing on the right bank floodplain from April 2009 to January 2012. Locations of trees and the morphological profile of vegetated areas were measured by using a handy GPS. Distribution of ground covers is categorized by colors in the figure. The predominant vegetation species are willow and bamboo. Bed materials were also sampled to estimateManningʼs roughness coefficient and to examine sedimentation in the vegetated areas.

For the purpose of controlling vegetation growth by promoting inundation on the floodplain, the floodplain encircled by a red broken line in Fig.2 was excavated by 0.5 m-1.5 m in 2008. In the excavation project, it was also targeted to lead a flood flow to a direction of the downstream-side vegetated area to destruct the overgrown willows. A horizontally scanning Acoustic Doppler Current Profiler “H-ADCP” was equipped at the cross section of 23.6 km, and collected a two-dimensional velocity profile every ten minutes during flood events.

Fig.3 Distribution of stem diameter at breast height which is categorized every 0.05 m by grey patterns

Fig.4 Distribution of tree height which is categorized every 1.0 m by grey patterns

1.3Distribution of vegetation and their properties

The investigated items are species, stem diameter, height, location and destructed situation of willows. Observed stem diameters are plotted in Fig.3. One can recognize that most mature trees with thick stem are concentrated close to the embankment as well as in the central areas of floodplain. Both of them are far from the shoreline. On the other hand, thinner or younger trees are mostly inhabited just in front of the shore of the main channel. The same tendency is observed in Fig.4 where data points show tree height. Bear in mind that all the trees on the area excavated in 2008 encircled by a broken red line are younger than four years.

The field data suggest that willows began to grow mostly along the shoreline and grew up with years. If willows experience little severe floods, they continue to grow up and sediments are frequently trapped and settled around the willows after every small flood event. This is how sand bars developed in front of the riparian willows and willows tend to be less frequently damaged. This may be the mechanism of willows overgrowth. It is supposed that the mature willows have grown up in the areas far from the shoreline in this manner. Aerial photos of river morphology pictured in the last fifty years indicate that several narrow belts of mature willows arranged on the floodplain are estimated to be ruins of shorelines. A new shoreline will possibly be produced in front of the present shoreline by sedimentation after years. The key issue for a proper management of vegetated rivers is to investigate hydrodynamics of the riparian vegetation.

2. Modelling of hydrodynamics in the vegetated channel

Hydraulic modeling is carried out to examine how vegetation properties such as stem diameter, density and spacing of trees, etc., affect shear flow structure in an open channel with riparian vegetation. Two types of hydrodynamic models are applied in this study. The first one is a uniform flow model with the depth-averaged single flow layer, which is mentioned as “1D1L model” hereafter. The 1D1L model has been applied to this test reach in order to evaluate a historical change of flow fields with river morphological change and vegetation growing. The second one is a 2-D two-layer model (already mentioned as “2D2L model” above) that was originally developed by the authors and successfully applied for flood routing of the vegetated reach[14,15].

2.1One-dimensional single-layer model (1D1L model): Fig.5(a)

Concept of the model is based on a uniform flow model developed by Rameshwaran and Shiono[7]that was applied to a flow in a trapezoidal open channel with vegetation. By rewriting the flow drag force in terms of Manningʼs roughness coefficient instead of Darcy-Weisbachʼs friction coefficient, the momentum equation was rewritten as

where ρ is the water density, g is the gravity acceleration, y is a horizontal coordinate from the left to right bank, S0is bed slope, H is the water depth, n is the Manningʼs roughness coefficient, and 1/s is the local bank slope. The vegetation is treated as a porous body with the porosity p. The flow field in the vegetation is described in terms of the apparent velocity us, where the corresponding fluid velocity is written as u=us/p. The depth averaged shear stress is expressed by using a so-called zeroth-order turbulence closure assumption in which an eddy viscosity is described by the product of dimensionless eddy viscosity DH(DH=0.3), water depth H and friction velocity. According to the popularly used formula, the drag force coefficient CDdepends on vegetation parameters such as roughness vegetation density λveg, stem diameter D, height hvand spacing ΔS of the trees. λvegis parameterized by the frontal area per unit volume as

Approximating a cross section profile by a polygon consisting of horizontal bed and sloping bank, it is divided into subsections as schematically shown in Fig.5(a). Equation (1) is numerically integrated in each subsection for a given water depth H. The integral constants are determined by equating the solutions of velocity and velocity gradient at each subsectionʼs border. In this manner a solution of streamwise velocity profile is obtained. The total discharge Q is computed by integrating the velocity solution in the horizontal direction.

