Numerical simulations of flow and large-scale bed variation
using quasi-3D flow analysis methods in a river confluenceduring a large flood
Kosuke Tabata
Graduate School of Science and Engineering, Chuo University
1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-85511:
Tel. +81 (03) 3817 1615, Fax: +81 (03) 3817 1617,
e-mail : k-tabata@civil.chuo-u.ac.jp

Shoji Fukuoka
Professor, Research and Development Initiative, Chuo University
1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-8551:
Tel. +81 (03) 3817 1625, Fax: +81 (03) 3817 1625,
e-mail : sfuku@tamacc.chuo-u.ac.jp

Strong flow attacking point and flow separation area due to a large flood were formed and large-scaleerosion and sediment deposition occurred at the confluence of the Shinano River and Ikarashi River.
In this paper, we apply the general bottom velocity computation (BVC) method to the confluence of aShinano River and Ikarashi River to estimate three-dimensional flow and bed variation during thelarge flood. The general BVC model shows that the depth of the erosion and the deposition inseparation area are not sufficiently reproduced, but structures of unsteady three-dimensional flow andbed variations are described on the whole.

Key words
River confluence, flood flow, flow attacking point, three-dimensional flow, bed variation, generalbottom velocity computation (BVC) method , separation zone.

IINTRODUCTION

The Ikarashi River is the main tributary in the lower Shinano River that is known as a typical
low-lying river in Japan. In the record-breaking flood observed in 2011, large discharge inflowing
from the Ikarashi River caused large-scale erosion and sediment deposition around the confluence ofthe Shinano River and Ikarashi River. Therefore, it is important to establish a numerical model forinvestigating complex flow structures and bed variation mechanism around the confluence during thelarge flood. In recent years, Uchida et al. [1] have developed the general Bottom Velocity
Computation (BVC) method capable of analyzing flood flows and bed variations considering thethree-dimensionality of the flow. It has been shown that the general BVC method can evaluate thepressure deviation from hydrostatic pressure distribution and bottom velocity and elucidate thedeveloping mechanism of the local scour around hydraulic structures in the laboratory experiments.
However, the applicability to the river fields with a complex three-dimensional flow and large scale
bed variation like the confluence of the Shinano River and Ikarashi River has been not been
investigated enough. In this study, we apply the general BVC method to the river confluence andverify the reproducebility of flood flow and bed variation in the 2011 flood. In addition, we investigate
the time change in flow and bed variation in the confluence area from the calculation results. These
calculation results are compared with results observed during and after the flood.
1

Corresponding author

40.8kAramachi

41.0k
41.2k
41.4k

Deposition

ErosionShinano River
Ikarashi River

Fig.2 Aerial photograph in riverconfluence after 2011 flood.
Table 1. 2011 flood discharge.

Fig.1 Plan form of the lower Shinano River and waterlevel observation points.

IIdischarge infirst peak2013 flood（m3/s） second peakdesign flood
discharge（m3/s）

ShinanoRiver439
1,035

Ikarashi
River
2,088
2,292

800

2,400

OBJECTIVE AREA AND FLOOD

Fig.1 shows the plan form of the lower Shinano River and water level observation points.
There is no inflow from the Arai weir located around 51 km point of the lower Shinano River because
the flood-control gates are completely closed during floods. Therefore, the flood discharge in thelower Shinano River is determined by discharges from the Ikarashi River and Kariyata River. As
shown in Fig.1, the Ikarashi River joins the Shinano River at almost right angle. Three-dimensional
flow structures and bed variations at the confluence change complicatedly during the floods due to theplan shape of the confluence and the inflow conditions of the Ikarashi River and Kariyata River. Table
1 shows the peak discharges observed in the Shinano River and Ikarashi River during the 2011 flood.
The flood hydrograph has two peaks. The peak discharge at Isshinbashi in the Ikarashi River is over
2,000 m3/s and as large as the design flood discharge. On the other hand, the peak discharge at theKanbara weir in the Shinano River is smaller than that of the Ikarashi River. As a result, the erosion atleft bank around 41.2 km and the sediment deposition at right side in the main channel from 40.6 kmto 41.0 km were seen in Fig.2.

