Journal of Japan Society of Civil Engineers, Ser.
B1 (Hydraulic Engineering), Vol. 69, No. 4, II_1-II_10, 2013.

TOWARD INTEGRATED MULTI-SCALESIMULATIONS OF FLOW AND SEDIMENTTRANSPORT IN RIVERS
Shoji FUKUOKA1 and Tatsuhiko UCHIDA2
1 Fellow of JSCE, PhD., Dr. of Eng., Professor, Research and Development Initiative, Chuo University(1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan)
2 Member of JSCE, Dr. of Eng., Associate Professor, Research and Development Initiative, Chuo University (ditto)

An integrated multi-scale simulation method of flow and sediment transport in rivers is required forriver channel designs and maintenance managements. This paper highlights the need of a new depth
integrated model without the assumption of the shallow water flow for integrated simulations of 2D and3D phenomena in rivers, indicating the applicable ranges and limitations of previous depth integrated
models. The general Bottom Velocity Computation method without the shallow water assumption is
proposed and its applicability for flows with 3D structures and bed variations is discussed in this paper.
The unified calculation method for integrated multi-scale simulations is presented to elucidate flow andsediment transport in laboratory channel and rivers during flood. Finally, we discuss issues to be solved
and the future works toward integrated multi-scale simulations of flow and sediment transport in rivers.
Key Words: integrated multi-scale simulation, depth integrated model, shallow water assumption, flood
observation, phenomena scale in river

Flows and sediment transport are controlled by two kinds ofboundaries confining the river width in the lateral direction andthe water depth in the vertical directions. River engineers andresearchers have applied one-dimensional analysis method forthe objective scale which is much larger than the river width,
two-dimensional analysis method for the problem of thephenomena scales between the river width and the water depth,
and three-dimensional analysis method for the target
phenomena much smaller than the water depth1),2). Fig. 1 shows
various phenomena scales of flow and sediment transport inrivers and their calculation methods. Because many importantphenomena related to the river management and design areaffected by the large scale phenomena compared with the water
depth, many calculation methods based on 2D models havebeen developed for practical problems in river 1)~5). On the other
hand, smaller scale phenomena than the water depth, 3D flow
structures, can affect larger scale phenomena through bed
variations and flow resistances. Although simulations ofcomplex turbulence flows and local scouring have been madepossible by recent advanced 3D turbulence models 1),2),

Watershed
area

Flood
propagation

Cascade up

River
width

Water
depth

Sediment dynamics near gravel bed

Spatial areas impact scales of the objective phenomena

1. INTRODUCTION

Sand
wave
(depthscale)

Sand wave(width scale)Local
scouring

Sediment
diameter

Sediment
diameter

3D method

Horizontal
structure

Verticalstructure

Water
depth

Longitudinal
structure

Prandtl's first kindof secondary flow

Dominant scales of the objective phenomena
Watershed
area

River
width

2Dmethod

1D method

Fig. 1 Scales and calculation methods of various phenomena inrivers.

applications of the 3D model are still limited to small scale
phenomena such as flows and bed variations in experimental
channels, because of large computational time, many memories,
and the huge computational task.
For an integrated multi-scale simulation method of flow andsediment transport in rivers, a new calculation method isnecessary to complement the 2D and 3D models. This paper
indicates the applicable ranges and limitations of previous
models, and then highlights the need of a new depth integrated
1

II_1

3D model

Bottom Velocity Computation (BVC) method. As shown in
Fig.2, bottom velocity computation methods are distinguishedby whether the shallow water flow is assumed 18) or not 19)~21).
The important equation of the BVC method is the bottom
velocity equation (1), which is derived by depth-integrating
horizontal vorticity.

Full 3D model
Hydrostatic pressure distribution[neglecting vertical momentum equation]

3D model with the assumption ofhydrostatic pressure distribution
Functions of vertical velocity distribution

Depth integrated model

General BVC method
Shallow water assumption (SWA)(including hydrostatic pressure distribution)

Quasi‐3D model (hydrostatic)

BVC method with SWA

ui  usi  ubi   ij 3 j h Helical flow model due to centrifugal force
in curved flow

Secondary flow model

Wh
z
z
 ws s  wb b
xi
xi
xi

(1)

Where, ubi: bottom velocity, usi: water surface velocity, j:depth averaged (DA) horizontal vorticity, h: water depth, W:
DA vertical velocity, zs: water level, zb: bed level, ws, wb:
vertical velocity on water surface and bottom. The bottom shear
stress acting on the bed bi is evaluated with equivalentroughness ks, assuming the equilibrium velocity condition in thebottom layer zb 21).

