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

Quasi-three dimensional analysis on the flushing mechanismof sandbar at a river mouth
M. Tateyama

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

Research and Development Initiative, Chuo University, Japan

ABSTRACT: The river mouth bars in the Aganogawa River estuary extend toward the center of riverfrom both banks. The sandbar causes the discharge capacity to decrease and the water level to rise. Therefore, it is important to understand flushing mechanism of river mouth sandbar during a flood event. The
authors’ studies on river floods showed that the flow and bed variation during a flood could be explainedby means of a suitable numerical analysis method using temporal changes in observed water surface profiles. The objective of this paper is to clarify the extension process of channel through the river mouth dueto the sandbar flushing during a large flood by the quasi-three dimensional numerical analysis, which iscapable of estimating the bottom velocity and the non-hydrostatic pressure distributions of flows.
1

INTRODUCTION

The sandbars at the mouth of the Aganogawa Riverextend to the center of the river from both sides of
the river bank (Fig. 1). The narrow channel throughbetween the bars was expanded by the largest floodin July, 2011. River mouth sandbar causes the riseof water level and brings large scale bed variation in to surrounding area during the flood. For
this reason, it needs to reveal river mouth channel
expansion process in the Aganogawa River estuary
during the large flood of July, 2011.
The water surface profiles in the estuary areachange by the tidal level and deformation of rivermouth sandbar. Fukuoka (2011) presented 2D-­
numerical analysis method using observed water
surface profiles to clarify flood phenomena,
because the time variation in water surface profiles
reflected all kinds of flow resistances during theflood. For example, Okamura et al. (2010) applied
analysis methods of a quasi-three-dimensional
flood flow and bed variation using observed water
surface profiles during a flood in the ­Ishikarigawa
River estuary. Numerical studies on sandbar flashing by flood flows have been conducted for the
Aganogawa River (Hosoyamada et al., 2006),
the Himekawa River (Sagawa et al., 2007), andthe Natorigawa River (Kuwabara et al., 1995),
using two dimensional flood flow and bed variation analysis. But the flow near river mouth sandbar is affected by the shape of river mouth andbehaves as the three dimensional flow. Secondary

Figure 1.

The estuary of the Aganogawa River.

currents generated by streamline curvatures andnon-­hydrostatic pressure distributions of flood
flows become important in determining the sandbar shape. It is difficult to consider these effects
by means of a conventional two dimensional calculation method. However, a three dimensional
calculation for flood flows and bed variation inrivers are not so easy task because of enormous

1377

c­ omputational load. Recently, Uchida & Fukuoka(2012) have developed quasi-three-dimensional
computation method (general Bottom Velocity
Computation (BVC) method), which is capable ofevaluating bottom velocity and non-hydrostaticpressure acting on bed surface. The method would
make possible to calculate the flow and bed variation around river mouth sandbar, because the shallow water assumptions such as hydrostatic pressure
distribution are not employed in the method.
In this study, the general BVC method together
with bed variation analysis in the general curvilinear coordinate system is developed to clarify theeffects of river mouth sandbar on flood flow andsurrounding bed variation by the flood in July,
2011. Prior to bed variation analysis, fixed bed
analysis using the river bed topography observed
at 5 months after the 2011 flood is made to know
when a channel through between sandbars reaches
the maximum during a flood. Then, we discuss thecalculation results of bed variation analysis aroundthe sandbars during the flood.

No. 6 are located on the sandbars. No. 7 to No. 9
are in the river channel. Most bed materials consistof medium or fine sand. The water level observation systems at the Aganogawa River estuary consist of water level stations of ­Mastugasaki (1.2 km),
Kurumiyama (5.0 km), and ten water level gauges,
and provide the temporal water surface profiles
that reflect changes in sea level and flood discharge, the sandbars deformation, and estuarine
bed ­variation. The systems worked well in obtaining data of the time variation in the water surface
profiles during the largest flood of the Aganogawa
River at July, 2011.
2.2

Objective flood

The heavy rainfall which caused the flood of 2011
recorded the largest rainfall until now. Many river
structures damaged severely such as levee failures
and revetment breaks. The maximum discharge

2 objective area and flood
2.1

Objective area

Figure 1 shows an air photo of the estuary of theAganogawa River. Figure 2 shows a plan view ofobjective area from river mouth to 16.0 km whereobservation stations of water level and discharge
are located. The river mouth sandbars are formed
around 0.0 km. Because of the bed gradient of
1/1000 to 1/10000, the salt water reaches to the distance 14.0 km from the mouth under the normal
flow conditim. Figure 3 shows distribution of particle sizes sampled at the estuary (Fig. 1). No. 1 to

Figure 3. Particle size accumulation curves in the­Aganogawa River estuary.