IIINUMERICAL ANALYSIS METHOD

The general BVC method [1] is able to evaluate non-hydrostatic pressure distributions andbottom velocities by not using the assumption of the shallow water flow. A set of governing equations
as shown in Fig.3 are solved for the following unknown quantities: water depth h, depth averaged(DA) horizontal velocities Ui, DA horizontal vorticities Ωi, horizontal velocities on water surface usi,
DA vertical velocity W, bottom pressure deviation from hydrostatic pressure distribution dpb andbottom velocities ubi. The bottom velocity equations (Eq.(1)) is derived by integrating horizontal
vorticities respect to depth.

 ∂Wh∂z∂z ubi = usi − ε ij 3Ω j h − − ws s + wb b ∂xi∂xi  ∂xi(1)

Where, zs: water surface level, zb: bed level, ws, wb:vertical velocities on water surface and bottom.
The bed variation analysis is calculated by the continuity equation for sediment and grain sizes(Hirano, 1971) using bed load formula (Ashida and Michiue, 1972) and suspended load formulas(Itakura-Kishi, 1980 and Lane-Kalinske, 1972). The transport of the suspended sediment is calculatedby 3D advection and diffusion equations in this study.

IVANALYSIS OF THE FLOOD FLOW AND BED VARIATION IN THE RIVER
CONFLUENCE DURING THE 2011 FLOOD

IV – 1 Conditions of the numerical analysis

z

DA horizontal momentum eq. ; U i
Depth-integrated hcontinuity eq. ;ws usη
water surfaceusξ
W
Ωηξ

UξUη

wbubξ ubηub

DA horizontal vorticity eq. ; Ω i

Bottom velocity eq. ; ∂Wh∂z∂z ub i = u s i − ε ij 3Ω j h − − ws s + wb b ∂xi∂xi  ∂xi

Horizontal momentum eq. usi
on water surface ;Bottom shear stress ; τ b i = cb 2ub i 2ΩξηPoisson eq. for time variation W
in DA vertical velocity ;BottomDA vertical momentum eq. fordPb
bottom pressure intensity ;cb ; Estimated assuming theequilibrium velocity
condition in bottom layer

Bed variation analysis

Fig.3 Flow of calculated method.
survey result in 2013
（in main channel)

806040Ikarashi River(Average value)
Shinano River(Average value)

200
0.01

0.1

1Grain Size(mm)

10

100

Fig.4 Garain size distribusion.
3Discharge （m /s）

4,000

Aramachi (observed)

3,000

Aramachi(calculated)

2,000
1,000
0

Isshinbashi(calculated)
Kanbara weir(calculated)-1,0007/29 12:00

7/30 0:00

7/30 12:00

14
Ikarashi River
H.W.L.
13 calculated water level（7/30 9:00）
12
11 calculated water level（7/29 20:00）
10
9 calculated water level（7/29 15:00）
observed water level
87
Averaged bed elebation (calculated)deepest bed elebation (calculated)
6
Averaged bed elebation (observed)
deepest bed elebation (observed)
54
3
2
10
-1
separation area
-2
39.0
39.5
40.0
40.5
41.0
41.5
42.0
42.5
43.0

Elevation （T.P.m）

Volume percentage
finer than(%)

100

longitudinal distance from river mouth（km）
7/31 0:00

Fig.6 Discharge hydrographs in ShinanoRiver and Ikarashi River.

Fig.5 Comparison between calculated and observed water
surface profiles and longitudinal distribution of theaveraged and deepest bed elevation in Shinano River.

We apply the general BVC method to the 2011 lower Shinano River flood shown by Fig.1.
The grid size of the confluence is set sufficiently small to calculate the three-dimensional flowstructures. Boundary condition of the upstream end of the Shinano River is given by no-flux condition.
Inflow discharge hydrographs from the upstream ends of the Ikarashi River and Kariyata River areprovided so that the calculated water surface profiles coincide well with the observed ones in theobjective area. The boundary conditions at the downstream ends are given by the observed water level
hydrographs at 34.5 km point in the Shinano River and 23 km point in the Nakanokuchi River (seeFig.1). Fig.4 shows the grain size distributions to be used as the initial condition in the Shinano Riverand Ikarashi River. The bed material is composed of silt and sand and average diameter is about 0.5mm. The Manning roughness coefficient is determined by the trial so as to explain the observed water
surface profiles and bed variation in the 2011 flood. The eroded area around the left bank in 41.2 kmpoint as shown in Fig.2 is treated as movable bed condition in this analysis.

