自然災害科学 J. JSNDS 36 特別号 123 -137（2017 ）DYNAMICS OF SAND BARS IN A
BRAIDED RIVER: A CASE STUDY
OF BRAHMAPUTRA-JAMUNA RIVER
SHAMPA1, Yuji HASEGAWA2, Hajime NAKAGAWA2, Hiroshi TAKEBAYASHI2 and Kenji KAWAIKE2

DYNAMICS OF SAND BARS IN A BRAIDED RIVER:
A CASE STUDY OF BRAHMAPUTRA-JAMUNA RIVER
SHAMPA1, Yuji HASEGAWA2, Hajime NAKAGAWA2,
Hiroshi TAKEBAYASHI2 and Kenji KAWAIKE2
Abstract
Simultaneous reworking with numerous channels and bars makes a dynamic braiding
network. In this study, we investigated the response of a braided river planform due tounsteady ﬂow, focusing on the dynamics of bars using a numerical simulation tool in a reachof Brahmaputra-Jamuna River with dominant compound bars. The results indicate that thefrequency of deposition on the river bed or a braided plain was higher compared to erosion
within the study reach due to unsteady changes of the ﬂow boundary conditions. The results
also indicate that the development processes of braided bars are quite different from bars ofstraight and meandering channels. The spatial growth of the bars seems to be dependent on thewidth-depth ratio of the river up to a certain range and the migration rate of the bars recedeswith the spatial growth of the bars.
Key words：Braided River, Brahmaputra-Jamuna, Bar dynamics, Numerical model, Delft3D.

1. INTRODUCTION

gy and intense bedload transport condition, which

Characterized by numerous transient

accelerates instability especially for mid-channel

mid-channel bars and channels, braided rivers

bars (Ashmore, 2013; Egozi et al., 2009). These

possess fascinating, distinctive planforms. The

bars show various planforms, which seem to beplanform changes rapidly and unpredictably in thestage-dependent and eventually construct a ver ycase of a sand bed due to the relatively high ener-

wide range of alluvial planforms due to upstream

1

2

Department of Civil and Earth Resources Engineering,
Kyoto University, Japan

123

Disaster Prevention Research Institute, Kyoto University,
Japan

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DYNAMICS OF SAND BARS IN A BRAIDED RIVER

and downstream erosion and sedimentation

amined. Attention was also given to the migration(Bridge, 1993; Ashworth et al., 2011). Therefore,

process of the sand bars. A 225-km reach of Brah-in the case of a highly sediment-laden, sand-bed

maputra- Jamuna (downstream continuation of the

braided river, different types of bars are found such

Brahmaputra River in Bangladesh, see Fig. 1) was

as unit bars and compound bars (in accordance

selected as the study site. The river is extremelywith formation) as well as free bars (mid-channel

dynamic, with a high sediment transport rate (Bakibars) and force bars (based on forcing) (Schuur-

and Gan, 2012; Sarker et al., 2014). The morpho-

man et al., 2013).

logical features of the river (bars and channels) ex-

The linear bar theory clariﬁes the relationshipperience major changes in area, shape and spatial

between the bar dimensions and the geometr y

distribution each year in response to the pulsationof the channel, which has also been verified byof discharge and sediment load during periods ofmany laboratory experiments, field observations,flooding (the annual fluctuation of discharge isand mathematical analyses (Muramoto and Fujita,

more than 60,000 m3/s) (Sarker et al., 2014).

