Advances in River Sediment Research – Fukuoka et al. (eds)© 2013 Taylor & Francis Group, London, ISBN 978-1-138-00062-9

A new method for measuring and calculating flows and bed forms
around river banks
M. Koshiishi

Graduate School of Science and Engineering, Chuo University, Tokyo, JapanT. Uchida & S. Fukuoka

Research and Development Initiative, Chuo University, Tokyo, Japan

ABSTRACT: Three-dimensional velocity distributions and bed-forms were measured around flow
attacking zones in the experimental meandering channel in the Jyoganji River by using the Acoustic­Doppler Current Profiler (ADCP). This paper presented a measuring method for accurate ­velocity andbed profiles using individual beam data for current profiles. We proposed a numerical analysis method forthe local three-dimensional flow configuration around the revetment using bottom velocity ­computation
method without the shallow water assumption. We validated the accuracy of new analytical method
through the comparison with velocity distributions measured by the experiment. Results demonstrated thatcombined use of the measuring and calculating method presented here was useful to understand threedimensional flows around structures.
1

INTRODUCTION

Revetments were constructed to prevent the erosion against natural banks, but they also caused
severe bed scouring along revetments (Osadaet al., 2007). It is necessary for a reliable bank protection to reveal flow configurations and to develop
a calculation method of local flows around river
structures.
The recent advances in computational technologies and numerical method make possible to investigate effects of the length and orientation angleof spur dikes on surrounding flows (e.g., Halting
et al., 2007) and to reproduce the main features of
bed scouring (e.g., Duc & Rodi, 2008). However,most applications of three-dimensional analysis
are limited to the small scale phenomena in thelaboratory channels. As it stands now, it is safe to
say that three-dimensional numerical methods arerather hard to apply to scour problems for actual
flood in rivers. Because, flows attacking on revetments and resulting bed variations are influenced
by the large scale phenomena such as the channel
plan-form, water surface profiles, the dischargehydrograph, sand bars and so on. Then, a computational method for flows around structures, which
can apply to flows in a long reach during a flood
event, is required. The reliable measurement data
for model verifications is also needed to develop
a numerical model for actual flow phenomena inrivers.

Uchida & Fukuoka (2012) have developed a
new depth integrated model without the assumption of the shallow water flow to capture threedimensional flows and bed variations aroundstructures: general Bottom Velocity Computation(BVC) method. To understand flow configurations
attacking on revetments and to obtain detailed
three-dimensional velocity data for verifications of
numerical models, Koshiishi et al. (2012a) proposed
the new method for measuring three-dimensional
velocity profiles around structures using Acoustic
Doppler Current Profiler (ADCP). We applied
the method to the field experiment with the actual
scale conducted in the Jyogaji River. But problems in measurements of flows and bed-forms still
remain; bottom tracking beam data for measuring
river bed-forms in ADCP could not be collected
at many points. Some studies have suggested thaterrors in measuring bed-forms by ADCP could be
brought by side banks in the cross-section, resulting from averaging beam data from four transducers in different directions (Gunawan et al., 2010,
Nihei et al., 2008).
This paper has twofold purposes. First, wedevelop a new method for measuring three­dimensional flows and river bed-forms using
ADCP. ­Second, we apply the general BVC method
without the assumption of the shallow water flow
to the field experiment in the Jyoganji River, andvalidate its applicability to flow attacking zones
around revetments.

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2

A New METHOD FoR MEASURINGFLOWS AND BED-FORMS USING ADCPIn this section, we develop the integrated measurement method of flows and river bed-forms using
the individual current beam data of the ADCP.
And, we validate the accuracy of the methodby the field experiment in the Jyoganji River in
2011. One of the purposes of the experiment was
to investigate characteristics of erosion and bed
scouring beside revetments (Koikeda et al., 2012).
The other was to obtain the detailed data of theactual flood scale to develop and validate thecomputation method for flow and bed scouring inflow attacking areas. Figure 1 and Table 1 show
the plan view of the experimental channel andexperimental conditions, ­respectively. The experiment was conducted in a compound meanderingchannel with two vertical revetment walls: flow
attacking zone 1 and 2 in F
­ igure 1. Figure 2 shows
the picture of the velocity measurements at theflow attacking zone 1. The three-dimensional
components of velocities and bed-forms bymeans of ADCP were measured around theflow attacking zone 1. The time and the crosssectional space intervals are 10.0 s and 0.1 m,­respectively. The draft of the ADCP was decided
to avoid the effects of bubbles, because the velocity is very high around 2.5 m/s. Therefore, velocity
data couldn’t be collected in the range of about
0.4 m depth from water surface. In the two cross­sections, velocities to 0.15 m from water surface
are measured by the electromagnetic current
meter. ­Velocity variations around water surface
induced by the draft of ADCP were investigatedby Muller et al. (2007). For their experimental caseof mean velocity 2.0 m/s, the velocity was reduced
by about 5 percent at the distance 0.20 m fromtransducer of ADCP. Effects of the ADCP’s draftin this experiment were negligibly small, because
we measured velocity profile under 0.22 m fromthe transducer of ADCP.
2.1

