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\begin{document}
\title{Numerical simulations to understand spatial sedimentation characteristics in a shallow reservoir}
\author[1]{SUBHASRI DUTTA}%
\author[2]{Harshvardhan Harshvardhan}%
\author[1]{Dhrubajyoti Sen}%
\affil[1]{Indian Institute of Technology Kharagpur}%
\affil[2]{Indian Institute of Technology Delhi}%
\vspace{-1em}
\date{\today}
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\selectlanguage{english}
\begin{abstract}
Sedimentation is a great concern for designers and managers of
reservoirs, as it is responsible for reduction of reservoir's
operational life. This inevitable but unfortunate phenomenon reduces
storage capacity of reservoirs and diminishes utility of infrastructure.
Therefore, a hitherto unexplored and unreported area of sedimentation in
reservoirs -- spatial distribution of deposited sediment in a shallow
reservoir -- is investigated, employing numerical simulation model
(TELEMAC-SISYPHE). Present study considers the Hirakud Dam on the River
Mahanadi in eastern India as a test case. The study established generic
trends between reservoir geometry variables and sediment distribution
patterns in a reservoir through a heuristic set of numerical experiments
for several configurations of reservoirs. The research work comprises of
the following steps: Defining significant geometric parameters defining
any typical water storage reservoir; Setting up and running numerical
model for simulating flow and sediment movement for a range of possible
geometries; Expressing characteristic parameters defining extent of
sedimentation (height of sediment mound, spatial width, longitudinal
extent) in terms of reservoir geometric parameters; Validating proposed
generic relations with field observations of sedimentation of the
Hirakud Reservoir within its two branches of Mahanadi and Ib. The study
shows that the reservoir geometry and bathymetry significantly influence
the flow velocity which, in turn, dictates the conditions of sediment
transport and deposition within the reservoir. Lateral spread of
sediment increases with an increase of expansion angle resulting in
lower peaks of sediment dunes. Increase in cross slope increases the
flow velocity, causing higher movement of sediments. Further, cross
slope has direct influence in increasing transverse movement of sediment
towards central dip resulting in a narrower sediment footprint across
the reservoir section. Maximum height of evolution moves upstream, while
minimum isoline moves downstream with an increase of longitudinal slope.
The developed relations would be helpful to the reservoir managers in
understanding the nature of bed elevation rise in respective reservoirs
and for arranging proper desiltation of sediments for conserving
reservoir capacity.%
\end{abstract}%
\sloppy
\section*{1 INTRODUCTION}
{\label{765765}}
Human activity, like construction of dams and reservoirs, alter the
dynamic balance of water flow and sediment budget. On entering a
reservoir, the flow velocity, turbulence, bed shear stress and transport
capacity of a river decrease, resulting in deposition of sediment
particles to form a delta in the headwater zone, ultimately extending
further into the reservoir with the passage of time. This progressive
deposition of sediments has a negative impact on the flood mitigation
performance of a reservoir and reduces its storage capacity.
Various studies (Garde et al., 1990; Ranga Raju et al, 1999) were
carried out to develop the empirical and semi-empirical methods to
determine the amount of sediment deposits. Stovin (1996) studied the
influence of several physical parameters on the flow rate, reservoir
geometry etc. The bed shear stress distribution was found to play an
important role on the sediment deposits. Morris and Fan (1998) analysed
in details the deposition patterns in various types of reservoirs. They
concluded that the sediment deposition patterns along the longitudinal
direction vary significantly from one reservoir to another depending on
their geometry, discharge, sediment characteristics, reservoir
operation, etc. Most of the sediments are transported within the
reservoirs up to the point of deposition by the following three
processes: 1) transport of coarse particles as bed load along the
reservoir surface, 2) transport of fine particles by turbidity density
currents and 3) transport of very fine particles as non-stratified flow.
Initially, the longitudinal growth of the deposition remains rapid due
to the shallow and low storage capacity of the upstream reservoir.
Rahmanian and Banihashemi (2011) proposed a new semi-empirical technique
based on the reservoir geometry characteristics for evaluating
cumulative sediment distribution along the reservoirs in the
longitudinal direction. Further, Behrangi et al. (2014) predicted the
sediment amount and longitudinal distribution pattern for estimation of
the useful lifespan of reservoirs and identification of optimal
locations for intakes and outlets at the initial stages of dam design.