1978; Colombini et al., 1987; Ikeda, 1990; Yalin,
1992; Garcia and Nino, 1993; Schuurman et al.,2013) but in the case of a highly-sediment-laden

2. METHODOLOGY
2. 1 GENERAL APPROACH

braided river that contains many compound bars,

As mentioned earlier, according to the process

the theor y may not always apply. Nevertheless,of development, the bars of Brahmaputra-Jamuna

linear bar theory simpliﬁes some nonlinear phys-

can be divided into two categories, compound bars

ical processes that dominate fully developed bars(A) and unit bars (B) as shown in Fig. 2. Similar

in a braided river. Moreover, the interaction of

to sand-bed braided rivers, compound bars arecompound bars and unit bars with a braided plain

more frequent in this reach compared to unit bars.

is poorly understood (Kleinhans and van den Berg,

Although most of these compound and unit bars

2011; Schuurman et al., 2013). Some researchers

are free mid-channel bars, some force bars are(Sarker et al., 2003; ISPAN, 1993) used satellite

also found (as shown by C in Fig. 2). The growth

imagery analysis to understand this type of interac-of unit bars is comparatively straightforward com-tion but the relation between the river hydraulics
and the bar dynamics needs clarifying, and in thiscase, two-dimensional numerical simulations canbe used to understand the river behavior. Hence, inthis study, we examined the response of a braided
planform due to the change of the ﬂow hydrographfrom the start of the wet period to the peak ﬂow of
the wet period, focusing on the bar properties of ahighly-sediment-laden, sand-bed braided river.
The main objective of this study was to assess
the morphological changes of the river, especiallythe response of braided bars during unsteady ﬂow
changes (flow changes in the monsoon season).
The relationship of the geometrical properties ofthe bar and channel during the peak ﬂow was ex-

Fig. 1

Map of study area

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自然災害科学 J. JSNDS 36 特別号（2017 ）pared to that of compound bars, which can migrate

and Deltares (2009) for a detailed explanation of

upstream, downstream, and even laterally by being

the Delft 3D model.

collated with other bars (Bridge, 1993). Hence the

The simulation was performed for one mon-planform changes of the river become very unpre-

soon period from the 1st of June, 2011 to the 15th

dictable due to the dynamic characteristics of theseof October, 2011. The assumption was that the ma-bars. To understand these dynamics, in this study,

jor morphological changes for that particular year

we developed a two-dimensional morphodynamic

occurred within the peak discharge period of themodel by incorporating the real river bathymetryhydrograph. The model was well calibrated andand boundary conditions for the year 2011 using

validated for the year 2012. Then, we calculated

Delft3D (ﬂow version 4.00.01.000000) software.

some bar scale properties and tried to develop the

Delft3D is a nonlinear physics-based mor-

relationship with the river hydraulics.

pho-dynamic model and its ﬂow module can solve

In addition, we deﬁned and calculated the mi-shallow water equations (unsteady) in two dimen-

gration rate of the compound bars. As the growthsions (depth-averaged) and three dimensionsof the compound mid-channel bar is not unidirec-(Lesser et al., 2004), but for the sake of compu-

tional; merging of two or three bars during a hightational time, we only used it in two dimensions.

flood is ver y common, we consider the highest

In the model, the system of equations consists oflateral distance from the old bar to the newly devel-

horizontal momentum, continuity, transport andoped bar in a particular direction as the migration

turbulence closer. It assumes vertical accelerations

amount/celerity, ωm of that particular bar for thatare ver y small compared to gravitational ones,

par ticular year using Eq. [1]. The analysis wastherefore, the vertical momentum equation is re-

carried out considering every bar as an individual

duced to the hydrostatic pressure equation (Lesser

object and it only reﬂects the annual alteration of

et al.; 2004). The ﬁnite difference method of alter-the bar shape.

nating direction implicit (ADI) was used to solve[1]

the dif ference equations. Here, the turbulencecloser model was achieved by applying a constanthorizontal eddy viscosity. See Lesser et al. (2004)

Where(amax)bn=Area of minimum bounding rectangle
determined by using Freeman and Shapira (1975),
lbn=Longer side length of the minimum bounding
rectangle determined by using Freeman and Shapira (1975), amax is determined by using the following
algorithm (Eq. [2] to Eq. [4])[2][3]j=number of segments=1, 2,…, nFig. 2 Examples of dif ferent types of bars in
Brahmaputra-Jamuna