Note that applicability of the 1D1L model is limited to the emerged vegetation, since the flow has just a single layer with depth-averaged velocity. In order to analyze flow fields with submerged vegetation by this model, an equivalent bed roughness parameter is required. Even so, velocity solution is absent for the flow in the vegetation canopy.

2.2Two-dimensional two-layer model (2D2L model): Fig.5(b)

The 2D2L model was developed in order to describe both the slow flow through the vegetation canopy and the fast flow outside of the canopy. A two layer interface is arranged so that it encompasses the top of the canopy. Mass and momentum conservations are formulated in layer-averaged forms. The system is two-layered not only in the vegetated area (Domain-A in Fig.5(b)) but also in the non-vegetated area (Domain-B in Fig.5(b)) so that the interfacial shear layer developing around the outer edge of the vegetation could be described. The two-layer interface in the present system is defined as shown in a broken line in Fig.5(b). The details about the model could be referred to the authorsʼ previous study[14]. Here, only the momentum equation for the vegetation layer is shown as below.

Fig.5 Configuration of hydrodynamic models for a vegetated compound open channel

The drag force coefficient CDis given as functions of vegetation parameters such as vegetation density λveg, stem diameter D, height hvand spacing ΔS of the trees. According to literatures, λvegis equivalent to the projected plant area per unit volume as

The entrainment velocity across the two-layer interface qiis provided by mass conservation for the upper and lower layers as

Equation (7) is valid both in the Domains-A and B. The 2D2L model gives solution of velocity not only outside but also inside of the vegetation.

Although the original model is 2-D, it is applied to a 1-D uniform flow examined in the present experiment as discussed later.

3. Experimental setup

Considering that willows are mostly vegetated along the riparian zone as shown in the field measurement, a physical model experiment was carried out in order to investigate hydrodynamics of riparian vegetation.

Fig.6 Experimental set-up

Test flume is an open channel with the length of 6.4 m and the width of 0.8 m as shown in Figs.6(a)and 6(b). The channel's bed slope is adjustable ranging between 1/300-1/2 000. A 0.035 m thick panel was installed to simulate the floodplain and a trapezoidal compound cross-section was formed as shown in Fig.6(c). The vegetation simulated in the experiment is willow that is the most dominant species in our test reach in the Kako River. Considering the river morphology and the vegetation structure observed in the test reach, a reduced scale ratio of the physical model to the prototype is approximated to be about 1/50. As was discussed in Section 1, most willows are concentrated in the riparian zone, a vegetation belt is arranged at an edge of floodplain as shown in Figs.6(b) and 6(c). Vertical wooden cylinders with hv=0.06 m in height and three different diameters, D=0.003 m, 0.006 m and 0.012 m, were arranged in staggered rows as shown in Figs.6(c) and 6(d). A flashboard installed at the channelʼs downstream end was adjusted so that a steady uniform flow condition was established under a given discharge Q. A Cartesian coordinate system (x, y, z) is defined as shown in Figs.6(b) and 6(c), where the x-axis is originated at 0.80 m distance from the channelʼs upstream end and directed to downstream, the y-axis is directed from the left to the right bank and the z-axis is taken vertically upward, respectively.

Table 1 Experimental conditions (Vegetation is emerged in RUNs 1a-4a (Q=10.0 L/s)and submerged in RUNs 1b-4b (Q=18.0 L/s), respectively. The bed slope I was kept 1/1 000 in all RUNs)

Hydraulic conditions in the experiment are listed in Table 1. Eight experimental runs were carried out for various values of cylinder diameter D and discharge Q. The channel bed slope was fixed to be I=1/ 1 000.

