Introduction
Bar and channel dynamics in braided rivers
The complicated and dynamic network of bars and branches in large
braided rivers poses a challenge to scientists and engineers. In
particular, the morphological effects of river training and other
human-induced perturbations on this network are still a puzzle. Both human-induced disturbances and intrinsic instability put
the enormous social, economic, and ecological values of large
braided rivers under pressure. For example, fertile land along
the Brahmaputra River (India) and Jamuna River (Bangladesh) has been
consumed by the rivers due to severe bank erosion
e.g.,Fig. c, while
navigation is hampered by large and still unpredictable channel
shifts. Furthermore, engineering works within and along these rivers are, in general,
susceptible to failure by the massive rates of channel erosion and
deposition. Despite the existence and application of basic engineering
rules, attempts to control large braiding rivers have rarely been
successful . A crucial reason for
this is the inability to predict migration and reshaping of bars and
branches within the river. Another issue is that identifying
morphological effects of human-induced disturbances is difficult, and in most cases it
is impossible to isolate these from the autonomous morphodynamics. Enhanced insight and prediction capability of the dynamics within large braiding rivers are required to improve
the success rate of river training and other engineering works in
large braiding rivers, and to reduce undesired side effects and
large-scale morphological reaction.
Examples of disturbances in and along large braiding
sand-bed rivers: (a) engineering works in and along the
Jamuna River in Bangladesh: Jamuna Bridge; (b) geological
constraint by a non-erodible bank along the Irrawaddy River in
Myanmar; and (c) bank erosion along the Jamuna River in Bangladesh
(courtesy of Royal HaskoningDHV).
The dynamics within large braiding rivers include the interplay among bars,
branches, islands, and floodplains . A major
role is played by channel bar bifurcations that distribute discharge and
sediment through the braided channel network . Commonly,
bifurcations are unstable, meaning that the distribution changes over time
. The distribution of discharge and sediment determines
the migration and reshaping of bars, and it determines the initiation and
closure of branches . At the same time, discharge and
sediment distribution are controlled by the bifurcation topography and local
flow pattern. For example, the branch with the smallest angle to the
approaching flow is likely to experience the least amount of sedimentation
and to become the dominant branch . Bar
migration and reshaping might change the local flow pattern, thus affecting
the nearby upstream bifurcations through the backwater effect and nearby
downstream bifurcations by changing the approaching flow direction. This
starts a cascade of effects that links all bars and branches together. Hence,
a single disturbance in a large braiding river could affect an entire reach,
beyond the extent of individual engineering projects.
The bar and branch dynamics of braided rivers have been studied by means
of flume experiments e.g.,,
numerical modeling e.g.,, and field observations e.g.,. However, in
these studies, any artificial constraints and disturbances such as
non-erodible (flume) walls, engineering works
(Fig. a), and dredging were not considered. Also, these studies did not consider natural constraints such as rock outcrops
(Fig. b) and vegetation. Another group of studies identified and explained the
hydrodynamic and morphodynamic effects of engineering works, but
without placing them in the wider context of a river reach or
the interconnected network of branches and bars e.g.,, or only
considered the spatial distribution of bank erosion e.g.,. A third group of studies applied statistical analyses and metrics based on regime theory to describe
the long-term effects of river engineering and human interferences on
rivers. Commonly used metrics are, for example, mean channel width and
longitudinal slope e.g.,. However, these studies have not addressed the short-term
response of bars and branches on the long-term equilibrium conditions.
Physics-based numerical models provide a way to explore the
morphological effects of river training, discharge regulation, and
other human-induced pressures beyond the scale of pilots and flume
experiments, and without risks of undesired social and environmental
impacts. By comparison of scenarios, modeling can be used to isolate
the effects of a change in a single boundary condition, in model schematization, or
in model settings, which is impossible in the field and subject to noise
in flume experiments. Application of numerical models for decision
making is common in, for example, the highly regulated river Rhine in
the Netherlands. Furthermore, the natural behavior and general bar
dynamics in large braiding rivers were successfully modeled by
, , and . However, the
application of numerical models in morphologically dynamic rivers for
decision making, especially in large braiding rivers, is still in its
infancy.
Disturbances in braiding rivers
River training works and other human activities such as sand mining
and discharge regulation are disturbances to a “natural” river,
additional to disturbances caused by the intrinsic instability of
braiding rivers described by, for example, . If we consider
a river reach on the order of 100 km and without downstream
tidal influence, four groups of additional disturbances can be
identified: (1) external at the upstream inflow, (2) external along
the outer channel banks, (3) external at the downstream end, and (4) internal within the reach.
Discharge is one of the dominant external boundary conditions for
a river, regarding the abundance of hydraulic geometry relations that
use discharge as the independent parameter e.g.,. Discharge variation is attenuated by human-made
hydropower dams and water storages, and affects the downstream
morphodynamics . Many river modeling studies have
applied constant discharge, assuming a morphologically dominant or
representative discharge exists that gives similar yearly
morphodynamics to the “real” hydrograph e.g.,. However, other studies have shown that discharge
variation has a large effect on river morphology
e.g., due, among other things, to vegetation
colonization on exposed bar sections . Also, demonstrated that braiding
intensity increased with increasing discharge, although this was
temporary and braiding intensity decreased after the channel adapted
to the new discharge. In the context of both river training and morphological studies, the effects of discharge variation
on the braided river network are still largely unknown.
In addition, the direction of the flow pathway needs further
attention. Asymmetrical inflow stimulates bar and bend formation,
which has been deployed in flume experiments to generate meander bends
e.g.,. Inflow asymmetry enhances the
initiation of steady bars and subsequent channel bending that
propagates over a distance of at least several meander lengths
, but the direct effect of the disturbance damps
rapidly in the downstream direction . Linear theory also explained that
a disturbance in a river with, among other things, a sufficient width–depth
ratio amplifies in the downstream direction . However, this theory is based on the
initial stage of bars on a flat bed, and its application to
a developed braiding river is questionable.