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DYNAMICS OF SAND BARS IN A BRAIDED RIVER

season satellite imager y, Indian Remote Sensing[4]Linear Integrated self-scanning III (IRS-LISS III)
images from 2011 to 2012, as described in SectionHere,

3. The images represent the dry season scenario

A f=Area of new compound bar, A i=Area ofas most of the images were captured in February.

old bars from which the compound bar is formed,
ΔA=Newly accredited area of that particular com-

2. 2 BAR PROPERTIES

pound bar., aj=Equal width segmented area to the

We defined the bar properties following themean ﬂow direction, amax=Area of the largest seg-

definitions used by previous researchers, Garcia

ment ajand Nino (1993), Schuurman et al. (2013) and Ea-

Fig. 3 shows a simple example of bar migra-

ton and Church (2011). For determining the bartion calculation definitions of a compound bar.

length, one bar was treated as an individual object

Here, b1,b2 and b3 (Fig. 3a) are the old bars fromand the longest axis gave the length of the bar, L

which a new compound bar bf (Fig. 3b) has been

and the difference between trough and crest levels

formed. Figs. 3c and d show the definitions ofgave the value of bar amplitude, H. For dimension-

terms used in Eq. [3] and [4].

al analysis, dimensionless bar height Hb was calcu-

We validated the migration rate using dr y

Fig. 3lated by dividing the bar amplitude H by the maxi-

Schematic definition figure for bar migration calculation

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自然災害科学 J. JSNDS 36 特別号（2017 ）mum scour depth S 0 (S 0 represents the general[8]):scour due to ﬂuvial erosion). The constant channel
width of the river, W was determined by measuring[8]

the width of the bankline of the river of the year
2011 ever y 10 km and calculating their average.
This constant channel width, W was considered for
estimating the river＇s width/depth, β and it is de-In the y-direction, conservation of momentum (Eq.

ﬁned by dividing this width by the monthly maxi-[9]):

mum water depth d within the simulation area. The
relative migration rate, ω was deﬁned by the ratioof the migration rate of that particular bar to the[9]monthly mean flow velocity, Uo. Aspect ratio, α isdeﬁned by the bar length to the width ratio,

.

Where

The dimensionless stream power Ω was calculat-

η=water level elevation with respect to datum＊(here in m), h=water depth (m), u,v=depth average

ed by Eq. [5]velocity in the x and y directions, respectively (m/[5]s), g=acceleration due to gravity (m/s－2), vt=kinetic eddy viscosity (m2/s), n=Manning＇s coefficient

Here g is gravitational acceleration, S defines the(sm－1/3)

slope and D50 represents the median grain size of

Kabir and Ahmed (1996) compared different

the sediment. Δ is the submerged speciﬁc gravity

sediment transport formulae using ﬁeld data (col-of sediment calculated by using the following Eq. [6]lected by Flood Action Plan -24) and concluded
that Van Rijn (1984) estimates the peak period sed-

[6]

iment discharge well. Therefore, we also adopted
this formula for estimating sediment discharge

where ρs is the density of sand and ρf is the density

considering the equilibrium sand concentration atof water.

the inﬂow boundary. The total load, qθ(Eq. [10]) is

2. 3 DESCRIPTION OF 2D MORPHODYNAMIC MODEL

calculated using the bed load transport, qθb and thesuspended-load transport, qθs:
[10]

A two-dimensional depth average morphodynamic model was developed using Delft3D software (ﬂow version 4.00.01.000000) by applying the

The bed load transport rate qθb is computed by Eq.
[11]following hydrodynamic equations.
Conservation of mass was calculated by using
the continuity equation (Eq. [7]):[7]In the x-direction, conservation of momentum (Eq.