The experiment was carried out for the two cases of discharges, Q=10 L/s and 18 L/s, which corresponds to the emerged vegetation and submerged vegetation, respectively. Velocity profiles in a cross section were measured by using a micro-propeller velocimeter. The measurement was made only on the left bank side, considering the cross section to be axisymmetric to the central vertical axis. The surface velocity was measured by using the PIV technique.

Fig.7 Surface velocity vectors obtained by PIV analysis in the cases of emerged vegetation

4. Experimental results

4.1Emerged vegetation

Figure 7 shows surface velocity vectors obtained by PIV in RUNs 1a, 2a, 3a and 4a that are the cases of emerged vegetation. The abscissa denotes distance along the streamwise direction x and the ordinate shows distance from the left bank y, respectively. The velocity scale USUis indicated by the vector arrowʼs length and categorized by grey patterns. The black-colored dots are the tree models. It is shown that flow is significantly reduced in and around the vegetation. Flow is more significantly decelerated with increasing the vegetation density. The water surface rises as a result of obstruction to flow in the vegetation.

In Fig.8 velocity distributions in the spanwise cross section are shown. In the figure, the grey pattern indicates magnitude of the stream-wise velocity component and the vertical bars are the vegetation models. The abscissa is distance from the left bank y and the ordinate is vertical distance from the channel bed z, respectively. Flow is more decelerated in RUN4a than in RUN 1a, because the former has a denser vegetation of λveg=2.0 m-1than the latter (λveg= 0.5 m-1). As a result of the reduced flow conveyance capacity in RUN 4a, the water surface level is higher than that in RUN 1a.

Fig.8 Stream-wise velocity in a spanwise cross section (emerged vegetation)

First, let us compare the velocity distributions between RUNs 2a and 3a. Both of them have the same vegetation density, λveg=1.0 m-1but the stem diameter D is smaller in RUN 2a (D=0.003m)than in RUN 3a (D=0.012 m). The velocity profile is similar to each other but flow in the vegetation is faster in RUN 3a than in RUN 2a. This means that vegetation causes more significant obstruction to the flow in a case of thicker stem or narrower vegetation spacing ΔS.

Secondly, let us compare the flow structures between RUNs 1a and 3a. Both of them have the same vegetation spacing of ΔS=0.11m , but the vegetation density is smaller in RUN 1a (λveg=0.5 m-1) than in RUN 3a (λveg=1.0 m-1). The velocity observed in both RUNs has a similar profile but flow in the vegetation at y=0.20 m is faster in RUN 1a than in RUN 3a. This result shows that vegetation brings more significant obstruction to flow in vegetation with thicker stem.

Fig.9 Surface velocity vectors obtained by PIV analysis in the cases of submerged vegetation

4.2Submerged vegetation

Figure 9 shows surface velocity vectors from the PIV measurement for RUNs 1b, 2b, 3b and 4b. They are the cases of submerged vegetation, where the coordinate system is the same as in Fig.7. Description of velocity vectors are in the same manner as in Fig.7. Compared to the emerged case, the surface flow is not so much reduced even over the vegetated area. In other words, a remarkable velocity difference is notrecognized between the floodplain and the main channel in the surface layer when the vegetation is submerged under water. Especially, in RUN 1b that has the sparsest vegetation among the cases, the surface velocity is very uniformly distributed in the span-wise direction. Therefore, the PIV that measures only the surface velocity is not a proper technique for estimating discharge in rivers with submerged vegetation.

Fig.10 Stream-wise velocity in a spanwise cross section (submerged vegetation)

Figure 10 shows velocity contours in the spanwise cross section for the submerged vegetation. The data are represented in the same manner as in Fig.8. A sharp two layer structure is developed in the area with submerged vegetation, where flow over the vegetation is much faster than that through the vegetation. As a result, a predominant shear layer is generated along the vegetation canopy. Focusing in the vegetation, velocity gradually increases in the vertical direction, which is driven by the fast flow running over the vegetation canopy. Flow near the water surface is little influenced by the vegetation.