Neglecting vertical velocity distributions

2D modelFig. 2 Various types of depth integrated model including bottom
velocity computation method.

model without the assumption of the shallow water flow. The
present integrated simulation method is based on the general
Bottom Velocity Computation method without the shallow
water assumption. We apply and verify the method to flows
and bed variations in laboratory channels, which were difficult
phenomena to be calculated by previous depth integrated
models. This paper also presents a calculation method
combined with observation data to elucidate flow and sedimenttransport in rivers during a flood. Finally, we discuss issues andfuture works.

 bi  (cb ) 2 ui ub ,1
1  z  ak s  Ar  ln bcb
  ks(2)

Where, h/zb =e31, a=1. On the other hand, the bottompressure intensity is given by Eq.(3), depth-integrating thevertical momentum equation.

dpb





h zjzhW hWU j  bj b 

x j
x j
x j
t

(3)

Where, dp: pressure deviation from hydrostatic pressure
distribution (p=g(zsz)+dp), dpb: dp on bottom, bj : bed shear
stress, ij: shear stress tensor due to molecular and turbulence
motions and vertical velocity distribution. To calculate Eqs. (1)and (3), the governing equations for the following unknown
quantities are solved: water depth h (Eq.(4)), DA horizontal
velocity Ui (Eq.(5)), DA turbulence energy k (Eq.(6)), DA
horizontal vorticity i, (Eq.(7)) horizontal velocity on water
surface usi (Eq.(8)), DA vertical velocity W (Eq.(9)).

2. VARIOUS DEPTH INTEGRATED MODELSAND THEIR APPLICABILITY RANGE
An advanced depth integrated model, an improved 2Dmodel, is one of the effective methods to compute large-scale
horizontal flow phenomena with considering 3D flow effects.
Many improved depth integrated models have been developed
especially for a helical flow in a curved or meandering channel,
as shown in Fig. 2. Those include fully developed secondary
flow model6),7) without considering effects of secondary flowon vertical distribution of stream-wise velocity, and refinedsecondary flow models with non-equilibrium secondary
flow8),9) and mean flow redistribution effects10),11). A quasi-3D
model is a more versatile method to evaluate vertical velocity
distributions by depth integrated equations. Equations forvertical velocity distributions for quasi-3D models have been
derived from the 3D momentum equation by using a weighted
residual method12)~17). Many quasi-3D models employ theassumption of the hydrostatic pressure distribution12)~15),
because the non-hydrostatic quasi-3D model based on theweighted residual method 16),17) is difficult to be solved.
To dissolve the limitations of the previous depth integrated
models, we have developed a new quasi-3D method, theh U j h

0
t
x j
z
U i h U iU j h  gh s

x j
xi
t
hdp0 dpb zb  bi h ij




xi
 xi  x j

2
II_2

(4)

(5)

k
k 1   vh k   Pk  
U j

t
x j h xi   k xi (6)hDiji h
 Ri  P i 
t
x j

(7)

u si
u
  dp   z s
 Psi
 u sj si   g  
 
t
x j
  z  z  zs  xi

(8)

usx

0.8

usy

x =0

q

0.6

W
x
z

Uy

ubx

dpb u

by

x

y

Ux

z (m)

0.4

y

0.2
0

q(m2/s)

Case1

Case2

0.045

0.13

x =x0=1.2 (m)

‐0.2
‐1
‐0.5
0
0.5
1
1.5
x (m) 2
Fig.5 The experimental conditions on rapidly varied flow over a
structure22)ub

Case2(本解析法)
Case1 BVC

0.12

Case2(実験)Case1 Exp.
Depth-integrated continuity eq.: hDA turbulence energy transport eq.: kk 1   vh k k
  Pk  U j
x j h xi   k xi tBottom velocity eq.： ubi
z
z
Wh
 ws s  wb b
xi
xi
xi

DA horizontal vorticity eq.： iGeneral BVC method

BVC method with SWA

 U h U U h h ij  hdp0
z 
z

 dpb b   i  i j    gh s   bi x j 
x j  xi
xi 
xi
 t

Water depth h (m)DA horizontal momentum eq.: Ui

2D modelVertical velocity distribution: ui Ui ui 3 2 ui (43 32 ),h U j h

0
t
x j

ubi  u si   ij 3 j h 

Case1(本解析法)
Case2 BVC

0.10

hDij i h Ri  P i tx j

Horizontal momentum eq. on water surface： usi

Case1(実験)Case2 Exp.

0.08

Case1(2D)2D

2D
Case2(2D)

0.06
0.04
0.02
0.00
‐0.5

0.4

 
  P(Ct ) 2
   0
x j 
x j 

1.5

Case1(本解析法)
BVC
Case1(実験)
Exp.

0.3

Case2(本解析法)
BVC

pb /g (m)DA vertical momentum eq. for bottom pressure intensity: dpb
1

over a structure20)

Poisson eq. for time variation in DA vertical velocity: W



0.5

x (m)
Fig.6 Longitudinal changes in water depth for rapidly varied flow

u si
u
  dp   z s
 u sj si    g  
 Psi
 
t
x j
  z  z  zs  xi

dpb0hW hWU jz h zj  bj b 
t
x j
x j
x j

DA: Depth Averaged, BVC: Bottom Velocity Computation, SWA: Shallow Water Assumption

0.2

Case2(実験)
Exp.