Figure 2. Plan view of objective area and the observation stations of water level and discharge hydrographs.

1378was observed about 11,000 m3/s in the Yokogoshi
observation station (13.5 km). It was comparable with the design flood discharge 13,100 m3/s.
Figure 4 shows observed water level hydrographsof the 2011 flood and the 2004 flood which had
been the largest flood until the 2011 flood measured at the Yokogoshi observation station in the
Aganogawa River. The 2011 flood water level anddischarge were more than those of the 2004 flood,and the maximum water levels were close to H.W.L.
We can see three peak discharges in the 2011 flood.
This paper calls the three peaks ‘Peak 1’, ‘Peak 2’,and ‘Peak 3’ in chronological order. Figure 4 shows
two shore lines surveyed at 5 months before and5 months after the 2011 flood. The shore lines were
defined by the level of 0.5 T.P.m. The markedly
eroded shore line is seen despite of the measurement of 5 months after the flood.

3

ANALISIS METHOD

3.1 Flood flow analysis method
To calculate three dimensional flow and bed variations around river mouth sandbar, pressure intensity and shear stress acting on bed surface must
be appropriately evaluated. We develop the BVC
method in the general curvilinear coordinate system. In the BVC method, bottom velocity is solved
semi-directly without computing vertical velocity
and pressure distributions, using the bottom velocity equation (Eq. 1) derived by depth integrating
horizontal vorticity:ubi = usi − ε ij 3Ω j h −(1)where, i,j = 1,2 (x,y); z = vertical axis; ubi = bottom
velocity; usi = water surface ­velocity; Ωj = depth-­
average vorticity; h = water depth; W = depth-­
average vertical velocity; ws = water surface verticalvelocity; wb = bottom vertical velocity; zs = water
surface level; zb = bottom level; ws and wb are
defined by the kinematic boundary conditions onwater surface and bottom surfaces:w( s ,b ) =Figure 4. Observed water level on Yokogoshi (13.5 km)
water level and discharge observation station.

∂z
∂z
∂ Wh
+ ws s − wb b 
∂xi
∂xi
∂ xi

∂z( s ,b )
∂t

+ ui

∂z( s ,b )
∂xi



(2)

To evaluate bottom velocity in Equation (1), thegeneral BVC method solves simultaneously depth
integrated continuity equation (Eq. 4), depth­averaged velocity (Eq. 5 and 6), depth-averaged­vorticity (Eq. 8), water surface velocity (Eq. 9 and
10), depth-average vertical velocity (Eq. 11) andbottom pressure (Eq. 12) by assuming verticalvelocity distribution:

(

)

(

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

)

(3)

where, Ui = depth averaged velocity; ∆ui = usi − Ui;δui = usi − ubi; η = (zs − z)/h.
To apply the BVC method to flood flow analysis,
we employ the general curvilinear coordinates system. The time variation in water depth is calculated
by depth integrated continuity Equation (4). The
depth-averaged velocity equation (Eq. 5 and 6) has
terms of the horizontal shear stress due to verticalvelocity distribution and pressure deviation fromhydrostatic pressure distribution. In this paper, theξ, η directional momentum equations described byphysical components are used.
Figure 5. Shore line before and after the 2011 flooddefined by the level of 0.5 T.P.m.

∂h ∂∆ηUξ h ∂∆ξUη h
+
=0 
+
∂ξ
∂η
∂t

1379

(4)

shear stress composes of turbulence and verticalvelocity distribution. The Cartesian form:(ξ direction)
∂U ξ
∂U ξ
∂U ξ
+ Uη h+ Uξ h
h

∂η
∂t
∂ξ

∂θ ξ ∂θ ξ− J Uη − Uξ cos θ ηξ Uξ h+ Uη h∂η ∂ξ( ∂ Ui ∂ U j −τ ij = 2ν t 
 − ui ′ u j ′  ∂ x j ∂ xi 

)