Fig.11 Dependencies of average velocities in the upper and lower layers, (Uwa,Uve), and its fraction, Uwa/Uve, on roughness density of vegetation λveg

In order to furthermore examine the two-layer flow characteristics, averaged velocities in the upper and lower layers inside the vegetation belt, Uwaand Uve, are plotted against the roughness density of vegetation λvegin Fig.11. Here, Uwaand Uveare defined as cross-sectional average velocities in the layers over and through the vegetation, respectively (see Fig.5(b)). The average velocity for the emerged vegetation U is also plotted for comparison. The lines in the figure are the best fitting curves to the experimental data. The figure shows that the velocity ratio Uwa/Uvemonotonically increases with increasing λveg. This means that, with increasing the vegetation density, acceleration of the upper layer is more significant than deceleration in the vegetation layer.

4.3Comparison between experiment and hydrodynamic model: Emerged vegetation

Figure 12 shows spanwise profiles of the surface velocity from the PIV measurement and the depthaveraged velocity u obtained from the micro-propeller velocimeter in the case of emerged vegetation. They are compared with the analytical solution u from 1D1L model that are shown in solid curves. Adrag-force coefficient CDproposed for prototype was not well fitted to the present experiment. Therefore, CDand Manning's roughness coefficient n were identified by considering the experimental results. As results, CD=2.0is identified in the analysis to provide the best fitting solutions. Manningʼs roughness coefficient n for the wall friction is fixed to be n= 0.015 so that the analytical solution is fitted to the experimental data.

Fig.13 Solutions of spanwise velocity profiles, comparison of the laboratory data with the 1D1L and 2D2L models

Despite adjusting the model parameters in this way, there is still a difference between the experiment and the analysis. Since the depth-averaged velocity and the surface velocity from PIV are well correlated each other, it is confirmed that both of the velocity measurements were correctly conducted. The problem might be left in the modeling of vegetation drag force, where velocity is overestimated by the model especially in the main channel. Although a homogeneous porous body is assumed in the numerical model of riparian vegetation, the physical model has a different structure consisting of a few tree streets. This may be one of the reasons why there is a gap between the analysis and experiment. It is expected that the analytical solution asymptotically approaches to the experiment with increasing the vegetation density. However, a macro flow structure around a tree becomes more predominant in a case of sparser vegetation in which the assumption of homogeneous porous structure of vegetation is no more valid. Another reason of poor fitting to the experimental data may come from scaleeffect in the physical model. However, little examination is completed so far regarding the scale effect.

4.4Comparison between experiment and hydrodynamic model: Submerged vegetation

The 1D1L model is no longer available in the case of submerged vegetation. As was discussed above, predominant shear stress is generated around the outer edge of vegetation where the depth-averaged velocity is no more valid even in shallow flows like rivers. The 2D2L model provides solutions for the cases not only of emerged (RUN *a in Table 1) but also submerged vegetations (RUN *b in the table). Spanwise profiles of the layer-averaged velocity (u1, u2) are shown in Fig.13, where the numerical solution of 2D2L model is compared with the experimental data obtained from the probe measurements. The surface velocity from the PIV measurements is also plotted for reference. Figure 13(a) is the result from emerged vegetation, where the solution from the 1D1L model is plotted in broken lines for comparison. Figure 13(b) is for the cases of submerged vegetation and average velocity both in the upper and lower layers are given by the 2D2L model.

Fig.14 Comparison of the results in Fig.11 with the solution of 2D2L model

In the case of submerged vegetation in Fig.13(b), the layer-averaged velocities given by the 2D2L model qualitatively shows a similar tendency with the experiment. However, the velocity is still overestimated by the model in the main channel, especially in RUN 4b. The experimental results of layer-averaged velocities (Uwa,Uve) and Uwa/Uveare compared with the analytical solution as shown in Fig.14. Although the solutions of functional dependencies of (Uwa,Uve, Uwa/Uve) on λvegqualitatively agree with the experimental data, the difference between the analysis and experiment in Uwa/Uveis not negligible.