The second group of disturbances involves bank erosion
(Fig. c) and non-uniform channel width. Although
braiding rivers are known for their dynamics of bars and branches
within their braidplain , channel migration and local
widening of the braidplain are common . Bank erosion results in local braidplain widening
and thus higher braiding intensity as predicted by linearized models
e.g., and observed in nature
. It could also result in fixation of bars
. At the same time, and
demonstrated that the bank erosion along the
braidplain is linked to bar dynamics, as mid-channel bars steer the
flow towards the braidplain banks. Bank erosion is also an important
sediment source for mid-channel bars . Furthermore, lateral constraints by non-erodible banks
can cause local bed degradation and attract
flow. In numerical models, both erodible floodplains and fixed walls
have been applied with variable results. Erodible floodplains in the
simulations of resulted in major local
braidplain widening. In contrast, reported
a relatively small difference in bar pattern statistics between
a braided channel with erodible floodplains and non-erodible
walls. However, that model failed to produce sustained bar and branch
dynamics that would cause bank erosion, because the grid resolution
was too low to produce cross-bar channels and thus new
bifurcations. Thus, a robust comparison of bar and channel dynamics in
a braiding river with and without erodible floodplains is still
lacking.
The third group of disturbances is related to engineering and
training works, such as groynes , bridges
Fig. a and sand
mining. Although the structures are static, they introduce
a disturbance to the original situation. River training is a common
practice in meandering rivers to control meander migration and channel
depth, but it is scarcely applied in large braiding rivers. This is due to
the enormous dimensions of these rivers, the high costs, and the
large uncertainties and risks of uncontrollable negative impact. Furthermore, bar
and channel dynamics affect the efficiency of the training works
. Both the capability of the river to destroy the training works and the
difficulty of predicting the effects of training works are problems
engineers face in controlling large braiding rivers.
Research questions, hypothesis and approach
In this study, we analyzed the natural response of several simplified generic types of
human-induced disturbances in large sand-bed braiding rivers using
the numerical model Delft3D.
The main research question is, how do
disturbances within and along a large braiding river affect the
reach-scale braided channel network? Minor research questions are,
what are the local effects of engineering works and how do these effects
propagate through the braided channel network, and what are the effects of
discharge attenuation and bank protection along the river on the bar
and branch dynamics in braiding rivers?
The hypothesis is that the local bed level change due to
a disturbance can be estimated using basic engineering rules. For
example, a decline of channel width is expected to result in
deposition upstream of the narrowing, bed degradation in the vicinity of
the narrowing, and deposition further downstream. These bed level
changes are expected to modify the discharge and sediment division
over nearby bifurcations and the bifurcations become instable (“bifurcation instability”). Then, the
network aspect described by is expected to
emerge: bars are reshaped and migration directions are altered by the
bifurcation instability, which again affects both the upstream
bifurcation through the backwater curve and the downstream
bifurcation through redirection of the approaching flow. Thus, it is
hypothesized that a single disturbance within, along, or upstream of a
braiding river reach causes a local bed level change that triggers a cascade of morphological changes in the network, eventually affecting the entire reach.
We tested the hypotheses using a physics-based numerical model to
systematically set up a “data set” of braiding rivers with different
types and degrees of disturbances. These disturbances are loosely comparable with real cases,
and our goal was to show the generic effects of perturbations rather than evaluating specific
training works. We compared the morphodynamics in the
disturbance scenarios with a reference case without the
disturbance. In general, first the local morphological effects were
determined, and second the larger-scale effects were identified and
analyzed.
Model descriptions and methods
Numerical three-dimensional model
We used the physics-based numerical model Delft3D to construct
a braided channel morphology for different scenarios of disturbance. This approach is
similar to our earlier work in and
. The hydrodynamics were computed in three
dimensions by applying conservation of momentum
(Eqs. and ) and
conservation of mass (Eq. ). The hydrostatic
pressure assumption was adopted (Eq. ).
∂u∂t+u∂u∂x+v∂u∂y+w∂u∂z=-g∂zw∂x-guu2+v2C2h+Vh∂2u∂x2+∂2u∂y2+∂∂zVv∂u∂z,∂v∂t+u∂v∂x+v∂v∂y+w∂v∂z=-g∂zw∂y-gvu2+v2C2h+Vh∂2v∂x2+∂2v∂y2+∂∂zVv∂v∂z,∂∂xhu+∂∂yhv+∂w∂z=0,dPdz=-gρw,
where x is the downstream coordinate (m), y is the lateral
coordinate (m), z is the vertical coordinate (m), zw
is the water surface level (m), u is the flow velocity in the
x direction (ms-1), v is the flow velocity in the
y direction (ms-1), w is the flow velocity in the
z direction (ms-1), h is the water depth (m), C is
the Chézy roughness (m1/2s-1), g is the gravity
acceleration constant (ms-2), Vh is the
horizontal eddy viscosity (m2s-1), Vv is
the vertical eddy viscosity (m2s-1), ρw
is the water density (kg m-3), and P is the pressure
(Nm-2). The bed friction terms in
Eqs. () and () are only
applied in the first near-bed layer. Near the bed w=0 ms-1, and at the water surface w=dh/dt. A detailed description of the hydrodynamics
and numerical scheme of Delft3D can be found in
, , and .
The bed level change in Delft3D is the result of sediment transport,
bed slope effects, bank erosion, and mass conservation in the bed. The
sediment transport rate in each grid cell is equal to the sediment
transport capacity calculated with :
qs=0.05U5gC3Δ2D50,
where qs is the total sediment transport per unit width
(m2s-1), U is the depth-averaged flow velocity in the
streamline direction (ms-1), Δ is the relative mass
density of sediment underwater (-), and D50 is the median grain
size (m). The amount of upstream sediment inflow at the upstream
boundary was set equal to the local sediment transport capacity, which
keeps the bed level along the upstream boundary constant. The
transverse bed slope effect, which is the downslope pulling of
sediment by gravity and essential in morphodynamic models
e.g.,, is computed
according to . After each time step, the bed
level was updated using the Exner equation. To reduce computational
time, an acceleration factor of 25 was used for bed level change on
the basis of spatial sediment transport gradients, which is allowed
because morphology changes much slower than hydrodynamics. The chosen
acceleration factor has no significant effect on morphology
.