[11]

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DYNAMICS OF SAND BARS IN A BRAIDED RIVER

The suspended-load transport qθs is deﬁned by Eq.

determined by Eq. [18]

[12]
[18]

[12]
Where, τc=critical bed shear stress and τ=bed shear

Here, T is the nondimensional bed share stressstress, μc is the ratio between the total bed rough-and is determined using VanRijn (1984).

ness and the grain related bed roughness and U is

The bed slope effect was considered and di-

the depth-averaged ﬂow velocity in the ﬂow direc-

rectional sediment transport derivatives qx and qy

tion. The dimensionless particle parameter is D＊

were calculated by using the following equations

deﬁned by Eq. [13](Eq. [19] and Eq. [20]).
[19]

[13]

[20]

Here, s is the speciﬁc density (ρs/ρf), ϑ is the kinematic viscosity coefﬁcient[21]

fs=the shape factor for the vertical distribution ofsuspended sediment and is determined by Eq. [14]

θ is the shield mobility parameter, ηb is the bed level ε, γ is the calibration parameter and φτ is the angle between the downstream direction (x-axis) and[14]

the sediment transport vector, and modiﬁcation ismade by the spiral ﬂow using Eq. [22][22]Here, a=Van Rijn＇s reference height and is determined by Eq [15].
R=radius of local streamline curvature[15]

is the change in bed level and it is calculated
by using the Exner (1925) equation for conserva-[16]tion of mass for sediment calculated following Eq.
[23]

Z is the suspension parameter and is determined[23]by Eq. [17] and φ is the overall correction factor.
[17]Here, MF is the morphological acceleration

Here ωs is the particle fall velocity of suspended

factor to reduce the computational time step tosediment, Ψ is the coefficient related to the dif-

adapt the morphology.

fusion of sediment particles, κ is the constant of
Von-Karman and u＊ is the overall bed share velocity.

2. 3. 1 MODEL SCHEMATIZATION
For the numerical model, a 225-km long curvi-

fa=Van Rijn＇s reference height proportionality factor

linear grid was constructed with an average width

ks=Current related effective roughness heightof 13 km; starting from almost 10 km downstream

Ca=reference concentration (VanRijn, 1984) and isof the Noonkhawa water level measuring station

129

自然災害科学 J. JSNDS 36 特別号（2017 ）and ending near Aricha (Fig. 4). The reach was

The simulation period of our model was thediscretized by 1117x73 grid cells. This grid resolu-

1st of June, 2011 to the 15th of October, 2011 andtion was chosen to cover every bar by at least two

the boundary conditions are shown in Fig. 5. As

grid cells (grid cell size 201x178 m2) because thethe upstream boundary condition discharge databar size ranges from 549.83x205 m to 28635x10475

was used. The river Brahmaputra-Jamuna has only

m2 within study reach of Brahmaputra-Jamuna.

one discharge measuring station at Bahadurabad

2

The measured river cross-section by the Ban-

(Fig. 4), which is situated almost at the middle

gladesh Water Development Board (BWDB) in

part of the study reach, and one major contributing

2011 was used as the bathymetry data Along withtributary, Teesta, also lies within the upper part ofthis, for bar-top topography, Shuttle Radar Topog-

the study reach (Fig 1). Hence, for estimating theraphy Mission (SR TM) data was used in somedischarge at the upstream boundary, a 1D model

places.

was used and the model was calibrated to the ﬂow

Fig. 4The model domain

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DYNAMICS OF SAND BARS IN A BRAIDED RIVER

Table 1 Boundary Conditions and Model Parameters
PARAMETER

Fig. 5Boundary conditions of the model

data at Bahadurabad. As the discharge data for

UNIT

BASE
CONDITION

MEDIAN GRAIN SIZE, D50

µm

277

DENSITY OF SEDIMENT, ρs

kg/m3

2650

DENSITY OF WATER ρf

kg/m3

1000

SUBMERGED SPECIFIC DENSITY
OF SEDIMENT, Δ

－

1.65

VAN RIJN＇S REFERENCE HEIGHTFACTOR, fa－

2

HORIZONTAL EDDY VISCOSITY

m2s－1

1

HYDRODYNAMIC TIME STEPs48

MORPHO-DYNAMIC TIME STEPs

144

GRID CELL DIMENSION

m2

201＊178

Teesta, daily average time series data was used.