 ∂z
∂z 
= −τ bξ − gh  s + cos θ ηξ s 
∂η 
 ∂ξ
 ∂hdp0∂
hdp
0+ cos θ ηξ
−



∂
η
 ∂ξ


(

)

(

(

where, νt = eddy viscosity calculated by zero equation model with the assumption of locally-balanced
turbulence kinetic energy due to vertical velocity
distribution; ui ′ u j ′ = depth averaged ui ′ u j ′.
The depth integrated horizontal vorticity equations are:



 ∂z
∂z 
− dpb  b + cos θ ηξ b 
∂η 
 ∂ξ

∂
1 ∂
+ 
∆η ⋅ hτ ξξ +∆ξ ⋅ hτ ξη ∂ηJ  ∂ξ

ξ

θ
∂

ηξ
  −τ cos θ + τ
− Jh
ξξ
ξη
∂ξ

∂θ ξ + −τ ξη cos θ ηξ + τ ηη∂η 

∂h∆η Dωξ i ∂h∆ξ Dωηi ∂J Ω i h+= J  ERσ i + Pω i +

∂ξ
∂η
∂t


)

)

(

ERσ i = usiω sσ − ubiω bσ
Pω i = C pω vtb (ω bei − ω bi ) / h, C pω = κ /α , α = κ /6

)

(5)

)

 ∂hdp0∂hdp0 + cos θ ηξ
−


∂
η
∂ξ 

 ∂z
∂z 
− dpb  b + cos θ ηξ b 
∂ξ 
 ∂η

(

(

)

(

+

)

)

)

∂Ω i 
ν t  ∂Ω i
+ cos θ ηξσ ω  ∂η
∂ξ 






∂
1 ∂
∆η ⋅ hτ ηη +∆η ⋅ hτ ξη ∂ξJ  ∂η

η

θ
∂
ηξ
  −τ cosθ + τ
− Jh
ηη
ξη
∂η

∂θη 
ηξ
+ −τ ξη cos θ + τ ξξ

∂ξ 

+

∂Ω i 
ν t  ∂Ω i
+ cos θ ηξ∂η σ ω  ∂ξDωηi = −Uη Ωi + U i Ωη + ω ′η u ′ i − ω ′ i u ′η∂θ η ∂θ η+ J Uξ − Uη cos θ ηξ Uξ h  + Uη h∂η 
∂ξ

 ∂z
∂z 
= −τ bη − gh  s + cos θ ξη s 
∂ξ 
 ∂η

(

Dωξ i = −Uξ Ωi + U i Ωξ + ω ′ξ u ′ i − ω ′ i u ′ξ+(η direction)
∂U η
∂U η
∂U η
h
+ Uξ h+ Uη h

∂t
∂η
∂ξ

(

(7)

(6)

where, Uξ,Uη = depth-average velocity in ξ, η directions; J , J = coordinate transform Jacobian matrix;
g = gravity acceleration; ∆ξ, ∆η = length of gridinterval in ξ, η directions; τbξ, τbη = bed shear stress;
dp = pressure deviation from hydrostatic pressure distribution (p = ρg(zs−z) + dp); dp0 = depth averaged dp;
dpb = dp on bottom; τ ξξ , τ ηη , τ ξη = horizontal shear
stress. All velocity vectors and shear stress tensors
indicate physical components. This paper follows
the definition of the general curvilinear coordinate
system indicated by Fukuoka (2005). The horizontal(8)

where, Dωξi, Dωηi = depth-average vorticity flux
due to advection, rotation, deformation anddiffusion; ERσi = rotation of vertical vorticity;ωsσ, ωbσ = rotation of usi, ubi; νtb = eddy viscosity on bottom converted to depth averaged scale;ωbei = equilibrium vorticity on bottom calculated by the bed shear stress; κ = Karman constant number; σω = 1.0; ωξ ′ ui ′ , ω i ′ uξ ′ = depth
averaged ωξ ′ ui ′, ω i ′ uξ ′; ωξ ′,ω i ′ = deviation from
depth-­average vorticity. The vertical vorticity
distribution is defined as the differential form ofEquation (3).
The water surface velocity equations are:(ξ direction)
∂usξ
∂usξ
∂usξ
+ usη
+ usξ