Sediment transport was only calculated above threshold water depths of
0.1 m. Grid cells with smaller water depth were considered to
be inactive. Inactive grid cells reactivated when the threshold water
depth was exceeded, either by water level rise or by a simplified
formulation of bank erosion. Here, “bank erosion” of a dry grid cell
occurred when a neighboring wet grid cell eroded, where 50 % of
the incision in the wet cell was applied to the dry cells
. This prevents unnatural effects of
accidentally emerged cells. Test runs showed that the resulting
morphology is relatively insensitive to the bank erosion percentage.
Default model settings and boundary conditions
We adopted the river dimensions and conditions from
for the default scenario conditions
(Table ): a straight initially plane bed with
3200 m width, 80 km length for scenario series A and 40 km for scenario series B, an initial bed slope of
9.3×10-5, uniform fine sand (D50=200 µm), and a constant discharge of
40 000 m3s-1 (which is close to the effective
discharge of the Brahmaputra River). Fixed channel walls were applied by default.
The computational domain was discretized by 50m×20 m grid cells, and the water column was divided into seven
grid cells with boundaries at constant fractions of the water depth
(thus σ grid). Thus vertical grid resolution was
relatively high at low water depths. The length of each grid cell was
2.5 times the grid cell width in order to keep the aspect ratio
around 2 and to optimize computational speed at the same time.
Default initial and boundary conditions.
Parameter
Unit
Value
Discharge
m3s-1
40 000
Channel width
m
3200a
Channel length
m
80 000b
Bed slope
–
9.30×10-5
Grain size D50
m
2.00×10-4
Constant ks
m
0.15
Initial water depth
m
8.6
Initial Froude number
–
0.16
Initial Shields number
–
2.42
Grid cell length × width
m
50×20
Sediment transport predictor
–
EH
Disturbance max. initial bed level
m
0.01
Disturbance period of Q
days
2.28
Disturbance SD amplitude of Q
%
0.5
Hydrodynamic time step
s
6
Morphodynamic time step
s
150
a Additional 1400 m in runs with floodplains. b 40 000 m for Runs B0 to B4.
The hydraulic boundary conditions were as follows: the inflow condition
was set at the upstream and the water level was specified for the
downstream. The upstream boundary was split into 20 separate boundary
sections, i.e., eight grid cells per boundary section. For each
boundary section, the amount of inflow was defined in
a time series. The water level at the downstream boundary was based on
initial uniform flow conditions. The hydrodynamic time step was 6 s;
thus the morphodynamic time step was 150 s.
Following, for example, , , , and
, a constant uniform bed roughness was applied,
assuming bed forms were subgrid and thus captured by the bed roughness
parameter. We applied a uniform Nikuradse ks of
0.15 m, which is recomputed to a Chézy roughness in Delft3D.
By default, the inflow and initial bed level were perturbed in the
same way as in . The upstream inflow disturbance
was a random time- and spatially varying noise added or
subtracted to the inflow at each of the upstream boundary
sections. The standard deviation of the inflow disturbance was 0.5 % of the total
discharge and the discharge disturbances changed every 2.3 days. The initial bed level
disturbance was spatially varying with a maximum of 1 cm added
to or subtracted from the initially smooth bed. The maximum bed level
disturbance was 2.4 % of the initial water depth. As these
disturbances had a much shorter time and spatial scale than the bars,
they were considered noise rather than forcing.
Scenarios
An overview of the model scenarios is given in Table
and Fig. . We used two series of simulations: series A to
simulate a “realistic” situation starting with a “realistic” bed
topography constructed by Delft3D as described by , and
series B, which is a simplified situation starting with a regular symmetrical
bar pattern. The focus of our study is on series A, as it provides a better
representation of reality than series B. The reason for using series B is
that it enables analysis of the instability of initially regular and
symmetrical bifurcations.
Model scenarios, also illustrated in Fig. .
Run
Initial bars
Extra
A0
No
–
A1
Run A0
Branch closure
A2
Run A0
Bar protection – north side
A3
Run A0
Bar protection – both sides
A4
Run A0
Structure on bar
A5
Run A0
Structure on bar
B0
Droplet
–
B1
Droplet
Branch closure
B2
Droplet
Bar protection
B3
Droplet
Sand mining
B4
Droplet
Asymmetrical inflow
Model scenarios with different types of disturbance: series A with
training works in the channel starting with bars from Run A0; and series B
with training works and sand mining starting with droplet bars. Runs A0 and
B0 are undesturbed and act as reference cases.
In series A, we applied different kinds of engineering works: a non-erodible
construction on top of one of the bank attached bars (Run A4) or mid-channel
bars (Run A5), protection at the upstream of a large mid-channel bar along
one side of the bar (Run A2) or two sides (Run A3), and closure of one branch
(Run A1). As a reference situation, the simulation was also run without
engineering work (Run A0).
In series B, we also applied closure of one branch (Run B1), upstream bar
protection (Run B2) and a reference case without engineering work (Run B0).
Furthermore, we conducted two extra situations in series B: removal of a bar,
as a simplified sort of sand mining (Run B3), and asymmetrical inflow at the
upstream boundary (Run B4).
The dams and bank protection works were schematized as impermeable
infinitely high dams, called “thindams” in Delft3D. Thindams are
infinitely thin, only block the flow in the direction perpendicular to
the dam, and do not add roughness to the flow parallel to the
dam. Because of these properties, the dams and bank protection in the
model schematization deviated from their real-world counterparts. For
example, real-world bank protection works usually have the same height
as the bank, thus allowing overflow in the case of a sufficiently high
water level.
Method for analysis
We used different methods to analyze and compare the model
simulations. The first method was the use of 2-D time series of the bed
level detrended by the initial slope. In addition, we used 2-D depth
average flow velocities to identify the dominant branches and flow
diversion by the bars and islands.