0.1

uiusiUiuiusiubi

0.0

Fig.3 Governing equations and unknown quantities of BVC method‐0.1

2Dmodel3Dmodel
三次元解析法

二次元解析法‐0.5

DA flow field(Water surface
profile)

0

0.5

1

1.5

x (m)
Fig.7 Longitudinal changes in bottom pressure intensity for
rapidly varied flow over a strucutre20)

水深平均流速場
河床変動の解析法
準三次元解析
Non‐SWA
Quasi‐3D model

準三次元解析SWA Quasi‐3D
model(浅水流仮定無)Bottom velocity
field(bed topography)

turbulence diffusion, Psi: the production term of surface velocity(shear stress under the water surface layer), C= k1h/t，k1=1/20,
=(Wh)n+1(Wh)n, P=(Wh)P(Wh)n, (Wh)P: the predicted Wh
calculated by the continuity equation using (ui)P, (ui)P:
predicted velocity difference calculated by Eq (1) with (Wh)n.
These equations are obtained by assuming vertical velocity
distributions. The BVC method is summarized in Fig.3. Referto the literatures 18)~21) for details of the equations and thenumerical computation methods for the BVC method.
To clarify the applicability ranges and limitations of various
numerical methods in Fig.2, we have investigated magnitude ofeach term in depth averaged momentum equation (5) for depth
averaged flow analysis and bottom velocity equation (1) for bed
variation analysis19). Fig.4 shows summary of the results19) andlimitations of various models for the shallowness parameter s(s=h0/L0<<1, h0: the representative vertical scale (water depth),
L0: the representative horizontal scale of objective phenomena).

(浅水流仮定有)
H0/L0
10-3

10-2

10-1

1

10

Fig. 4 Limitations of various models for shallowness parameter ofobjective phenomena

 
 
(Ct ) 2
 P   0

x j 
x j 

(9)

Where, dp0: depth-averaged dp, k=1, v=vmvt, vm: kinematic
viscosity coefficient, vt: kinematic eddy viscosity coefficient,
Pk: the production term of turbulence energy, : the dissipation
term of turbulence energy, Ri: the rotation term of verticalvorticity (Rσi=usisubib), s,b: rotation of usi, ubi, Pi:the production term of horizontal vorticity, Dωij: horizontal
vorticity flux due to convection, rotation, dispersion and3
II_3

Table 1 Experimental hydraulic conditions and the various bed forms 26).
Iqd(m2/s)(m)Fr

Bedform type

Water surface level:9.6‐10.0min.

Exp.

Cal.

0

Bed level:9.6‐10.0min.

1

1/178

41.8*10-3

0.76*10-3

0.66

Dune

Dune

2

1/147

43.0*10-3

0.76*10-3

0.65

Duen

Dune

Anti-dune

Dune withmovinglong wave

downstream

length3

1/73.044.3*10-3

0.76*10-30.88

039.5*10-3

0.76*10-3

1.74

Plane bed

Plane bed

5

1/31.0-3

10.8*100.19*10-3

1.11

Anti-dune

Anti-dune

6

1/31.026.8*10-3

0.19*10-3

1.24

Anti-dune

Anti-dune

1/20.0

-3

-3

0.65

Anti-dune

Anti-dune

7

13.3*100.19*10

Bed level:8.6‐9.0min.
0

Bed level:7.6‐8.0min.
01/31.04

0.1

I: channel slope, q:discharge per unit width, d: sediment particle diameter, Fr :averaged Froude number (Local Fr varies longitudinally especially for case 5 ~7.).

For depth averaged (DA) flow fields, the applicability range ofthe 2D model covers wide ranges of the shallowness parameter.
On the other hand, for bottom velocity fields, the applicabilityof the 2D model is limited to the narrow range of theshallowness parameter due to variations in vertical velocity
distributions. This means that a quasi-3D model plays a moresignificant role in bed variation analysis. However, the shallow
water assumption is unsuitable for 0.1 < s, because themagnitude of spatial difference terms in vertical velocity ofEq.(1) and non-hydrostatic pressure terms of the horizontal
momentum equation (5) and the water surface momentum
equation (8) becomes larger with increasing s. For above
results, a quasi-3D model without the shallow water
assumption is required for multi-scale simulations of flow andsediment transport in rivers.

Bed level:6.6‐7.0min.
0

Bed level:5.6‐6.0min.
0

Bed level:4.6‐5.0min.
0

Bed level:3.6‐4.0min.
-0.1

2

3

4

Fig.8 Calculated dunes for Case 2

5

6

(m)

method. We can see the abrupt drop in the bottom pressure
intensity at x=0 in Fig.7. For Case2, the negative pressure
intensity was measured there. Although the flow is supercritical,
the water depth for x<0 decreases due to the change in slope at
x=0. On the other hand, water depth increases due to pressure
rising produced by the stream curvature at x=1.2. Thesephenomena caused by non-hydrostatic pressure cannot becalculated by the 2D method, as shown in Fig.6. It isdemonstrated that the general BVC method can calculate
longitudinal profiles of water depth and pressure intensity
acting on the bed for rapidly varied flows over a structure, as
shown in Fig.6 and Fig.7.
(2) Flow resistance and sediment transport with sand waves
The generation of sand waves complicates behaviors of flood
flow, rate of sediment transport and structure of bed topography
in rivers. Recently, some researchers have explained thepatterns of dunes in a narrow experimental channel by using a
vertical 2D turbulence model with a sediment transportmodel23),24). However, it would be unrealistic to apply thesemodels to 3D flows and bed morphology in rivers due toextremely high computational cost. A few researchers have
tried to calculate these phenomena by a depth integrated
model25). In this section, the applicability of the general BVC
method for various sand wave calculations is discussed. Table
1 shows experimental conditions with a variety of channel
slopes, discharges and particle size diameters. Those are a partof experimental conditions on various bed forms conducted by
Fukuoka et al.26). Boundary conditions of the upstream end for
calculations are given by experimental discharge. The shear
stresses acting on the bed and side wall are evaluated withequivalent roughness ks=d (d: sediment particle diameter) andManning’s roughness coefficient n=0.008, respectively. The
time variation in the bed level is calculated by the 2D continuity