The method for measuring three-dimensional
flow configurations (Koshiishi et al., 2012a)

Figure 3 shows the concept of the conventional ADCP method. The conventional ADCP
method gives three-dimensional velocities vx, vy,
vz in Equation 1 by using four individual beamdata v1–v4 (Teledyne RD Instruments, 2006).
vx =−v3 + v4
−v + v, vy = 1 2 ,2 sinθ
2 sinθ

v +v 
 v +vvz =  1 2 + 3 4  2
 2 cos θ 2 cos θ (1)However, the conventional method cannot giveaccurate velocity distributions of flows with local
velocity gradients and deep water depth, becauseof velocity variations within the focus spot L
which expands towards the vertical direction by
the angle of 20 degrees. So in this method, lateraland vertical velocity at any point are calculated
by Equation 2 using superimposing spatially-interpolated individual beam data v1in, v2in which aremeasured continuously in lateral direction andaveraged over time as shown in Figure 4. For theabove method, we introduce the assumption of

Figure 1. Plan view of the experimental channel.
Table 1. Experimental conditions.

Main channel
Flood plane
Total channel

Mean velocity[m/s]Water width[m]Mean depth[m]

Froudenumber

Discharge[m3/s]

1.4
0.8
1.1

5.0
15.0
20.0

0.7
0.2
0.3

0.53
0.57
0.64

5.2
2.4
7.6

Channel length: 170.0 m. Channel slope: 1/200.

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accuracy compared to the conventional ADCP
method with averaged four beam data.
2.2 A new method for measuring river bed-forms
using current profile data of ADCP

Figure 2. Picture of the measurements around the flow
attacking zone 1.

Figure 3.

Concept of the conventional ADCP method.

Figure 4.

Concept of the present ADCP method.

l­ ittle variation in temporal mean velocity during
the measurement.
vy =−v1in + v2inv +v
, vz = 1in 2in
2 sinθ
2 cos θADCP transmits bottom tracking beam for bedform mappings in addition to the current beam. In
the measurement towing ADCP, absolute velocities are calculated by using relative velocity of thewater and the ground (i.e., ship velocity) measured by bottom tracking beam (Gunawan et al.,2010, Nihei et al., 2008, Teledyne RD Instruments,
2006). However, bottom tracking beam data areoften lost or erroneous, because it is necessary to
prepare applicable values of some parameters suchas backscatter intensity (dB) and pulse-to-pulse
correlation (count) for capturing the river bed.
These values would vary depending on observation conditions in rivers. In the Jyoganji River field
experiment with cobbles on the bed surface, bottom tracking data could not be obtained in a lotof points due to the use of the factory-default setting for those parameters. In the present measuring method, velocity and bed profiles are analyzed
by the post-processing of individual beam data for
current profiling by ADCP. Figures 5 and 6 show

Figure 5. Distributions of correlation values and the
bed-form observed by the total station.

(2)

In this paper, it is assumed that variations instream-wise velocity component vx are negligiblysmall compared with those of the lateral and vertical direction; only the stream-wise velocity vx is
calculated by Equation 1 using in similar way tothe conventional method. Koshiishi et al. (2012a)
have shown that the method could measure concentrated flows in front of the revetment withaccuracy. Especially in the vicinity of bed surface,
the measuring method performed the improved

Figure 6. Distributions of intensity values and the bedform observed by the total station.