∂η
∂t
∂ξ


∂θ ξ ∂θ ξ− J usη − usξ cos θ η ξ u sξ
+ u sη∂η ∂ξ  ∂z ∂dp η ξ ∂zss+ Ps ξ
= − g −    + cos θ



∂η
z
∂
∂
ξ

z = zs 



(



1380

)

(9)

(η direction)
∂usη
∂usη
∂usη
+ usξ
+ usη

∂t
∂η
∂ξ

 ∂∆η ⋅ qBξ ∂∆ξ ⋅ qBη 
∂zb
1
+
+
∂t (1 − λ ) J 
∂ξ
∂η 
1

+
(c w − q ) = 0(1 − λ ) b 0 su∂θ η ∂θ η+ u sη
+ J usξ − usη cos θ ηξ u sξ∂η ∂ξ  ∂z∂z  ∂dp s
+ cos θ η ξ s + Psη= − g − 





z
∂
η
∂
∂ξ 

z = zs 



(

)



(10)

where, usξ, usη = water surface velocity in contravariant ξ, η directions; Psξ, Psη = shear stress acting
on very thin layer under the water surface.
An equation of depth-average vertical velocity is
obtained by continuity equation (Eq. 4) and bottom
velocity equation (Eq. 1) (Uchida & Fukuoka, 2012).
For the general curvilinear coordinates system:∂∆η ⋅ h2φξ∂∆ξ ⋅ h2φη

φP − φ
=0
J ∂ξ
J ∂η
k1
 ∂φ
∂φ ∂φ
∂φ 
φξ , φη =   + cos θ ηξ,
+ cos θ ηξ  ∂η ∂η
∂ξ 
 ∂ξ

(

+

+

)



where, λ = void ratio; qBξ, qBη = ξ ,η directional
contravariant vector of bed load rate; cb = sediment concentration on the reference boundary
calculated by the Lane-Kalinske formula (1972);
w0 = settling velocity calculated by the Rubey formula (1933), qsu = suspended sediment rate calculated by the Itakura-Kishi formula (1980). The
bed load rate is calculated by the Ashida-Michiue­formula (1972). Suspended sediment load is calculated by 2D advection and diffusion equation(Eq. 14).
∂C
1  ∂∆η ⋅ U ξC∂∆ξ ⋅ U ηC 
+ 
+

∂t
∂ξ
∂η
J

∂C 
∂C  ∂ ∂ =   εs ⋅   + ε s ⋅ ∂η ∂ξ  ∂η ∂ξ  ∂ ∂C  ∂ ∂C  
+ cos θ ηξ    ε s ⋅ + ∂η  ε s ⋅   


η
∂
ξ
∂
∂ξ  ξη
ε  ∂C ∂θ∂C ∂θ + s+
 + qsu (z = zb ) − cbw0∂η ∂ξ J  ∂ξ ∂η(11)

where, φ = (Wh)n+1 - (Wh)n; φP = (Wh)P - (Wh)n;k1 = 1/20; (Wh)P = predicted depth integrated vertical velocity by using δuiP; δuiP = predicted velocity difference between water surface and bottom
velocity by Equation (1) with (Wh)n, n = time step.
The bottom pressure intensity is evaluatedby integrating the vertical momentum equation.
The equation is described in the general curvilinear coordinate system by omitting the terms of
unsteady and horizontal shear stress:
∂z
∂z
dpb
∂W
∂W
= U ξ h  + Uη h
+ τ bξ b + τ bη b  (12)

∂η
ρ
η
∂
∂ξ
∂ξ
The vertical distribution of pressure deviation dp
is defined by a linear distribution for evaluating thenon-hydrostatic pressure term in the depth-­averagevelocity equation (Eq. 5 and 6) and the pressure
distribution at water surface in water surface velocity equation (Eq. 9 and 10).
3.2 Bed variation analysis method
In this study, bed variation analysis considers bothsuspended load and bed load. Because particle
sizes are almost uniform, this study assumes bed
material as uniform d50 (0.5 mm) sand. The temporal variations in bed elevation are evaluated fromsediment continuity equation (Eq. 13).