ROUGHNESS (MANNING＇S)s/[m1/3]

0.027

As the downstream boundary, the water level data

MORPHOLOGICAL ACCELERATION FACTOR, MF－

3of Aricha of the year 2011 was used. The water

CALIBRATION PARAMETER ε

－

0.70

level was measured with respect to Public WorksCALIBRATION PARAMETER γ－

0.5

Datum (PWD), which is widely used datum in Ban-

THRESHOLD SEDIMENT THICKNESS

m

0.005

gladesh. It represents 0.46 m below the Mean Sea
Level (MSL) datum. The other parameters used in
the model are described in Table 1.

rabad station (Locations are shown in Fig. 1). Figs.

As the initial condition, the space var ying

6a and 6b show the discharge, water level cali-

water level, which confirms the minimum water

bration results of the model at Bahadurabad anddepth in all channels, was given. The equilibrium

Mathura, respectively. The calibration of sedimentsand concentration (VanRijn, 1984) was considered

was performed using the data set of sediment fromat the inflow boundar y for sediment calculation.

1968 to 2001 measured by BWDB and by the Flood

The initial sediment layer thickness was assumed

Action Plan-24 (FAP-24) study due to the lack of

to be 5 m at the bed. The minimum depth for sed-recent data, which is shown in Fig. 6c. In FAP-24

iment calculation was considered to be 0.1 m. The

study, sediment data represents the river condi-

morphological acceleration factor (MF) ranges

tions for a particular period (mainly the year 1993).

from 1 to 500 (Jang and Shimizu; 2005, Crosato et

For this reason, some discrepancies are foundal., 2011, 2012, Roelvink; 2006 Van der Wegen andin this dataset. As mentioned earlier, using the

Roelvink; 2008 and Lesser et al., 2004). However,equilibrium sediment concentration profile at the

we chose the MF value for a braided river andinﬂow boundary and using the Van Rijn sediment

finalized it through trial and error to best match

transport formula we calculated the sediment loadwith the real river planform and bathymetry.

at Bahadurabad. A comparison between the calculated and the observed sediment load is shown in

2. 3. 2 MODEL CALIBRATION AND VALIDATION

Fig. 6c.
A veriﬁcation of the model for the water level

The water level calibration was per formedat Sirajganj is shown in Fig. 6d. In this study, thealong four points Chilmari, Kazipur, Sirajganj andmodel was veriﬁed for the hydraulic conditions ofMathura respectively while the discharge and sed-

the year 2012.

iment calibration were performed only for Bahadu-

131

自然災害科学 J. JSNDS 36 特別号（2017 ）Fig. 6 Calibration of the model for the hydraulic conditions of the year 2011 (a,b and c) and validationof the model for the hydraulic conditions of the year 2012 (d)3. RESULTS

except in some confluences, where a huge scour

3.1 OVERALL PLANFORM, BED LEVEL(like 23.66 m PWD in Sirajganj) was observed (Fig.

AND BAR MIGRATION RATE OF THE

7b). Fig. 8 shows an example of the cross-section-

RIVER

al change of the river during the simulation period

The planform from the satellite image and(the cross-section was taken along the Bahadu-

the simulated planform are shown in Figs. 7a andrabad discharge measuring station). This figureb, respectively. The model can predict the mainindicates that a major change occurred within 2.5

anabranch but in the case of small-scale morpholo-months as the peak discharge occurred duringgy, there are some discrepancies. For example thethis time. During this period, the average of net

model did not predict the alignment of chute chan-river bed change was -0.22 m (erosion) along thisnels well (Figs. 7 c and d).