1051

Figure 7. Bed-forms estimated by present method andobserved by total station.

contours of the correlation and the intensity
measured continuously in the lateral-section. The
river bed-forms observed by the total station are
also shown in their figures as blue solid lines. The
intensity values had varied quite a bit throughmeasurement sections or measurement points. On
the other hand, the correlation values show significant changes at the vicinity of the bed surface incontrast to those of the intensity values. For thesereasons, this method evaluates river bed-forms byusing the correlation values. Figure 7 shows river
bed-forms measured by the total station, and estimate values of the bed surface by BEAM1 andBEAM2 that are defined as the bed surface at 210
count of the correlation values. While estimatedbed profiles have an error of up to 0.1 m comparedto the total station because of maximum particle
diameter of 0.1 m on the bed surface and use of
0.05 m depth cells, this method reproduces bedforms with practical accuracy.
As above discussions, the new method by using
individual current beam data can provide us accurate bed-forms data in addition to detail dataof velocity distributions. So, the method makes
it possible to obtain effective data of scouring
problems.
3

Concept of the bottom velocity computation

Here, ub2 = ubi2, ubi: bottom velocity, u*: shear
velocity, ks: equivalent roughness height, a: coefficient for the origin height of the log low. The
bottom velocity is obtained in the Equation 4,
depth-integrating horizontal vorticity.
 ∂Wh
∂z
∂z 
ubi = usi − ε ij 3Ω j h − − ws s + wb b 
∂xi
∂xi 
 ∂xi

(4)

Here, i,j = 1,2(x,y), usi: water surface velocity,Ωj: depth averaged vorticity, W: depth averaged
vertical velocity, zs: water surface level, zb: bottom
level, ws, wb: vertical velocity on water surface andbottom. The vertical distribution of velocity is
described by Equation 5.

(

)

(

u ′ i = ui − U i = ∆ui 12η 3 − 12η 2 + 1 − δ ui 4η 3 − 3η 2

GENERAL BOTTOM VELOCITYCOMPUTATION METHOD WITHOUTSHALLOW WATER ASSUMPUTION



Figure 8 shows the concept of the bottom velocity computation method. In this method, the bottom level zb on the thin vortex layer over the actual
bed z0 (zb = z0 + δzb, δzb ≒ 0.05 h, h: water depth)
is defined, and flows between the bottom and thewater surface are calculated. The thickness of thebottom layer δzb is decided to give the relationshipbetween bottom velocity and shear velocity by
Equation 3.
ub 1  δ zb + aks = ln
 + 8.5
u* κ 
ks

Figure 8.
method.

(3)

)

(5)

Here, Ui: depth averaged velocity, ∆ui: usi − Ui, δui:usi − ubi, η = (zs−z)/h, z: vertical level. If the verticalscale was much smaller than the objective horizontal scale, the terms in parentheses of the ­Equation 3
could be omitted (shallow water assumption: Uchida & Fukuoka, 2011). Koshiishi et al. (2012b)
applied the BVC method with the shallow water
assumption to a river confluence. They provided
that the method could reproduce characteristics ofthe secondary flow distributions and depth averaged flow field in the river confluence. ­However,at the objective domain in this study such as flow
attacking zones along revetments, these terms

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couldn’t be neglected for following reasons. First,
the vertical scale would be considered as the samerange with the horizontal scale due to downward
flows in front of revetments. Second, distributionsof the pressure deviate from those of the hydrostaticpressure. Therefore, to obtain the bottom velocity inEquation 4 it is required to calculate the depth averaged vorticity equations (Eq. 9), the water surface
velocity equations (Eq. 10) and the depth averaged
vertical velocity equation (Eq. 11) in addition to
the continuity equation (Eq. 6), the depth averaged
momentum equations (Eq. 7) and the depth averaged turbulence energy transport equation (Eq. 8).
∂h ∂U j h
=0
+
∂x j
∂t

(6)

 ∂U h ∂U iU j h ∂zs ∂hdp0−
ρ i +
 = − ρ gh
xi
t
x
∂xi
∂
∂
∂


j
∂hτ ij∂z− dpb b − τ bi +
∂xi
∂x j
∂k
∂k 1 ∂  vh ∂k 
+U j=
+ Pk − ε∂t∂x j h ∂xi  σ k ∂xi 

(7)

(8)

Here, τbi: bed shear stress, dp: pressure­ eviation from hydrostatic pressure distributiond(p = ρg(zs−z) + dp), dp0: depth averaged dp, dpb: dp
on bottom, τij: horizontal shear stress due to turbulence νt Sij and vertical distribution of velocity
ui ′ u j′ , Sij: depth averaged strain velocity, ui ′ u j′ :depth averaged ui ′ u j′ evaluated by the vertical distribution of velocity of quadratic curve (Eq. 5),
ν: νm+νt, νt: eddy viscosity (νt = Cµk2/ε, Cµ = 0.09),
νm: kinematic viscosity, k: depth averaged turbulence energy, Pk: production term, ε: dissipation
term (ε = Cεk3/2/∆, Cεh/∆ = 1.7).
∂hDω ij∂Ω i h= ERσ i + Pω i +∂x j∂t
ERσ i = usiω sσ − ubiω bσ
Pω i = C pω vtb (ω bei − ω bi ) / h, C pω = κ / α , α = κ / 6
Dω ij = −U j Ωi + U i Ω j + ω ′j u ′ i − ω ′ i u ′ j +ω ′j u ′ i =vt ∂Ωiσ ω ∂x j