(13)



(14)

where, ε s = diffusion coefficient (ε s = ν t).
3.3 Calculation conditions
Table 1 shows the calculation conditions.
­Figure 6 shows about 5 m computationalmesh around the river mouth. Figure 7 shows
upstream and downstream boundary conditions
which were observed water level hydrographs
at Yokogoshi (13.5 km) and Niigata West Port,­respectively. The bed resistance is evaluated by
the equivalent roughness ks(m). The ks values are
determined to reproduce water surface profiles
for Peak 2 and Peak 3. Initial cross-sectional profiles are important for the deformation analysis
of river mouth sandbar. So, initial cross-sectional
profiles set for this analysis are made carefully by
the data surveyed at 200 m intervals, contour mapof ocean floor topography observed in March
2008 (for the area downstream from -0.6 km), a
detailed bathymetry map below 0.5 T.P.m between-0.6 km and 1.0 km surveyed in February, 2011,
and images of CCTV camera installed near rivermouth and aerial photos taken during July, 2011
flood. ­Figure 10(a) shows the initial bed topography used for the bed variation analysis.

1381

Table 1. Calculation conditions.
Range ofcalculation
Boundary
condition
Mesh size
Initial bed
topography
data

Upstream end
Downstream end
Sea:
River:

Flood plane
Equivalentroughness
ks (m)

Bed material

Low water channel

Fixed bed analysis

Bed variation analysis

Sea of Japan∼6.0 km

Sea of Japan∼16.0 km

Kurumiyama water level
Yokogoshi water level
observation point (5.0 km)
observation point (13.5 km)
Niigata West Port tadal level
30 m × 30 m
5m×5m
Observed conter map of Japan Sea in Mar. 2008[-0.6 km∼1.0 km]
Observed cross(Under 0.5 T.P.m) Observed
section bed at 200 m
conter map around the bars
intervals in Dec.
(Upper 0.5 T.P.m) Observed
2011
cross section bed at 200 m
intervals in Jul. 2009[1.2 km∼16.0 km]
Observed cross section bed at
200 m intervals in Jul. 2009
Reed: 2.97, Wooded: 0.6 + Permeability coeffcient, the playing
ground & cultivation: 0.2, others: 0.6[Japan Sea∼5.0 km]
0.005 (Change on 5 hours
before Peak 3) 0.005, 0.04
(Only -0.6 km∼1.0 km)[Japam Sea∼6.0 km][5.0 km∼9.0 km]
0.005
0.005 (Change on 5 hours
before Peak 3) 0.02∼0.074[9.0 km∼]0.074
Uniform particle diameter: 0.5 mm

4 calculation rEsults
and dicussion
4.1

Figure 6. The mesh shape around the river mouth thatis adapted for bed variation analysis.

Figure 7. Boundary conditions in the movable bed
computation.

Fixed bed analysis

The river mouth sandbars changed in shape andreduced in size with time by the flood. At first,
the fixed bed analysis was carried out using bed
topography measured after the 2011 flood. This
analysis was made to estimate roughly when the
maximum deformation of sandbars occurred.
Since the flow resistance due to sandbar deformation becomes smaller, water levels around the bar
are calculated lower by means of the fixed bed
analysis. F­ igure 8 shows observed and computed
water surface profiles. At the Peak 1, especiallyfor 0.0 km–2.0 km section, the computed waterlevels are about 0.5 m lower than observed one.
This result reveals that the presence of river mouth
sandbar makes the great deal of water level rise.
At the Peak 2, the difference between observedand computed water levels is smaller than that ofpeak 1. But the computed water levels are still low
compared to the observed ones. Hence, it is considered that the river mouth bar has not yet fully
deformed. At the Peak 3, on the other hand, the1382

computed water level is higher than the observed
water level. The fixed bed analysis suggests thatthe river mouth cross-sectional area should
be expanded around the time of Peak 3 because thecross-sectional area around river mouth after theflood would become smaller than that of Peak 3 by
the river flow and the action of sea wave.

4.2 Movable bed variation analysis

Figure 8. Comparisons between observed and computed water surface profiles (fixed bed condition).

Figure 9. Comparisons between observed and computed water surface profiles (movable bed condition).

Figure 9 shows observed and computed water­surface profiles at Peak 1 (52 h), Peak 2 (69 h), andPeak 3 (86 h). The time indicated is described on
the water level hydrograph in Figure 7. Equivalentroughness coefficient ks is determined to coincide

Figure 10. Comparison of observed and computed morphologies at the peak discharge times, before and after theflood.