Furthermore, metrics were applied to describe the bar and branch
morphology: the active braiding index (ABI), active channel width, and
bar height, following . Additionally, we used
a channel width ratio, which we defined as the ratio between the width
of the widest branch and the width of the second widest branch. It
gives a measure of the dominance of the largest branch. The ABI
indicates the reach average number of parallel active channels, using
cross-sectional average sediment transport rates as a threshold to
discriminate between active channels and both bars and non-active
channels. The active channel width is defined as the percentage of the
braidplain width occupied by the active channels, indicating the
degree of flow concentration within the cross section. The bar height
is defined as the difference in height between the lowest 5 % and
highest 5 % of the bed level, indicating the bed level difference
between the channels and the bars.
The downstream celerity or propagation rate of the effects of the disturbances
was compared with the propagation rate predicted from theory :
c=nqsh,
with qs and h being the sediment transport and water
depth above the disturbance. For the initial conditions, the
predicted celerity, c, is around
17 kmyear-1. estimated the celerity in
the Brahmaputra at 16 to 32 kmyear-1, and compared this
with the propagation celerity observed in the field after an enormous
earthquake. They observed different propagation celerities for
different types of responses: around 50 kmyear-1 for bed
level change, which is much faster than the bars; 10 to
37 kmyear-1 for width adaptation; and
13 kmyear-1 for braiding index adaptation.
The evolution of bifurcations was analyzed using the ratio between the
discharges and sediment transport towards the left and right
branches. In our definition, a symmetrical bifurcation has a ratio of
1, and a ratio <1 indicates that more than half of the discharge or
sediment transport goes through the southern branch.
Evolution of a braided channel network and bar pattern in the
case of erodible floodplains and yearly hydrograph.
Results
Unconfined channel with natural discharge variation
A typical development of a braided channel pattern with mid-channel
bars, bank-attached bars, and multiple parallel branches is
demonstrated in Fig. . Bar formation started at the
upstream boundary. Flow concentration in the branches around the first
bars caused local incision, as well as sediment deposition downstream of the
first bars. This deposition resulted in a new bar, and again flow
concentration. This way, a migration front of new mid-channel bars and
bifurcations was created. As the bars reached the water surface, they
merged and formed large bar complexes. With this, the flow concentrated within
a few branches, increasing specific transport capacity and incision in
the branches. Together with this, braiding intensity declined to
a year-averaged ABI of 2.5. Consequently, bar and channel dynamics
declined and a dynamics equilibrium was reached, demonstrated by the steady statistics with only seasonal variation (Fig. ).
Although the bar and branch dynamics declined after reaching the
dynamic equilibrium, the river remained active with new branches
formed by cross-bar flow and existing branches closed. The channel
network statistics varied because of the seasonal water level
variation. During low discharge, the ABI was around 1.5 to 2 and only
around 10 % of the total channel width was transporting
significant amount of sediment. During high discharge, the ABI
increased to around 3.5 and active channel width increased to
30 %.
Evolution of the braided channel network and bar
pattern in case of (1) constant Q and fixed walls, (2) constant Q and
erodible floodplains, (3) hydrograph and fixed walls, and (4) hydrograph and
erodible floodplains. Panels (a)–(b) show the bed level after 16 months for
cases (1) and (2). Panels (c)–(e) show reach-average channel statistics, and
(f) shows average cross-sectional bed level profiles after 16 months for
cases (1) and (2).
Detail of short-term bar and branch dynamics in the case of a hydrograph
and fixed channel walls, starting from low discharge in month 36 and continuing to the peak discharge in
month 40 and a declining discharge thereafter.
If we take a closer look at the short-term bar dynamics within a year,
then we can identify characteristic processes of bar dynamics in each
stage of the hydrograph (Fig. ). During low discharge,
sediment mobility was low and bar dynamics were negligible. When the
discharge increased, the unit bars reactivated
(feature A in Fig. ). Also, large bar-tail limbs formed along and
downstream of the bars (features B and C in Fig. ). During the peak
discharge period, many bars were overtopped and aggradation of the
bars occurred as the flow velocity over the bars rapidly declined
(features D and E in Fig. ). At the same time, new branches formed
by cross-bar flow. During the declining discharge period, these newly
formed branches incised and widened (features F to J in Fig. ),
whereas other branches were closed by bars blocking their entrance
(feature K in Fig. ). Also, the bar margins became steeper as these
branches incised.
Simplification of model schematization and boundary conditions
Constant discharge
With a constant discharge of 40 000 m3s-1, the time
to reach a dynamic equilibrium reduced to around 13 months
(Fig. ). From that moment, the network statistics were
similar to the year-average equilibrium statistics reached after 3
years in the runs with variable discharge: an ABI of around 2.5, an
active channel width of around 20 to 30 %, and a bar height of
around 30 m. Thus, the bar pattern statistics were similar, but
the exact pattern of the bars and branches was different and bar
formation occurred at a higher pace.
Evolution of the braided channel network and bar pattern in
Run B4 with asymmetrical inflow: (a) time series of the bed
level in Run B4, (b) bed level in Run B0 after 6 months for
comparison with last time step of (a), (c) depth-average flow
velocity after 6 months in Run B4 and Run B0, and (d) discharge
and sediment distribution over the branches with Q1 and Qs1 for
the northern branches. The black arrows indicate the position of the
propagating front.
Non-erodible banks
Figure
shows the bed level after 16 months for a case with fixed walls and with erodible floodplains, both with a constant discharge. Obviously, the
exact bar and branch patterns were different and difficult to compare
directly. In both runs, large mid-channel bars and bank-attached bars
formed, and many sections were dominated by a single branch. However,
the reach-averaged bed level along the non-erodible channel walls
was clearly lower than in the case of erodible floodplains (Fig. f). On
average, the incision along the non-erodible walls was around
6 m deeper than with erodible floodplains. Despite the
erodible floodplains, overall incision along the initial channel
occurred in both runs.