3. APPLICATIONS OF THE GENERAL BVC
METHOD TO FLOW AND SEDIMENTTRANSPORT IN A NARROW CHANNEL(1) Rapidly varied flow over a structure
A calculation method for flow over a structure is required formany practical problems with respect to flood and inundation
flows. However, it is difficult to evaluate rapidly varied flow bymany depth integrated model because of the verticalacceleration with the non-hydrostatic pressure distribution. Thissection discusses the ability of the general BVC method for
calculating rapidly varied flows over a structure. Fig.5 shows
hydraulic conditions of the experiments22). Boundary conditionsof upstream end for calculations are experimental discharge andwater depth, for the state of flow over the structure was a super
critical flow.
Fig.6 and Fig.7 show comparisons of longitudinal
distributions of water depth and bottom pressure intensity
between the experiment22) and calculation20) by the general
BVC method, respectively. Fig.6 also shows results by the 2D
4
II_4

Cal.

0

Water surface level:4.6‐5.0min.

0.1

-0.1

0.08

Bed level:4.6‐5.0min.
-0.2
0Water surface level:3.6‐4.0min.

Case1

0.06

Case2
-0.1

Case3

0.04

Case4

Bed level:3.6‐4.0min.

-0.2
2

3

4

5

6

Case7
0
0

Water surface level

0.02

0.04

0.06

0.08

0.1

Exp.
5.52‐5.60min.

Bed level

-0.2

Case6

(m)

Fig.9 Calculated plane beds for Case 4

-0.1

Case5

0.02

(1) Water depth (m)Cal.
1.00E‐03

Water surface level-0.1

5.32‐5.40min.

Bed level

Case1

-0.2

Water surface level

-0.1

Case2

1.00E‐04

Case3

5.12‐5.20min.

Bed level

Case4
Case5

-0.2

Water surface level

Case6
Case7

4.92‐5.00min.

-0.1

1.00E‐05
1.E‐05

Bed level

-0.2
2

3

4

5

Fig.10 Calculated anti-dunes for Case 66

1.E‐04Exp.

1.E‐03(2) Sediment discharge rate per unit width (m2/s)(m)Fig.11 Comparisons of water depth and sediment discharge forvarious hydraulic conditions with sand waves

equation for sediment transport of the Exner’s form. The
momentum equation for sediment motion18) is used to evaluate
non-equilibrium sediment transport rate. The details of thecalculation method are discussed in the literature21).
Table 1 describes types of calculated bed forms for different
hydraulic conditions. Fig.8-10 show time variations in water
surface and bed profiles. Each figure shows 5 snapshots at theconstant time interval for the duration indicated in the figure.
Although the regime of the anti-dune moving downstream,
which was seen in the experimental channel, could not be
reproduced, the three different types of bed forms, dune (Fig.8),
plane bed (Fig.9) and anti-dune (Fig.10) were reproduced by
the general BVC method. We can see that development ofdunes moving downstream with coalescence (Fig.8) and antidunes with intermittent hydraulic jumps (Fig.10). Fig.11 shows
comparisons of measured and calculated water depth andsediment discharge for Case 1~7. The water depths andsediment discharge rates in the experimental channel withdifferent bedform types are reproduced by the general BVC
method.

4. APPLICATIONS OF THE GENERAL BVC
METHOD TO 3D FLOW AND BED
VARIATIONS(1) 3D flow structures around a cylinder
Many studies have been conducted to clarify the pier scour
mechanisms. However, few depth integrated models have been
proposed for complex 3D flows with the horseshoe vortex infront of the structure. We investigate the applicability of thegeneral BVC method for the local flow around the cylinder.
The method is applied to the experimental results27) for the flow
around a cylinder on the fixed rough bed. Table 2 shows theexperimental conditions. The size of computational gird aroundthe cylinder was 1/40 of the diameter. Experimental discharge
is given at the upstream end and water depth is given atdownstream end. The present computational method improves
our previous computation19) in evaluating bottom vorticity.
Fig. 12 shows instantaneous computed results of (a) depth5

II_5zzb/h

Table 2 Experimental conditions by Roulund et al.27)
Cylinder diameter (m)Depth (m)Channel width (m)Fr number

U/U0: -0.6 -0.4 -0.2 0

1

0.536
0.54
4.0
0.14

0.2 0.4 0.6 0.8

1

1

1.2

Measured by
Roulund et al.
(2005)

0.5
0

W (m/s):-0.2 -0.15 -0.1 -0.05

0

0.05

0.1

0.15

0.2

1

U=0.5 (m/s)

0.4

Calculated by
BVC method

0.5

0.2
0

0

-1.5

-0.2

-1

-0.5

0

0.5

1

1.5

2

x/D

Fig.13 Non dimensional vertical velocity distributions along thecenter line of a cylinder.