1383

with water surface profiles at each time. Value of
ks is assumed 0.005 (m) at the downstream andupstream reaches of 1.2 km till the time of Peak 2.
After the Peak 3, the respective values ks are 0.04 (m)and 0.005 (m). The step change in water surface
around 1.2 km indicates the rise of water levels dueto the ­reduction of the cross-section.
Figure 10 shows calculated bed topographies for(a) the initial condition before the flood, (b) Peak 1(52 h), (c) Peak 2 (69 h), (d) Peak 3 (86 h), and (e)151 h, and (f) measured 5 months after the flood.
Figure 11 shows observed and computed temporalvariations in the cross sectional forms at the rivermouth sandbar (0.2 km, 0.25 km) and in the main
channel (2.2 km, 3.2 km, 4.6 km). Figure 11 also
shows water levels at the river mouth corresponding to each flood time by dotted lines.
The computed cross-sectional area at 0.2 km
is widening over 100 m and deepening over 10 m
until the time of Peak 3 as shown in Figure 10.
This is because the flood at Peak 3 flowed over theright river mouth sandbar with the steep slope forrather long time. The 151 h computational crosssectional profile shows further channel widening
due to the erosion of the right sandbar. The computation time of 151 h would be regarded as the

Figure 11. Temporal variation of computed and observed cross-sections before and after the flood.

1384

151 h computed bed level around 4.6 km is deeper
than the observed bed level after the flood. The
resistances due to vegetated bank and bridge piersaround 4.6 km are not considered in the present
calculation.
Here, Figure 12 shows the velocity field aroundthe river mouth at Peak 3. There are clear directional gaps between water surface velocity and bottom velocity, so it means that velocity distributions
were very complex by the considerable streamline
curvatures near river mouth sandbars. The general
BVC method reproduces the process of observed
sandbar deformation. The BVC method together
with bed variation analysis is usable for estimating
the bed and bank variations in the three dimensional flow. However computed scouring depth atthe last stage is larger than observed one. It could
be related that the bed topography was measured
5 months after the flood. Hence, immediate observations of the estuarine sandbar topography after
the flood are expected in the future study.
Figure 12. Computed water surface, bottom and water
depth averaged velocity at Peak 3 around the river mouth(movable bed condition).

end of the falling stage of the flood. Figures 10(d)and (e) show that a bar moved into the river mouth
from the upstream around the time of Peak 3 andcaused a large amount of sediment deposition in
the channel center of the river mouth. On the other
hand, the left sandbar at 0.2 km in 151 h computation time does not alter in shape and differ frommeasured one. Main reason is because the overflow beyond the left sandbar did not occur during
the flood as seen in Figure 11. The cross-section
profile of 0.2 km is the survey data of the seasideof the left sandbar. The cross-sectional profile ofthe left sandbar at 0.25 km is that the riverside(0.25 km) is found to be expanded from the initialchannel form. However, the water level seems to
be not beyond the bed during the flood. However,survey data of the left sandbar before the flood
was not accurate enough compared to initial dataof the right sandbar. CCTV camera was not set
near the left sandbars and flood images taken. Thisreveals that initial river mouth sandbar topography
and camera images during floods play importantroles for the accuracy of the analysis results ofsandbar deformation.
River bed variations in the upstream of 1.2 km
are described as follows. Depositions (right side at
3.0 km–3.2 km, and center at 2.2 km) and erosions(right side at 2.0 km–2.2 km) are compared by
bed topographies computed in 151h and observed
after the flood. Computed bed variations agree
well with observed ones on the whole. However,

5 conclusions
In this paper, two kinds of numerical computations
using quasi-three dimensional analysis method(BVC method) were conducted to clarify the deformation mechanism of the river mouth sandbars by
the flood of 2011 in the Aganogawa River. One isthe analysis using fixed bed topography measured
after the flood. The other is the flood flow and bed
variation analysis by new computation method.
The main conclusions are given as follows:
1. Fixed bed analysis using bed topography after
the flood is a useful method for estimating whena channel through between sandbars reachedthe maximum cross-sectional area during aflood.
2. The BVC method using temporal changes inwater surfaces profiles and bed variation analysis provides a good explanation for deformationof the river mouth sandbars and the flushingmechanism of sandbar by a large flood.
3. Detailed survey of river mouth sandbars before
the flood and immediate survey after the floodare very important to estimate accurately rivermouth bar deformation during a flood.
references
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