The characteristics of complex flow pattern in rectangular shallow
reservoirs have also been discussed thoroughly (Kantoush and Schliess,
2009; Camnasio et al., 2011 and Peltier et al., 2015). These studies
mainly focused on the experimental investigations pertaining to flow
characteristics in shallow rectangular reservoirs. Different flow fields
were observed either with no reattachment of flow or a jet with one or
multiple reattachment points depending on the size of the reservoir.
Kantoush (2008) showed that reduction of length of a rectangular shallow
reservoir induced a transition from an asymmetrical flow with one
reattachment point to a symmetrical flow without any reattachment point.
Also, different numerical simulations were conducted to analyse the
sediment transport capacity (Lu and Wang, 2009; Zhou et al., 2009),
settling velocity (Zhou et al., 2009) and sedimentation quantity (Gao et
al., 2015).
The determination of hydraulic properties is a pre-requisite for
sediment transport modelling in general. The modelling approach enables
the calculation of reservoir life expectancy, the trapping efficiency of
the reservoir, the amount of the released sediments downstream of the
reservoir and the simulation of several reservoir sediment management
scenarios.
Sediment transport is important in case of affecting water quality and
the life expectancies of the reservoirs. Therefore, it is one of the
most important factors that should be considered and well assessed in
design of reservoirs. Studies about sediment transport mainly focused on
hydrodynamic processes and their driving forces to understand how
sediments are eroded, transported, deposited, and re-suspended in
different water systems through numerical modelling and surveying of
reservoirs (Blumberg and Mellor, 1987; Mehta et al., 1989).
Empirical formulae based on laboratory data are not always accurate
enough and unable to replicate the true field conditions properly due to
the error in the scale ratio and fluid properties. Also, field data
based on empirical formulae suffer from subjective errors. To overcome
these difficulties, computational fluid dynamic tools may be used to
predict hydrodynamic and morphodynamic parameters within the reservoir
subjected to varying flow conditions.
White (2001) summarised that 1-D model is suitable for long-term
simulation of reservoir sedimentation with elongated channel geometry,
while 2-D or 3-D models require much more field data for calibration.
1-D computational models provide information in a section-averaged
manner without giving any information about the flow characteristics in
the vertical and transverse directions. A 1-D model usually solves
differential conservation equations of mass and momentum for the water,
along with sediment transport mass continuity equations using finite
difference methods (Papanicolaou et al., 2008). Normally, the models
employ rectilinear coordinate system; however, some of them also use
curvilinear systems. Some of the widely used one dimensional models for
simulation of sediment behaviour in rivers and reservoirs are HEC-6
(USACE, 1993), FLUVIAL-12 (Chang, 1998), CONCEPTS (Langendoen, 2000),
CCHE1-D (Wu and Vieira, 2002), MIKE11 (DHI, 2003), etc. for erosion,
sediment transport and deposition in straight channels and rivers.
The depth-averaged 2-D models divide the total computational domain into
a network of two-dimensional elements. However, no variation is
considered in the vertical direction. Two dimensional models are most
popular than others as they provide enough information of the computed
parameters in the project assessment. The 2-D models solve the
depth-averaged form of the Navier-Stokes equations, with sediment
transport models having capabilities to describe both bed and suspended
load. These models assume the velocity of water and the concentration of
sediment to be uniform through the water column. So, these models do not
take into account secondary flow effects. Some of the widely used two
dimensional sediment transport models include TABS-MD (Thomas and
McAnally, 1990), HSCTM2-D (Hayter, 1995), CCHE2-D (Wu, 2001) MIKE21
(DHI, 2003), and SRH-2-D (Lai et al., 2008).
3-D numerical models are based on the assumption of hydrostatic pressure
distribution in vertical direction and provide information in all the
three directions within the reservoir. The 3-D models are avoided unless
very detailed distribution of different parameters needs to be simulated
in accounting with flow characteristics in all directions. Although they
are the most complicated and resource consuming in implementation, they
are nevertheless the most informative as they include all the space
dimensions. The 3-D models solve the Navier-Stokes equation using
numerical approaches such as the finite element, finite difference or
finite volume method (Papanicolaou et al., 2008). Some of the most
widely used three dimensional models are SSIIM (Olsen, 1994), Delft-3-D
(WL \textbar{} Delft Hydraulics, 2006), ECOMSED (HydroQual, 2002),
CCHE3-D (Stone et al., 2007).