to depth averaged value, ωbei: equilibrium vorticity
on bottom calculated by the shear stress. The equation concerning a water surface velocity is derived
from momentum equation in the very thin layer δzs(→0) below the water surface.

 ∂z
∂u
∂usi
 ∂dp s
+ Psi
+ usj si = −  g − 




∂x j
∂
z
∂
x
∂t
z = zs 
 i

Psi =

(9)

Here, ωsσ and ωbσ are evaluated by the rotation of
usi and ubi, νtb: eddy viscosity on bottom ­converted

{

}

(10)

Here, usei: Ui + (δui − ∆ui). Production term Psi is
only considered shear stress acting on undersurfaceof the very thin layer δzs, because δzs is defined as
an infinitesimal layer. It is obtained by vertical distribution of horizontal velocity (Eq. 5), satisfying
the constraint condition for uniform flow velocity
distribution. Time variation in the depth integrated
vertical velocity is calculated in Equation 11.
k1∂  2 ∂φ Ph
 +φ −φ = 0∂x j  ∂x j (11)Here, k1 = 1/20, φ = (Wh)n+1 - (Wh)n, φP = (Wh)P (Wh)n, (Wh)n: calculated Wh by the vertical distribution of velocity with δupi, δupi: calculated δui in
Equation 3 with (Wh)n, n: time step. Equation forbottom pressure (Eq. 12) is described by the depth
averaged momentum equation in vertical direction
without horizontal shear stress and unsteady terms.
∂hWU j
∂x j

=

dpb
∂z
− τ bj b
∂x j
ρ

(12)

In this method, the vertical distribution of velocity (Eq. 5) is defined as cubic polynomial by using
depth averaged velocity Ui, water surface velocity usi,bottom velocity ubi and assumption of non velocity
gradient at water surface ((∂u/∂z = 0)z = zs). ­Correlation
terms about vertical distributions of velocity and vorticity described by superscript bar in Equations 7, 9
and production terms in ­Equations 8–10 are calculated by using Equation 5. All governing equations
are interrelated through these terms with the vertical
distributions of velocity.
4

ε ki 3  6
1
1
δ u j ∆uk −  ∆u j + δ u j  δ uk 5h  522vt
12 (usei − usi ) − (3δ ui − 6 ∆ui )h2

4.1

APPLICATION TO THE FIELD
EXPERIMENT IN THE
JYOGANJI RIVER
Calculation setup

In this section, we apply the general BVC method
without the shallow water assumption to the field1053

Figure 9. Comparison of water surface profiles.

Figure 10. Water surface velocity, depth averaged velocity and bank water level at cross-section E.

experiment in the Jyoganji River in order to validate
its applicability to the large scale three-dimensional
flow. The observed water surface profiles are usedas boundary conditions of upstream and downstream, since they are considered to have higher
accurate values than observed discharge (Fukuoka,2005). The distributions of bed roughness on themain channel and the flood plane are determined
to reproduce measured water surface profiles, discharge and velocity distributions depending on
cobble diameter on the bed surface (ks = 0.2 m,
0.1 m, 0.25 m for x = 0–80 m, 80–120 m, 120–200 m
from the inlet, respectively). The length and widthof computational cells are 0.5 m and 0.25 m with
Cartesian coordinate. The bed level data are set byusing data observed by total station at intervals of
5.0 m. In the flow attacking zone 1, detailed observation results of bed-forms by the present ADCP
method are used to complement them.
4.2

Comparisons between measurement
and analysis

Figure 9 shows the comparison between measured and calculated water surface profiles.

Figure 11.
velocity.