-0.4
-0.5

0

0.5

Roughened flood plain

1 (m)(a) Depth averaged velocity
dpb/g (m): -0.005 -0.003 -0.001 0.001 0.003 0.005

Main channel with movable bed material

ub=0.5 (m/s)
Slope: 1/600

0.4
0.2

Fig.14 A compound meandering channel(m)0

3D flow fields in front of a structure.
(2) Bed variation in a compound-meandering channel
In a compound-meandering channel, flow patterns changewith increasing relative depth Dr=hp/hm (hp: water depth onflood plains, hm: water depth on a main channel) due to themomentum exchange with vortex motions formed between
high velocity flow in a main channel and low velocity flow inflood plains1),28). For this complex hydrodynamic phenomena,
bed variation in a compound-meandering channel could notbeen explained by the depth integrated models because of theirassumption of the shallow water flow. In this section, we apply
the general BVC method coupled with a non-equilibrium
sediment transport model18) to bed-variation analysis in acompound meandering channel. Fig.14 shows the experimental
channel, which has a meandering main channel with movablesand bed and roughened flood plains. The bed variations in themain channel for various relative depths were investigated in
the experiment28). Bed variations in the flows of Dr=0.0 in
addition to Dr=0.49 are computed and compared withmeasured results (Fig.15). For a simple meandering channel(Dr=0.0), we can see large scours along the outer bank.
However, the increment in the relative depth of a compound
meandering channel causes inner bank scours instead of theouter bank scour. The reason of the above phenomena is thatthe helical flow structure in a compound meandering channel isdifferent from that in a simple meandering channel due to 3D

-0.2
-0.4
-0.5

0

0.5

1 (m)

(b) Bottom velocity and non-hydrostatic bottom pressure
Fig.12 Calculation results by the general BVC method forflow around a cylinder in open channel flow

averaged velocity, (b) bottom velocity and non-hydrostaticpressure distributions. We can see downward and reverse
bottom flows induced with low pressure in front of the cylinderand high pressure in both sides of the cylinder. Those are
typical characteristics of the horse shoe vortex.
Fig. 13 compares calculation results with the experimental
results for velocity distributions on the longitudinal crosssection along the center line of the cylinder. The opposite
rotation vortex was calculated behind the cylinder compared tomeasured result. This seems to be caused by the overproduction of turbulent energy in the separation zone by theconventional turbulent model: unsteady turbulent flows with
the Karman Vortex behind the cylinder were not developed inthis calculation as shown in Fig.12. However, the calculation
result in front of the cylinder provided a good agreement withthe measurement result, which is important to calculate local
scouring at the bed. Although the calculation method in theseparation zone is still remained as issue, it assures to simulate
6
II_6

dz:

-2

-2

-1

-1

0

0

1
2

2

-2

-2

-1

-1

0

0

1

1

Dr=0.00（単断面流れ）4200.02 0.04

1

Dr=0.492-0.1 -0.08 -0.06 -0.04 -0.02

0

-2

dz:

-0.1 -0.08 -0.06 -0.04 -0.02

00.02 0.04

2
4

-4

2

0

-2

-4

Calculation

ExperimentFig.15 Bed variations in compound meandering channel for two different types of flow

flow interactions between a main-channel and flood plains. The
present calculation results give a better agreement withexperimental results rather than full-3D calculation results withthe periodic boundary condition29). This proves that the actual
boundary conditions should be given for the bed variation
analysis, because the periodic boundary condition would givean unrealistic assumption for the analysis. Therefore it would besafe to say that the general BVC method can reproduce bed
variations in a compound meandering channel flow withincreasing relative depth.

Bed elevation(T.P.m)Observation point of water levelFig.16 Plan-form and contour of bed level of the Ishikari Rivermouth and observation points of 1981 flood

clarified by using a suitable calculation method. This section
demonstrates the bed variation analysis during the August 1981
large flood of the Ishikari River.
The peak discharge of the flood at the Ishikari River mouth
exceeded the design discharge and a large bed scouring
occurred in the river mouth. During the flood, temporal data ofwater levels were measured at many observation points asshown in Fig. 16. The cross-sectional bed forms were surveyed
before and after the flood. A lot of researches on the bed
variation of the flood have been done. One of the importantresearches was conducted by Shimizu et al.31) and Inoue et al.32)
We developed the BVC method for flood flow with 2D bed
variation analysis using observed temporal changes in water
surface profiles. In this analysis, the concentration of suspended
sediment was calculated by 3D advection-diffusion equations
in order to evaluate suspended load affected by the secondary
flow in meandering channel33),34).
Fig. 17 shows temporal changes in observed and calculated

5. BED VARIATION ANALYSIS USINGOBSERVED TEMPORAL WATER LEVELPROFILES IN RIVER DURING A LARGEFLOOD EVENT

It is difficult to know temporal changes in bed elevations
during the period of floods because of the difficulty ofmeasurement. We have developed the calculation method withobserved temporal changes in water surface profiles based on
the idea that the influences of channel shape and resistance arereflected in temporal changes in water surface profiles5),30). The
influence of bed variation during flood events is also reflected
in temporal changes of water surface profiles in the section
where the large degree of bed variation occurs. The above
indicates that the bed variation during a flood event would be7
II_7Water level (T.P.m)

8
Observed W.L. (Right bank)7
Observed W.L. (Left bank)6
Calculated W.L.(Right bank)5
Calculated W.L.(Left bank)
4
3
2
1
0
-3k -2k -1k 0k 1k

03:00-6, Aug.
12:00-5, Aug.
00:00-5, Aug.