section. After that, the average of net change wasAs the model was simulated only for one peakseason, no huge bed level changes were observed

aggradation (0.02 m) along this section.
Fig. 9 shows a histogram of the bed level

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DYNAMICS OF SAND BARS IN A BRAIDED RIVER

Fig. 7Comparison of real and simulated planform and time series bed level changes

imum frequency is from 4 m to 5 m for erosion.
An example of bar migration is shown in Fig.
10. Here, the black line shows the area of the barin 2011 and the starting of the simulation and the
red line shows the area of the bar in 2012 or theend of the simulation. The satellite image analysis
indicates that the migration rate was 1.18 km while
the simulation results indicate that the migration
Fig. 8 Bed level at dif ferent time along thecross-section of Bahaduraba discharge
measuring station

rate was 1.10 km for that particular bar.
For the overall calculation of the bar migration rate, all bars (over 300 bars) were considered.
Fig. 11 shows a comparison of the bar migration

change by calculation of the model results. The

rate derived from satellite images and simulation.

bed level change data shows a bimodal distribution

This figure indicates that the prediction of theas it represents the distribution of two processes

spatial bar growth by simulation is comparable(erosion and deposition) combined into one data-

to the actual one. Both the simulation results andset. This figure indicates that the maximum fre-satellite imagery analysis show the migration ratequency of deposition is from 0 to 1 m. But the max-of the bar recedes with the growth of the bar. A

133

自然災害科学 J. JSNDS 36 特別号（2017 ）Fig. 9Fig. 11 Comparison of bar migration rate
derived from satellite image analysis
and numerical simulation

Histogram of bed level changes

Fig. 10.

Map showing an example of bar migration of one bar.

higher migration rate was observed when the bar

ly the small bars. But in the case of simulation, thearea was less than 25 km . This rate is very highmigration rate was measured just after the mon-(3 or 2.5 km/year) when the bar area is less thansoon season. Another reason for this discrepancy

2

6 km but after that, it becomes 1.5 to 1 km/year.

is the selection of the MF value. As mentioned ear-

The average migration rate of bars is 1.05 km/year

lier, this value has a very wide range, and bed level(standard deviation is 0.65 km/year) but satellite

adaptation and morphological changes depend on

image analysis shows this rate was 0.04 km/yearit.

2(standard deviation is 0.21 km/year). In the caseof estimating the migration rate from satellite im-

3.2 BAR PROPERTIES

ages, the images represent the situation for the dry

Here, bar properties were analyzed consider-period. The bars may experience erosion during

ing monthly changes. From the simulation results,

the end of the monsoon to the dry period, especial-

the dimensionless bar height and bar length are

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DYNAMICS OF SAND BARS IN A BRAIDED RIVER

Fig. 12 Relation between dimensionless widthdepth ratio to a) dimensionless barheight b) dimensionless bar lengthplotted in Figs. 12 a and b (the data represents
the monthly data). The results of the dimensionless bar height, Hb analysis indicates a good linear
correlation with width/depth ratio, β.
But the dimensionless bar length shows a nonlinear relationship with β and it seems there isa critical value of L/W (here it is around 15000)
beyond which the bar does not elongate laterally(Fig. 12b). But the linear theory of bar indicatesno such phenomenon for a straight channel andmeandering channels and according to this theory,
this value increases with the increment of β.

Fig. 13 Relationship between dimensionlessmigration speed to a) width-depth ratiob) bar aspect ratio and c) channel speed
stream power

Figs. 13a, b and c show the relationshipmigration rate also increases from 0.0024 to 0.019.

among the dimensionless migration speed of theFig. 13b reveals that the dimensionless migration

bar as the function width/depth ratio β, bar as-

rate is higher (0.019) for a relatively low aspect

pect ratio, α and the dimensionless stream power,

ratio bar. Fig. 13c indicates that with the increase＊Ω (the data represents the monthly propagation).

of dimensionless stream power Ω＊, the dimen-

Fig. 13a indicates that with the increase of width/

sionless migration decrease maintains a nonlinear

depth ratioβfrom 549 to 665 the dimensionlessrelationship.