A comparison of the bar pattern statistics is given in
Fig. c–e. Because of the bank erosion along the floodplains
and thus larger channel width, the ABI was higher in these runs, and the
active channel width and bar height were lower. The spatially average
floodplain erosion distance was around 300 m after 16 months, which
gives an annual braidplain width increase of around 7 % and on the same
order of magnitude as observed along the Brahmaputra River (on the order of 300–1500 m year-1; ). The lower active channel width can be explained
by an increase in bar number, occupying a larger part of the channel.
Overall, the lateral confinement of the river by non-erodible walls had
a relatively small effect on the bar pattern statistics.
Evolution of the braided channel network and bar pattern in
Run B1 with branch closure by a dam at x=20 km:
(a) time series of the bed level and (b) discharge
distribution with Q1 the discharge through the northern
branches. The black arrows indicate the position of the propagating
front.
Inflow asymmetry
The effect of an asymmetrical inflow is illustrated in
Fig. . In Run B4 (high discharge inflow along the
south), the asymmetrical inflow caused asymmetrical reshaping of the
most upstream bars. Bar-tail limbs along the dominating branches grew
parallel to the prevailing flow and faster than along recessive
branches. The expansion of the bar-tail limbs resulted in merging of
bars, forming long and slim compound bars. After 6 months, the river reach was
dominated by two parallel branches.
The many examples of asymmetrical deformation of bars indicate
instability – resulting in bifurcation asymmetry – of the directly
upstream-located bifurcations, which provoked instability of the
directly downstream-located bifurcations. This generated a cascade of
bifurcation instability, bifurcation asymmetry, asymmetrical bar
deformation, and instability of the next bifurcation. This cascade
started at the upstream boundary and propagated in the downstream
direction with a fairly constant celerity of 0.3 kmday-1
(Fig. d).
The development in Run B4 is in contrast to the development in Run B0
with uniform inflow. The upstream bars in Run B0 remained almost
symmetrical, and the asymmetrical bar deformation started at the
downstream end of the reach (Fig. d). This
deformation propagated slowly in the upstream direction, which could only
be the result of backwater effects that cause a reduction in upstream water level gradient and thus deposition. This backwater effect also
occurred in Run B4 and interfered with the downstream propagating cascade
triggered by the inflow disturbance. Although the downstream bars
were more complex than the upstream bars – which is an indication
of bifurcation instability as the instability results in closure of branches and merging of bars – the effect of the inflow disturbance in
Run B4 on the bar shapes and network morphology throughout the entire
reach was clear.
Evolution of the braided channel network and bar pattern in
Run A1 with branch closure: (a) time series of the bed level
for Run A1 (with dam) and Run A0 (no dam) and (b) width-average
bed level difference between Run A1 and Run A0, with negative values
indicating more incision in Run A1 than in Run A0.
Branch closure
Disturbance by an engineering construction in one of the
branches also affected the network morphology with its bars,
bifurcations, and branches. The bed level evolution after building
a dam at x=20 km in the idealized situation is shown in
Fig. a. As expected, the
flow through the closed branch steered around the dam, causing major
outflanking scour at the dam heads. The scour depth along the southern
edge of the dam was 50 m, and along the northern edge around
30 m. The deeper scour hole in the southern branch could be
explained by the non-erodible channel wall along the southern
branch. At the same time, sediment was deposited in front of the
dam. Also, deposition occurred downstream of the dam along the
dam heads where flow decelerated and lost sediment transport
capacity. These deposits formed long bar-tail limbs that reached the
mid-channel bar downstream of the dam. The scour holes and deposition
were a temporal response to the dam, because after 2 months, large
bar-tail limbs of the mid-channel bar upstream of the dam extended and
reached the dam (Fig. a). The flow was then guided by
the upstream bar and diverted from the dam, instead of being blocked
by the dam directly.
If we look at the network on the reach scale, we can clearly see an
insignificant upstream impact and a major downstream impact of the dam. The
bifurcations upstream of the dam remained stable and symmetrical (features A and B in
Fig. ), similar to the reference B0. Downstream of the dam,
we could see, besides the first-order morphological response to the dam, a
sequence that is the same as in Run B4 (Fig. a). The
flow asymmetry caused by the dam propagated in the downstream direction,
which we could see in month 2 at the long bar that starts from x=22 km and extends to downstream of x=35 km. This long bar
was formed by merging of bars. However, we could also see a difference with
Run B4: the long bar was deformed significantly in month 6 by annexation of
a bank-attached bar, which almost doubled the surface area of the bar
complex. Eventually, the dam ended in the middle of a large bar complex. From
the perspective of river management, this would be a disappointing
development if the dam was a hydropower dam but would be a good development
if the purpose of the dam was enhancement of river navigability.
Effect of the disturbance in Run A1 on bar pattern
statistics along the river, given as a ratio of Run A1 to the
reference Run A0. The dam is located at x=32 km. A moving
average filter of 2.5 km was used.
Figure shows the morphological development after dam
construction in one of the branches of Run A1. When the northern channel
was closed by the dam, the first
effect was a 1 m water level impoundment upstream of the dam. This
impoundment, and thus reduction of longitudinal water surface slope,
did not result in a clear deposition upstream of the dam. Along the
dam head, the southern channel incised several meters to compensate
for the channel width loss (Fig. b). The local incision
was around 6 m after 2 months. Further downstream, at around
x=35 km, the eroded sediment was deposited. Incision around
the dam and downstream deposition occurred immediately after dam
construction. For example, after only 2 days, a layer of 2 m
was deposited (Fig. b).
The water level impoundment caused by the dam enabled flow from the
northern branch to cross the large compound bar and drain into the
southern branch. It was remarkable that a large bar (D2) blocked more
than half of the remaining channel width, leaving the southern branch
with a width of around 800 m. An explanation for this is the
relict of bar D (D1) that redirects the flow towards the south and
protects bar D2.