2k

3k

4k

5k

6k

7k

8k

9k

10k 11k 12k 13k 14k 15k 距離標
16k

Water level (T.P.m)(a) Water level profiles during flood rising period
8
Observed W.L. (Right bank)7
Observed W.L. (Left bank)6
Calculated W.L.(Right bank)5
Calculated W.L.(Left bank)
4
3
2
1
0
-3k -2k -1k 0k 1k

03:00-6, Aug.
18:00-6, Aug.
12:00-7, Aug.
06:00-8, Aug.

2k

3k

4k

5k

6k

7k

8k

9k

10k 11k 12k 13k 14k 15k 距離標
16k(b) Water level profiles during the flood falling period
Fig.17 Temporal changes in water surface profiles
Cross-sectional averaged bed level

Bed level (T.P.m)

0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-3k -2k -1k

The lowest bed level in the cross-section
Observed before the flood
Observed after the flood
Calculated at the peak stage (3:00-6, Aug.)
Calculated after the flood

0k

1k

2k

3k

4k

5k

6k

7k

8k

9k

10k 11k 12k 13k 14k 15k 距離標
16k(a) Measured(b) Calculated

Fig.19 Comparison of bed topographies in the Ishikari River mouth

Fig.18 Longitudinal profiles of bed levels during the 1981 flood

between calculated and measured results after the 1981 flood

water surface profiles in flood rising and falling periods.
Calculated water surface profiles coincide with observed waterlevels affected by bed variations in each time and there are little
differences between calculated and observed water levels.
Fig.18 shows the comparison between observed and calculated
longitudinal bed forms before and after the flood. The crosssectional averaged bed elevations after the flood by thecalculation are similar and nearly coincide with those of theobserved result. Although the differences in the lowest bed
levels at the cross-sections between measured and calculated
results, large bed variations during the flood were explained by
the calculation. Fig.19 shows the comparison of bed
topographies in the Ishikari River mouth between calculated
and observed results after the 1981 flood. It would be safe to
say that calculated results capture the characteristics ofobserved bed topography in the meandering channel upstream
from the Ishikari River mouth due to the large flood event.

restricted by the shallow water assumption. However, themethod is difficult to reproduce complex 3D flow dynamics
such as separation zones behind structures. In relation to thisissue, it is needless to say that researches on detailmeasurements in laboratory channels and developments of
turbulence models would make an important contribution. On
the other hand, the basic researches in laboratories are notalways enough to clarify the large scale phenomena in rivers,
because turbulence and vortex motions depend on the flow
scale and vary with complex geometries. As discussed in the
introduction, practical problems related to flows and sedimentmotions in rivers include various scale phenomena which affecteach other. For example, Fig.20 and Fig.21 show comparisonsof horizontal and helical flow structures along a vertical wall in
the channel bend between the real scale field experiment andcalculation by the general BVC method35). For the section E,
computed secondary flow intensity and streamwise velocity inthe vicinity of the wall are relatively weak compared with thoseof the measurement. Main reasons are because the difference
between the measurement and calculation in the approachingflow at the section C should be considered. The secondary flowin the channel bend is produced by the rotation and deformationof the lateral voriticity in the approaching flow. The
approaching flow in the field experiment is affected by various
scale factors such as resistance due to sediment particles withdiverse sizes and shapes, complex bed topography, channel
plan shape and hydraulic conditions at the upstream end. The
above discussion indicates that a calculation method integratingthese different effects is necessary for actual flood phenomena.
Shimada et al.36),37) have carried out full-scale experiments on

6. ISSUES AND FUTURE WORKS TOWARD
INTEGRATED MULTI-SCALE SIMULATIONSAs discussed in this paper, it is important for river channel
designs and maintenance managements to elucidate flows andbed variations during floods by the reliable calculation methodwith use of observed data. The calculation method should be
examined and developed so as to predict the actual phenomenaof flows and sediment motions in rivers. The BVC method
based on the depth integrated model can be applied to various
flows as indicated in this paper, because the method is not8
II_8

10.2 10.4 10.6 10.8 11 11.2 11.4

2 (m/s)

(m)

(m)

(m)

Black: bottom velocity
Red: surface velocity-2-2

Revetment

Revetment
0

0

Large
stones

2

2

4

4

6

6

8

8

10

G
110

F

105

E

D C

100

B
95

(a) Measured

10

A

G
110

90

E

F

105

D C

100

A

B
95

90

(m)

(b) Calculated

(m)