Comparisons of water surface and bottom­ igure 10 shows comparisons of the longitudinalF
components of the depth averaged velocity, water
surface velocity and water level on both banks atcross-section E (see Fig. 11). While calculated water
surface profiles are slightly lower than measured
one downstream from 120 m, calculated values
provide good agreements with measured values onboth banks around flow attacking zone 1 (Fig. 9).
However in the case of main channel profiles asshown in the red line and plots, calculated values
are about 0.05 m higher than measured ­values1054within the section of 82–110 m. This would beconsidered as follows. Measured water levels of
the main channel were observed around interface
between the main channel and the flood plane. In
this area, there are complex momentum transports

Figure 12.

due to inflow from the flood plane to the main
channel as shown in Figure 11. And, the large gradient of water surface in the span-wise direction is
also induced by steep velocity variations as shownin Figure 10. Although calculated results reproduce

Comparison of primary flow contour and secondary flow vector.

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characteristics of depth averaged and water surface
velocity distributions, the calculated main stream
doesn’t sufficiently close to the revetment compared to measured results. Therefore, the locationof low water surface level is considered to be different from the actual one. However, about 0.05 m
difference of water level between the inner and theouter bank (Fig. 10, 0–5 m) is almost reproducedby the calculation (Fig. 9, 82–110 m). In ­Figure 11,
black vectors and red vectors show bottom velocities and water surface velocities, ­respectively. Measured bottom velocities are defined as averaged
velocities around 80 percent of depth and water
surface velocities are the measurement values by theelectromagnetic current meter at 0.15 m from thewater surface. Figure 12 shows vertical ­distributionof velocity of the primary flow as contour and thesecondary flow as vector at cross-sections A-G.
In cross-sections C and E, primary flow contours
also show measured results of electromagnetic current meter around water surface. According to themeasurement results, the secondary flow develops
around cross-section C-F with the downward flow
along the revetment at right bank (Figs. 11 and 12).
The momentum of the primary flow is transported
to the bottom of the outer bank from the surface of
the inner bank by the secondary flow, and the highvelocity region extends to the vicinity of the bottom at the cross-section F (Fig. 12, cross-section F).
In the calculation, intensity of the secondary flow
is lower than measured results, and the high velocity region around the bottom at the cross-section F
is not reproduced well. The reasons are discussed
below. In this field experiment, the primary flow
increases rapidly in vertical direction around water
surface, as indicated from cross-section C and E of
Figure 12. It is assumed that that large span-wisevorticity with the approaching flow would be converted to the stream wise vorticity due to the flow
deflection induced by the revetment with the channel bend. However, the calculated span-wise vorticity with the approaching flow is low: the difference
between water surface and bottom velocity of primary flow in the calculated results is smaller thanthat of the measurement as shown in Figures 10–12.
Therefore, the intensity of secondary flow andmomentum transports are ­underestimated. The
possible causes of the above discrepancy between
calculated and measured results are below. First, theapproaching flow which is the boundary conditionof the flow attacking zone 1 doesn’t be calculated
sufficiently. It depends on the given calculation
condition such as bed roughness coefficients inthe main channel and flood plain with diverse
grain size distribution, bed-forms around inlet
upstream cross-section No. 0 (i.e., angle and width,see Fig. 1). Second, the model parameters related
to vorticity intensity are not correct for calculatinglarge scale ­phenomena. Although, the general BVC
method have been verified by simplified laboratory
experiments, the flow conditions in the vicinity ofbottom are more complex for flows on gravel bed
rivers. Third, the present model employed the linear eddy viscosity model with only the turbulenceenergy transport equation by using dissipation
term related with water depth. Although these areproblems to be solved, calculated results provide
explanation for the measured characteristics ofthe secondary flow and the momentum transport
in the field experiment located on the complicatedchannel alignment. Especially, at the place where
the clockwise secondary flow is occurred at crosssection E-F, the calculation provides downward
flow around 3–4 m, while the absolute value is low.
The calculation results around E-F show the interactions between the flow from the flood plane tothe main channel and the flow the outer bank to theinner bank formed by secondary flow. The results
demonstrate that combined use of the new measuring and calculating method is reliable to evaluate
three-dimensional flows around structures.
5

CONCLUSIONS

We developed the new method for measuring threedimensional flow configurations and river bedforms using ADCP, and applied to the full scale
experiment in the Jyoganji River. And, the general
Bottom Velocity Computation method without
the shallow water assumption was validated using
the experiment data.
The new method using individual current profile data of ADCP makes it possible to measuredetailed velocity distributions and river bed-forms
around structures.
The general BVC method reproduces characteristics of the secondary flow and the momentum transport in the flow attacking zones along
revetments.
Complex three-dimensional flow fields andsevere scouring are expected to be solved by combined use of the measuring and the calculating
methods in addition to observations of temporalwater surface profiles and cross-sectional forms.
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