IV – 2 Results and consideration of the numerical analysis
Fig.5 shows the comparison between the calculated and observed water surface profiles andlongitudinal distributions of the averaged and deepest bed elevations in the lower Shinano River (39.043.2 km). The calculated results can elucidate the observed water levels, average and deepest bed
elevations on the whole, while the bed elevation is estimated lower than the observation in the section
indicated by an arrow in Fig.5 where the large separation area is formed due to the inflow from theIkarashi River. The calculated discharge hydrograph at Aramachi in the Shinano River is in good
agreement with the observed result as shown in Fig.6. Fig.7 shows the bed variation contour and depth
averaged velocity vectors, and Fig.8 shows main flow velocity contour and secondary flow velocity
vectors at 41.0 km and 41.2 km cross sections at the first and second peaks of the 2011 flood. Here,dark color corresponds to the velocity for downstream direction and light color indicates the velocities
for upstream direction in Fig.8. The flow attacking point is seen at the left bank in 41.1km point andScouring

Bed variation(m)

Bed variation(m)

Deposition
Erosion

Deposition areais spreading

Shinano River
41.0kmfalling intomain channnel
Shinano River
41.2kmVelocity(m/s)

Shinano River

Shinano River
Ikarashi River

Ikarashi River(b) second peak（7/30 9:30）(a) first peak（7/29 16:30）

Fig.7 Calculated bed variation contours and DA
velocity vectors in river confluence.

falling intomain channnel(a) first peak（7/29 16:30）
Shinano River
41.0kmBed elevation(T.P.m)Bed elevation(T.P.m)Deposition

Deposition

Erosion

Erosionhigh velocity zone

Shinano River
41.2kmShinano River
Ikarashi River(a) Calculated

Ikarashi River(b) Measured

Fig.9 Comparison between calculated and observed
riverbed elevation contours in river confluence.

(b) second peak（7/30 9:30）

Fig.8 Calculated main flow velocity contours andsecondary velocity vectors in cross sections.

the large separation area is formed at the downstream of the confluence at the first peak as shown in
Fig.7(a) since the inflow discharge from Ikarashi River is very large compared with that from theShinano River. Flood flows on the flood channel proceed to the upstream direction and fall into themain channel around 41.2 km point (see Fig.8(a)). Flow attacking to the river bank causes the bankerosion as shown in Fig.7(a). The bed scouring occurs along the left bank of the main channel around
41 km point (see Fig.7) where the inflow from the Ikarashi River concentrates, and the sedimentdeposition occurs along outer edge of the separation area. However, the lateral distribution of DA
velocities in the main channel becomes mostly uniform at the downstream of the confluence at thesecond peak (see Fig.7(b)) as the discharge from the Shinano River increases, and the sedimentdeposition area shifts slightly to downstream. Fig.9 shows comparison between the calculated andobseved riverbed elevation contours after the 2011 flood. As shown in Fig.9, the general BVC method
can not elucidate the depth of the bed scouring at the flow atackking point and sediment depositionarea in separation zone sufficiently. The eroded area is a rice field where the soil is very loose. But inthis study, the bed matarial on the floodplain is assumed to be the same as that of the main channel.
This is one of the reasons why the eroded area of the flood channel was estimated small.

VCONCLUSIONS

We apply the general BVC method to the confluence of the Shinano River and Ikarashi Riverfor estimating the three-dimensional flow structures and large bed variations in the 2011 flood. The
general BVC method cannot reproduce the depth of the bed scouring at the flow atackking point andsediment deposition at the flow separation area sufficiently. But it can describe the three-dimensional
flow structures and bed variations on the whole during the flood.

VIREFERENCES[1]Uchida, T. and Fukuoka, S. (2012) – Bottom velocity computation method by depth integrated
model without shallow water assumption, Journal of JSCE, Ser.B1 (Hydraulic Engineering),
Vol. 68, No. 4, I_1225-I_1230.