The incision and partial erosion of bar D provided sediment that was
deposited downstream at x=38 to 41 km, forming a large bar
over the entire channel width. Furthermore, it resulted in a long
bar-tail limb extending from x=33 to 37 km parallel to the
prevailing flow. As shown in Fig. b, the bed level
change due to the dam propagated in the downstream direction with
a celerity of around 0.5 kmday-1, which was on the same
order of magnitude as predicted with Eq. (). However, it
was much faster than the migration rate of the bars themselves. Thus,
the effect of the dam propagated through a change in flow field and
a sediment wave initiated by the local incision. For example, the flow
direction at x=35 km changed around 30∘ towards the
north, favoring the northern branch around bar F in Run A1, instead of
the southern branch in Run A0. Subsequently, this changed the flow at
the confluence downstream of bar F and the approaching flow of bars G
and H.
In addition to the local incision and deposition, as well as adjustment of
the location, shape, and dimensions of individual bars, the dam also
affected the bar pattern statistics (Fig. ). For
example, the active channel width near the dam reduced by around
50 % and local incision increased the bar height. This reduction
in width–depth ratio decreased the ABI in the vicinity of the dam. The
statistics near the dam in the section x=25 to 40 km adapted
in the first month to the new situation and remained constant
afterwards. Downstream of x=40 km, however, the statistics
changed in the downstream direction and fluctuated around the statistics
of the reference Run A0.
Evolution of the braided channel network and bar pattern in
Run B2 with bar protection: (a) time series of the bed level and
(b) discharge distribution with Q1 the discharge through
the northern branches. The black arrows indicate the position of the
propagating front.
Bar protection
Figure a shows the bed level change in the idealized situation of Run B2,
with protection of the bar head of one of the bars. After 2 months,
the effect of the protection works on the bar shapes is still small,
although the discharge distributions at the bifurcations downstream of
the protection works became increasingly asymmetric
(Fig. b). This started in cross section D after
around 40 days, and in cross section E after around 50 days. Interestingly, we could see a periodic behavior in the discharge
asymmetry. For example, after around 60 days, the discharge towards
the southern branch (Q2) in cross section E was slightly higher than
to the northern branch. However, after 80 days, Q1 was nearly
twice as large as Q2, but after 110 days, Q2 became 4 times
larger than Q1. It should be noted that this behavior was not caused
by migration of the bars, as the bars hardly migrated within the 6 months.
During the first 4 months, the bar protection favored discharge
through the northern branch, with Q1 being around 60 % of the
total discharge (panel C, Fig. b). This is attributed to
a lack of bar-tail limbs along the protected bar, while the other bars
formed bar-tail limbs that diverge the flow. Between months 2 and 6,
elongation of the protected bar and a lack of resupply from erosion of
the bar head resulted in severe trimming of the bar flanks. This
increased the local branch widths and attracted discharge in expense
of discharge through the northern branch in cross section C. As the
dominant branch has a tendency to meander through the channel – which
we saw in the other runs – the shift in discharge from the northern
branch to the southern branch also changed the discharge distribution
in cross section D, and later in E.
Through closer inspection of the network-aspect effect of bar protection in
the simulation with regular bars, we can see that the bar protection
affected the discharge and sediment distribution at the downstream
bifurcation (panel C, Fig. b). Also, the bar along the
right bank at x=20 km was largely removed and pushed
downstream, as the bar erosion attracted discharge towards the right
branch. This had major consequences for the bars and branches further
downstream, as much larger compound bars were formed compared to the
scenario where bar protection was absent.
The effect of bar protection in Runs A2
and A3 is demonstrated in Fig. a. The effect of
the bar protection after 3 months can be split into three sections:
(1) local effects mainly covering the protected bar itself, (2) medium-distance effects at around x=35 to 50 km with hardly any
morphological effect, and (3) long-distance effects downstream of
x=50 km. If we compare the exact bar shapes and locations,
the long-distance effects exceeded the medium-distance effects. This
might be partly because the bars downstream of x=45 km were not yet
developed at the moment we built the dam and thus might be more
susceptible to small flow adjustments from upstream, although the bars
at x=40 to 45 km were also not yet completely developed at
the moment of dam building and still have almost similar positions and
shapes. Thus, this is another example of increasing morphological
response in the downstream direction.
The local effects of bar protection works are illustrated in
Fig. b. Without bar protection, the upstream
bar head migrated around 1.5 km in 3 months in the downstream
direction and the bifurcation angle slightly increased. At the same
time, at the downstream side, a left bar-tail limb formed and extended
around 2 km, almost reaching the next downstream-located
bar. Also, the bar-tail limb along the right-hand side expanded by
around 3 km in 3 months, superpositioned on relict inactive
bar-tail limbs.
Evolution of the braided channel network and bar patter in
Run A2 and Run A3 with bar protections: (a) reach-scale
development and (b) detail of the development of the protected
bar with the bar protection (red line) and initial bar perimeter
(black line).
In the case of bar protection along the left-hand side, the protected
bar-head side remained fixed, minor erosion occurred along the
protected bar side, and a slim bar-tail limb formed. The left bar-tail
limb had the same length as the left bar-tail limb in the case without bar
protection, but with only half of the width. Because the bar head did
not migrate in the downstream direction and the upstream bars still
migrated in the downstream direction, the entrance of the left branch
narrowed, reducing discharge towards the left branch. Consequently,
discharge towards the right branch increased, causing deepening of the
right branch. At the same time, the right-hand side of the bar,
including the right-hand side of the bar head, migrated in the downstream
direction, similar to the case without bar protection. This bar-head
erosion was accompanied with expansion of the upstream bar. Although
the right branch became more dominant, the bar-tail limb along the
right-hand side did not extent as far as without bar protection.
With bar protection along both sides of the bar head, the local effect
along the left-hand side was similar to the single bar protection. At
the right-hand side, the branch entrance deepened. Interestingly, the
downstream bar-tail limb along the right-hand side had more
resemblance to the case without bar protection than with the case of
bar protection along the left-hand side.
Bed levels in month 15, 3 months after building of the
structures in Run A4 at x = 23 km (top) and in Run A5 at
x=22 km (below).