11.8

Meassured byelectromagnetic
velocity meter
電磁流速計

2

11.6

(m/s)

(m)

(m)

Fig.20 Comparisons of horizontal flow structures between the real scale experiment and the general BVC method35)
護岸

平均水位

11.4

11.2

11.2

10.8
10.6

護岸

(m/s)

Section C

11

Section C

10.8

Measured by ADCP

10.6

10.4

10.4

11.8

5

4

2

1

Meassured byelectromagnetic
velocity meter
電磁流速計

2

11.6

3

(m/s)

0

-1
(m)

6

護岸

2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8

平均水位

11.4
11.2

Section E

11

Measured by ADCP

10.6
10.4
6

5

4

3

2

(a) Measured

1

0

-1
(m)

(m/s)

(m)

6

10.8

2

11.6

11.4

11

(m)

11.8

5

4

3

2

1

0

-1
(m)

0

-1
(m)

11.8

2

11.6

護岸

(m/s)

11.4
11.2

Section E

11
10.8
10.6
10.4
6

5

4

3

2

1

(b) Calculated

Fig.21 Comparisons of 3D flow structures between the real scale experiment and the general BVC method35)

levee breaches. Nihei and Kimizu38) have developed a newmonitoring system for the estimation of river discharge
combining measured data and calculations. These researches
are also expected for the clarification of actual flood
phenomena. We should put forth a steady effort inmeasurements and analysis of the flood flows and bed
variations in rivers together with basic hydraulic researches in
the laboratory.

4) Nagata, N., Hosoda, T. and Muramoto, Y.: Characteristics of river
channel process with bank erosion and development of theirnumerical models, Journal of Hydraulic, Coastal andEnvironmental Engineering, JSCE, No.621/II-47, pp.11-22,
1999.
5) Fukuoka, S., Watanabe, A., Hara, T. and Akiyama, M.:
Highly accurate estimation of hydrograph of flood discharge
and water storage in rivers by using an unsteady twodimensional flow analysis based on temporal change in
observed water surface profiles, Journal of Hydraulic,
Coastal and Environmental Engineering, JSCE, 761/2-67,
45-56, 2004.
6) Engelund, F.: Flow and bed topography in channel bends, Journal of
hydraulics division, Proc. of ASCE, Vol.100, HY11, pp.1631-1648,
1974.
7) Nishimoto, N., Shimizu, Y. and Aoki, K.: Numerical simulation of
bed variation considering the curvature of stream line in ameandering channel. Proceedings of the Japan Society of Civil
Engineers, Vol.456/II-21，pp.11-20, 1992.
8) Ikeda, S. and Nishimura, T.: Three-dimensional flow and bed
topography in sand-silt meandering rivers, Proceedings of the

REFERENCES
1) Fukuoka, S.: Flood hydraulics and river channel design, Morikita
Publishing Company, 2005.
2) Wu, W.: Computational river dynamics, Taylor & Francis, London,
2008.
3) Shimizu, Y., Itakura, T. and Yamaguchi, H.: Numerical simulationof bed topography of river channels using two-dimensional model,
Proceedings of the Japanese Conference on Hydraulics, Vol.31,
pp.689-694, 1987.

9II_926)Fukuoka, S., Okutsu, K. and Yamasaka, M.: Dynamic andkinematic features of sand waves in upper regime,
Proceedings of JSCE, No.323, 1982.
27)Roulund, A., Sumer, B. M., Fredsøe, J. and Michelsen, J.:
Numerical and experimental investigation of flow and scour
around a circular pile, Journal of Fluid Mechanics, Vol.534,
pp.351-401, 2005.
28)Fukuoka, S., Omata, A., Kamura, D., Hirao, S. and Okada,S.: Hydraulic characteristics of the flow and bed topography
in a compound meandering river, Journal of Hydraulic,
Coastal and Environmental Engineering, JSCE, No.621/II47, pp.11-22, 1999.
29)Watanabe, A. and Fukuoka, S.: Three dimensional analysis
on flows and bed topography in a compound meanderingchannel, Annual Journal of Hydraulic Engineering, JSCE,43, 665-670, 1999.
30)Fukuoka, S.: What is the fundamentals of river design –utilization of visible techniques of sediment laden-flood
flows, Advances in River Engineering, JSCE, Vol.17, pp.8388, 2011.
31)Shimizu, Y., Itakura, T., Kishi, T. and Kuroki, M.: Bedvariations during the 1981 August flood in the lower Ishikari
River, Annual Journal of Hydraulic Engineering, JSCE,
Vol.30, 487-492, 1986.
32)Inoue, T., Hamaki, M., Arai, N., Nakata, M., Takahashi, T.,
Hayashida, K., and Watanabe, Y.: Quasi-three-dimensional
calculation of riverbed deformation during 1981-year floodin the Ishikari River mouth, Advances in River Engineering,
Vol.10, 101-106, 2004.
33)Okamura, S., Okabe, K. and Fukuoka, S.: Numericalanalysis of quasi-three-dimensional flow and bed variation
based on temporal changes in water surface profile during
1981 flood of the Ishikari River mouth, Advances in River
Engineering, Vol.16, pp.125-130, 2010.
34)Okamura, S., Okabe, K. and Fukuoka, S.: Bed variation
analysis using the sediment transport formula considering
the effect on river width and cross-sectional form –in thecase of 1981 flood of the Ishikari River mouth-, Advances inRiver Engineering, Vol.17, pp.119-124, 2011.
35)Koshiishi, M., Uchida, T. and Fukuoka, S.: A new method
for measuring and calculating three-dimensional flows andbed forms around river banks, Journal of JSCE, Ser.B1(Hydraulic Engineering), Vol. 69, No. 4, 2013, accepted.
36)Shimada, T., Watanabe, Y., Yokoyama, H., and Tsuji, T.:
Cross-levee breach experiment by overflow at the Chiyoda
Experimental Channel, Annual Journal of HydraulicEngineering, JSCE, Vol.53, pp.871-876, 2009.
37)Shimada, T., Hirai, Y. and Tsuji, T.: Levee breachexperiment by overflow at the Chiyoda Experimental
Channel, Annual Journal of Hydraulic Engineering, JSCE,
Vol.54, pp.811-816, 2010.
38)Nihei, Y. and Kimizu, A.: A new monitoring system forriver discharge with an H-ADCP measurement and riverflow simulation, Doboku Gakkai Ronbunshuu B, Vol.63,
No.4, pp.295-310,2007.