The estimation error found in the analysis may be caused by the same reason as Fig.13. Therefore, model parameters, such as diameter and roughness density of vegetation, etc., should be identified so as vegetation in the numerical model to be hydrodynamically equivalent to that in the physical model. Scale effects in the physical model might be another possible reason to bring the estimation error. Additional physical model experiments should be carried out in a larger test flume with wider vegetational conditions of denser and more cylinder rows.

Besides such a discrepancy between the analysis and experiment, the flow and shear layer structure in and around the riparian vegetation are quantitatively reproduced by the 2D2L model.

5. Conclusions

In this study, hydrodynamics of riparian vegetation has been experimentally and theoretically investigated in order to examine feasibility of utilizing the riparian vegetation as a natural structure for protecting the main channelʼs revetment. For preparing a physical model experiment, a field study was conducted to investigate ecological structures of willow vegetation. A laboratory experiment was carried out in hydraulic conditions ranging from the emerged to the submerged vegetation. The experimental result has been compared with solutions provided by a 1D1L model and a 2D2L model. The findings are summarized as follows.

(1) Based on a field measurement in a densely vegetated river reach, it is found that most of willows tend to be concentrated in riparian zones in front of the main channel.

(2) A PIV measurement was performed to obtain velocity distribution on the water surface. A velocity distribution in a cross section was also measured by using a micro-propeller velocimeter. In the case of submerged vegetation, the surface velocity from PIV is much higher than the layer-averaged velocity. Therefore, the PIV is not a suitable technique for estimating discharge in a river with submerged vegetation. On the other hand, in the case of emerged vegetation, the PIV measurement is well correlated with the point measurement with the micro-propeller velocimeter. It is found that flow is more significantly reduced in and around the denser vegetation. In this manner flow conveyance capacity in a river is decreased by riparian vegetation.

(3) Vegetation brings more significant obstruction to flow in a case of thicker stem or narrower vegetation spacing SΔ, which is known from the eme-rged vegetation.

(4) In the case of submerged vegetation, a welldefined two-layered flow structure is produced in the area of submerged vegetation. The flow over the vegetation is much faster than the flow through the vegetation. Velocity gradually increases in the vertical direction, which is driven by the fast flow running over the vegetation canopy. Flow near the water surface is little influenced by the vegetation. Functional dependencies of the layer-averaged velocities, Uwaand Uve, on the vegetation density λveghave been examined. It is found that Uwa/Uvemonotonically increases with increasing λveg.

(5) The experimental results for the emerged vegetation are compared with the 1D1L model analysis. Although the analytical solution for spanwise velocity profile shows a qualitative agreement with the experiment, the 1D1L model tends to overestimate the velocity especially in the main channel. The 2D2L model developed by the authors is applied for analyzing both of the emerged and submerged vegetation. The model shows a certain level of performance in reproducing shear flow structure around the riparian vegetation. However, discrepancy between the analysis and the laboratory data is not negligible for some cases. A larger scale test flume and vegetation models are recommended so that the flow configuration in the physical model approaches to that assumed in the analytical models.

The riparian vegetation has been modeled by rigid sticks both in the laboratory experiment and the numerical analysis, while willows are actually flexible and waving when they are submerged under water. Since there must be difference in hydrodynamic behaviors between the prototype and model vegetation, one should be careful about this point when the 2D2L is applied to a prototype riparian vegetation. It is one of the most important issues in the next version of 2D2L model to take fluctuation and turbulence production of flexible bluff bodies like willows into consideration.

Acknowledgements

The study was supported by the Himeji River Road Management Office, the Ministry of Land, Infrastructure, Transport and Tourism. The present study was financially supported by the Grant-in-Aid for Scientific Research (B) (Grant No. 23360212, Leader: Kohji Michioku).

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10.1016/S1001-6058(14)60088-3

* Biography: UOTANI Takuya (1990-), Male, Master, Engineer

MICHIOKU Kohji,

E-mail: kohji.michioku.47@hosei.ac.jp