Structures on bar
The effect of structures on a bar is demonstrated in
Fig. . The structures blocked flow over the bar, thus
diverting the flow around the bar. It is remarkable that the bar
morphology near the structureswas hardly affected by the
structures. For example, the large mid-channel bar at x=30 to
35 km was almost the same for both runs. Nevertheless, the bar
morphology further downstream was clearly different. The bar at
x=45 km showed a minor difference, the bar at
x=50 km showed more difference, and the bars downstream of
x=55 km were completely different.
If we compare the bar morphology downstream of x=55 km with the bar
morphology of Runs A0, A2, and A3 (Fig. a), then Run A4
had many similarities to Runs A0, A2, and A3, whereas Run A5 had a clearly
different bar morphology, with one large bar between x=55 km and
x=60 km. An explanation for this is that the structure in Run A4
was built on a relatively high bar which already had minor overflow, and thus
the effect of the structure was relatively small. The structure in Run A5,
however, was built in the middle of the river on a relatively low bar.
Evolution of the braided channel network and bar pattern in
Run B3 with sand mining: (a) time series of the bed level and
(b) discharge distribution with Q1 the discharge through
the northern branches. The black arrows indicate the position of the
propagating front.
Difference in bar pattern statistics between Run A0 and
Runs A1 to A5. The metrics are averages over time: averaged over
first month (yellow), second month (blue), and third month (red), and
averages over regions. The boundaries of these regions are defined
at specific distances from the disturbance (“pert.”).
Sand mining
The simulations show that after removal of a complete sand bar, a new
bar emerged on the empty spot (Fig. ). The bar was
formed by aggradation of the unit bar upstream of the gap. While the
other unit bars migrated downstream and wrapped around the droplet
bars, the unit bar forming the new bar was free to migrate
downstream. Sediment deposition on top of the unit bar diverted the
flow, stimulating further deposition on top of the unit bar. The new
bar was shorter, but with longer bar-tail limbs, and lower than the
original bar. The bar width was similar to the original bar.
Despite the appearance of a new bar, the sand mining significantly
affected the bar and channel morphology further downstream. For
example, the bank-attached bar downstream of the empty spot completely
disappeared. The empty spot also attracted flow, resulting in enhanced
channelization. This channelization stimulated elongation of the bars
by bar-tail limb formation and bar flank trimming, resulting in
merging of the droplet-shape bars into tall compound
bars. Furthermore, an enormous bar complex was formed downstream of
x=21 km along the south by merging of bars, with around
75 % of the discharge flowing through the northern part
(panel D, Fig. b). This merging of bars was much more
pronounced than in the case without sand mining
(Fig. ). Upstream of the empty spot, however,
there was no significant effect from the sand mining.
Overview of channel pattern statistics
Linear analyses e.g., suggest that the region near a
disturbance should have a different channel pattern than regions further away. For example, the braiding intensity should be lower in the case of
a dam due to reduction of the effective channel width. Indeed, this
difference can be seen in Fig. , in which the bar
pattern statistics are given for Run A1 to Run A5 relative to the
reference Run A0. The most pronounced differences occurred, as expected, in
Run A1 with branch closure: the active channel width and ABI near the
dam reduced, and the dominance of the dominant branch and bar height
increased. This pattern extended to around 2 km downstream of
the dam, after which the channel compensated and showed an opposite
behavior: slightly higher ABI, higher active channel width, and less
dominance of the dominant branch. Considering the five runs
together, an increase in effect emerged with time and a large
effect arose near the disturbance in regions c and d (Fig. ). Further away from the
disturbance, the effects on the channel statistics were relatively
small. Figure shows that the effects
on the statistics in region f of Fig. highly fluctuated, both along the river
and with time. Although the specific location, shape, and planimetry of
the bars and branches were clearly affected by the disturbances, the
reach-average statistics were insensitive to the disturbances. Only the
statistics of the region near the disturbance were affected.
Discussion
In this study, we conducted computer simulations of a large
hypothetical sand-bed braiding river and perturbed the river in
different ways. First, at the upstream inflow, the discharge was
varied: from the simplest inflow condition of uniform and steady
inflow to a steady asymmetrical inflow and a hydrograph. Second,
along the channel we applied fixed walls and erodible floodplains,
both perturbing the river in their own way. Finally, we perturbed
the river internally by adding dams and bar protection works or by
mining a bar. We analyzed the effects on a local scale, which was
either near the upstream boundary, along the channel walls, or in the
vicinity of the construction/mining, and on the reach scale. On the
reach scale, the propagation of both the local morphological effects and the bifurcation instability was found to be important.
Figure shows a
conceptual model, inspired by the model results, of how disturbances affect the local bed level and how this
effect propagates through the channel network by means of bifurcation
instability and asymmetrical reshaping of bars. An adjustment to one bar,
bifurcation, or branch initiates a sequence of adjustments in the downstream
direction through (1) asymmetrical division of discharge and sediment
transport over bifurcation branches, (2) elongation of the bar along the
dominant branch, and (3) change in approaching flow towards the successive
bifurcation. The celerity of this propagating wave was several
orders of magnitude larger than the migration rates of the bars
themselves, which is in agreement with the observations of
and with theory. A crucial driver behind the propagation was found to be the
asymmetrical reshaping of mid-channel bars in response to an unequal division
of discharge and sediment over the directly upstream-located bifurcations.
The importance of bifurcations for the evolution of rivers, as well as the
link between bifurcation asymmetry and bar asymmetry, has already been
demonstrated by . The novelty in this study is the
downstream propagation of disturbances by means of bifurcation asymmetry,
caused by bifurcation instability and bar reshaping.
Downstream propagation of the effects of a disturbance
through a braiding river: a change in flow and sediment transport
through branches affects bar reshaping, bar reshaping affects the
bifurcation stability and asymmetry, and these in turn affect
the downstream branches. Additionally, the change in flow through
the branches directly affects the downstream bifurcation, but the
effect of this on the morphology is relatively small. Numbers
indicate the sequence of effect with time.
Responses to a disturbance in a braiding river: (a)
hydrodynamic response by means of a change in approaching flow
direction and discharge division over bifurcations and (b)
morphological response by means of bar shape
adjustment.