Japan Society of Civil Engineers, Vol.369/II-5，pp.99-108, 1986.
9) Finnie, J., Donnell, B., Letter, J., and Bernard, R.S.: Secondary flowcorrection for depth-averaged flow calculations, Journal ofEngineering Mechanics, ASCE, Vol.125, No.7, pp.848-863, 1999.
10)Blanckaert, K. and de Vriend, H. J.: Nonlinear modeling of mean
flow redistribution in curved open channels, Water Resources
Research, Vol.39, No.12, 1375, doi:10.1029/2003WR002068,
2003.
11)Onda, S., Hosoda, T. and Kimura, I.: Refinement of a depth
averaged model in curved channel in generalized curvilinear
coordinate system and its verification, Annual Journal of
Hydraulic Engineering, JSCE, 50, pp.769-774，2006．
12)Ishikawa, T., Suzuki, K. and Tanaka, M.: Efficient numericalanalysis of an open channel flow with secondary circulations, Proc.
of JSCE, Vol.375/II-6，pp.181-189, 1986.
13)Fukuoka, S., Watanabe, A. and Nishimura, T.: On the groinarrangement in meandering rivers, Journal of HydraulicEngineering, JSCE, No.443/II-18, pp.27-36, 1992.
14)Jin Y.-C. and Steffler, P.M.: Predicting flow in curved open
channels by depth-averaged method, J. Hydraul. Eng., ASCE,
Vol.119, No.1, pp.109-124, 1993.
15)Yeh, K.-C. and Kennedy, J..F.: Moment model of nonuniform
channel-bend flow. I: Fixed beds, J. Hydraul. Eng., ASCE, Vol.119,
No.7, pp.776-795, 1993.
16)Ghamry, H. K. and Steffler, P. M.: Two dimensionalvertically averaged and moment equations for rapidly varied
flows, Journal of Hydraulic Research, Vol.40, No.5, pp.579587, 2002.
17)Ghamry, H. K. and Steffler, P. M.: Two-dimensional depthaveraged modeling of flow in curved open channels, Journalof Hydraulic Research, Vol.43, No.1, pp.44-55, 2005.
18)Uchida, T. and Fukuoka, S.: A bottom velocity computation
method for estimating bed variation in a channel withsubmerged groins, Journal of JSCE, Ser. B1 (HydraulicEngineering), Vol.67, No.1, pp16-29, 2011.
19)Uchida, T. and Fukuoka, S.: Bottom velocity computation
method by depth integrated model without shallow water
assumption, Journal of JSCE, Ser.B1 (HydraulicEngineering), Vol. 68, No. 4, I_1225-I_1230, 2012.
20)Uchida, T. and Fukuoka, S.: A computation method for flow
over structures, Advances in River Engineering, Vol.18,
pp.351-pp.356, 2012.
21)Uchida, T. and Fukuoka, S.: Numerical simulation on sandwaves using depth integrated model without the shallow
water assumption, Journal of JSCE, Ser.B1 (HydraulicEngineering), Vol. 69, No. 4, 2013, accepted.
22)Hashimoto, H. and Fujita, K. et al.: Investigations on theovertopping levee, Technical Note of PWRI, No.2074, 1984.
23)Giri, S., Shimizu, Y.: Numerical computation of sand dune
migration with free surface flow, Water Resources
Researches, Vol.42, W10422, doi:10.1029/2005WR004588,
2006.
24)Niemann, S.L., Fredsøe, J. and Jacobsen, N.G.: Sand dunes
in steady flow at low Froude numbers: dune height
evaluation and flow resistance, J. Hydrauic. Eng., Vol.137,
No.1, pp.5-14,2011.
25)Onda, S. and Hosoda, T.: Numerical simulation on
development process of dunes and flow resistance, Annual
Journal of Hydraulic Engineering, JSCE, 48, 973-978, 2004.

（Received December 31, 2012）10
II_10