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自然災害科学 J. JSNDS 36 特別号（2017 ）4. DISCUSSION
In this paper, several phenomena of a braided
bar are investigated using numerical simulations.

concluded the following:
・The complex growth of a compound bar can bepredicted using a 2D morpho-dynamic model.

Doeschl et al. (2009) and Ashmore (2013)

But finer bathymetry data is needed to simulateshow the change of bed elevation of another braid-some small-scale properties (e.g. formation ofed river using a physics-based model, laboratorychute channel over the bar).

experiment, and ﬁeld data and summarize a similar

・The frequency of deposition on a river bed

type of distribution, which we obtained in the bed

or a braided plain was higher compared toelevation change histogram shown in Fig. 9.

the erosion due to the response of unsteady

The rate of migration seems to be higher

discharge and water level change in the study

compared with that in previous researches; Bridge

reach of Brahmaputra-Jamuna for that particular(1993) estimates this rate is 500 m per year. But

year.

they consider only one mid-channel bar in Brahmaputra-Jamuna for their analysis.

・A dimensionless bar height behaves similar
to a straight or meandering river but the

The dimensionless analysis indicates that thedimensionless bar length behaves differently.

bar height of a braided bar behaves similarly to

The dimensionless bar proper ty analysis

bars in straight channels or meandering ones as

indicates that the spatial growth of a braided bar

shown by Garcia and Nino (1993), but it shows a

can be skillfully controlled by controlling thecritical point in the case of dimensionless bar

width-depth ratio and channel discharge.

length. This analysis indicates there may also exist

・The migration rate of a bar naturally recedes

a suppression point for a braided bar in terms ofwith its growth. Hence, this phenomenon cantheratio.

also be used for better management of a braided
river.

These simulation results also indicate that

ACKNOWLEDGMENTS

the bars in the upper part of the river experience alower average depth (Fig. 7). This part also shows

The authors are grateful for the JST-JICA

higher braiding intensity (Sarker et al., 2003;

funded SATREPS project“Research on Disaster

ISPAN, 1993). Sarker et al. (2003). Egozi and Ash-

Prevention/Mitigation Measures against Floods

more (2008); Bertoldi et al. (2009) and Sarker et al.

and Storm Surges in Bangladesh”for funding this(2014) showed that the braiding intensity increases

research. The authors express their thanks towith the increase of discharge both for gravel-bed

Bangladesh Water Development Board (BWDB),

and sand-bed braided rivers and our results of di-Center for Environmental and Geographic Infor-

mensionless migration rate and stream power anal-mation Services (CEGIS) and Prof. Dr. Mostafa Ali

ysis also indicate that higher stream power is lessof Bangladesh University of Engineering and Tech-favorable for the spatial growth of a bar. Therefore,

nology (BUET) for their immense support in datain the case of bars with a relatively higher spatialcollection.

area, the bar splitting process governs rather thanthe migration process.

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（投 稿 受 理：平成29年 4 月 7 日
訂正稿受理：平成29年 7 月13日）

旨

数多くの川と砂州が同時に変化し影響し合うことによって動的な複雑なネットワークが形成される。本研究で，著者は非定常流よる網状流路の反応特性の調査を行った。特に砂州の動的変化に着目し，ブラマプトラ・ジャムナ川の大部分を占める複合砂州を対象とした数値計算を行った。本研究で，流れの境界条件の非定常性により，研究領域の河床において浸食よりも堆積の方がより多く起こっていることが判明した。また網状流路における砂州の発達過程は蛇行河川と比較して全く異なることが分かった。砂州の空間的広がりは，ある程度流路の流路幅と水深の比によって変わるように見受けられる。そしてその砂州の空間的広がりに伴って，砂州の移動する割合は減少することが分かった。