Regions of morphological response to a disturbance (red
line): (1) direct effects such as local incision due to flow
confinement (solid lines) or local deposition after sand mining
(dotted lines), (2) indirect by compensation for the direct effects and
thus deposition downstream of flow confinement or incision
downstream of sand mining, (3) indirect by propagation of effects
through bifurcation instability and asymmetrical reshaping of bars, and
(4) upstream by backwater effects.
With downstream propagation of the effect of a disturbance, the
effect amplifies each time it destabilizes a bifurcation
(Fig. ). This way, even small disturbances, for
example a relatively small dam on top of a bar, may cause a major impact
on the bar and branch planimetry and dynamics, with closure and
initiation of branches. In addition to the destabilization of
bifurcations and asymmetrical bar growth, a change in bifurcation
division almost instantaneously affects the division of downstream
bifurcations, before the morphology responses. With a change in
bifurcation division, the flow conditions automatically changed at the
first downstream confluence and the next bifurcation. Such a purely
hydrodynamic response is expected to decay with distance and to shift
downstream simultaneously with the morphodynamic response
(Fig. a).
Besides the propagating wave, we could identify different regions of
morphological effects of disturbances (Fig. ),
starting with the morphological effect in the vicinity of the
disturbance. This local effect is
incision in the case of a flow-blocking structure or deposition in the case of
sand mining. The next region is the compensation region. Here, the local bed level change compensates for the upstream bed level change: deposition in case of upstream incision, or incision in case of upstream deposition. Further downstream, the
effect of the compensation region is still present, caused by flow
steering and thus alteration of the bifurcation stability.
Discharge variation had a relatively
small effect on the long-term bar pattern, demonstrated by the bar
pattern statistics that fluctuated around the steady statistics of the
constant discharge runs. However, it affected the short-term bar
dynamics and bifurcation stability, with the dominance of processes
depending on discharge stage. It also doubled the time required to
reach an equilibrium state, because for a large part of the year the
discharge and water level were too low for significant bar
dynamics. Based on these results, we conclude that it is correct
to use a single representative discharge for long-term bar pattern
analyses. For short-term modeling, on the order of months to a few years, it is preferable to use a hydrograph. The argumentation for
this is based on a distinctive bar and branch dynamics within each
stage of the hydrograph. This said, differences in bar and branch
dynamics between the discharge stages were relatively small, and it was
the sequence of importance of the processes that differed between
discharge stages. For example, bar trimming and incision of the
branches dominated during the declining limb of the hydrograph,
whereas bar migration and formation of bar-tail limbs dominated during
the rising limb of the hydrograph.
Erodible floodplains along large braiding rivers had a small effect on
the bar and branch dynamics and statistics. As predicted by theory of
, , and , the
braiding index increased with widening of the channel by bank
erosion. The widening of the channel had a similar rate to that observed
along the Brahmaputra. The small difference between fixed walls and
erodible floodplains can be explained by the large initial channel
width and the simulation time, considering that the simulation
conducted only covered a couple of years. In the long term, erosion
of the floodplains may have a major impact. Despite the similarity
in bank erosion rates with the Brahmaputra, the highly simplified bank
erosion procedure in Delft3D needs to be improved and more
physics-based, with, among other things, accounting for bank instability and failure. Furthermore, the opposite process of bank erosion,
which is bar–floodplain conversion by, for example, vegetation
encroachment, is not considered in Delft3D. The necessity of this
bar–floodplain conversion for channel migration was demonstrated by
, and the large effect of riparian vegetation on
braiding river morphology has previously been demonstrated by, for example, and . This missing
mechanism must be included to fully understand the contribution of
floodplain–channel interaction on the morphodynamics in braiding
rivers.
This study shows that disturbances in large braided sand-bed rivers
affect the bar pattern – described by statistics – as well as the
location, reshaping, and migration of individual bars and branches
throughout the entire downstream river. This finding has implications
for river training works and other interferences, as these may affect
the river over a large distance, far downstream of the project
area. Conversely, this mechanism gives the opportunity to adjust the river
over a long distance by means of a simple and low-cost disturbance. However, more
research is necessary to develop quantitative predictors of
reach-scale morphological responses to these types of
disturbances. For this, it is necessary that fluvial morphologists,
river engineers, and river managers join forces and collaborate more extensively.
Conclusions
The model simulations carried out in this study showed how the
morphological effects of disturbances in and along a large braided
sand-bed river propagate through the network of bars, branches, and
bifurcations. The interplay between bifurcations and bars was found to
be the essential mechanism driving the propagation. Different steps and
zones of disturbance propagation can be recognized. First,
a disturbance changes the local bed level and flow pattern over
a relatively short distance. Second, these local effects destabilize
nearby bifurcations, resulting in asymmetrical division of discharge
and sediment transport at the bifurcations. Third, the asymmetrical
division of discharge and sediment transport cause asymmetrical
reshaping and migration of the bars, which in turn destabilize
bifurcations further downstream. This cascade of bifurcation
instability and asymmetrical bar dynamics amplifies in the downstream
direction. In addition to the downward-amplifying morphological
propagation, there is an instantaneous disturbance of cross-channel
flow distribution along a reach that likely fades
away from the disturbance location. However, morphological effects of
this hydraulic disturbance are small. Furthermore, the effects of studied disturbances in
the upstream regions are minor and only occur through the backwater
effect. Furthermore, the channel pattern statistics only changed in
the vicinity of the disturbance, remaining unchanged further
upstream and downstream.
The study also showed that discharge variation in the form of an
annual hydrograph affects short-term and bar-scale morphodynamics but
hardly affects the longer-term and reach-scale morphology. In
addition, using a highly simplified bank erosion method, the study
demonstrated that floodplain interaction along large braiding rivers
only causes minor effects on the bar and branch morphology within the
river.
Furthermore, this study illustrated that physics-based models are
useful tools for fluvial morphologists and engineers to explore not only the
morphodynamic effects in the direct vicinity of disturbances such as
training works but also the propagation of these effects on the
reach-scale braided channel network.