In recent years, several 2-D and 3-D numerical morphodynamic models have
been developed that have the capability to predict bed deformation in
channels with non-moving boundaries. Minh Duc et al. (2004) proposed a
2-D depth-averaged model using a finite volume method with
boundary-fitted grids and fixed channel sides. Wu and Wang (2004)
proposed a 2-D depth-averaged model for computing flow and sediment
transport in curved channels, simulating sediment transport in a channel
bend with fixed sides. A 3-D model for the calculation of flow and
sediment transport was proposed by Wu et al. (2000). Suspended load
transport was simulated through the general convection-diffusion
equation with an empirical settling velocity term. Bed load transport
was simulated with a non-equilibrium method and the bed deformation was
obtained from an overall mass-balance equation. Elci et al. (2007)
discussed the erosion and deposition of cohesive sediments in a
thermally stratified reservoir using a 3-D numerical model for different
conditions. They reported that though sedimentation in a reservoir is
often modelled considering only the deposition of sediments delivered by
tributaries, the sediments eroding from the shorelines could have
significant effects to the sedimentation in the reservoir. Choi and Lee
(2015) numerically predicted the total sediment load in a river, using
information on channel geometry and slope, discharge and the size of bed
materials. They also carried out the flow analysis using the lateral
distribution method, which distributes the flow and sediment load across
the width, based on channel geometry and flow dynamics. Faghihirad et
al. (2015) applied numerical model to Hamidieh Reservoir in Iran,
associated with a dam, water intakes and sluice gates, in order to
investigate the flow patterns and sediment transport processes in the
vicinity of the dam. They found that an excess of sedimentation in a
reservoir leads to sediment entrainment in waterway systems and
hydraulic schemes.
However, these studies have been done to find out the progress of
reservoir sedimentation along the longitudinal and lateral directions,
as its lateral spreading (spatial distribution) has not been
investigated much. Also, there has been little effort to estimate actual
siltation in a shallow reservoir using physical based numerical
simulation models. Further, limited studies appear to have been carried
out on the influence of different geometric parameters of a trapezoidal
channel on the pattern of sedimentation. Therefore, the present study
has been done to find out the progress of reservoir sedimentation along
the longitudinal and lateral directions, as its lateral spreading
(spatial distribution) has not been investigated much. Also, there has
been little effort to estimate actual siltation in a shallow reservoir
using physical based numerical simulation models. Further, limited
studies appear to have been carried out on the influence of different
geometric parameters of a trapezoidal channel on the pattern of
sedimentation.
~
\section*{2 PROBLEM FORMULATION}
{\label{838804}}
Dutta and Sen 2016 discussed the sediment deposition characteristics in
the reservoir of the Hirakud Dam, in India, which has occurred in the
past and their likely impact on the reservoir performance. Though the
analyses are specific to the Hirakud Reservoir, a curious observation
comes to light while observing the sedimentation patterns in the
reservoirs of the two Rivers, Mahanadi and Ib, that flow into the
reservoir. It appears from the sequence of simulated progressive
reservoir sedimentation patterns that the sediment deposition at the
bottom of River Mahanadi is somewhat different than that for River Ib.
While the sediment in the former basin appears to deposit along the deep
channel -- more towards the centre of the river valley -- in the latter
it appears to deposit along the edges. This distinction is not directly
noticeable from the measured bathymetry maps of the reservoir which,
anyway, is very scanty. The minute differences, observable in the
numerical simulation results, almost certainly appear to depend on the
variables causing sedimentation, like the size of the sediment
particles, flow velocity and depth, apart from the geometrical
characteristics of the reservoir itself. Since the sediment size and
flow variables are nearly the same in the two Rivers (Mahanadi and Ib)
during the passage of floods, when the maximum deposition takes place,
the difference in deposition patterns is likely to be caused by the
uniqueness in the geometrical properties of the two rivers. Though a
large body of literature exists reporting the progress of deposited
sediments in a reservoir along the longitudinal direction of river flow,
not many examine the spatial distribution pattern of sediments in an
artificially formed reservoir behind a dam. Therefore, the objective of
this research work is to inquire into the reasons governing the
reservoir sedimentation patterns and to establish any generic trend that
may exist connecting the reservoir geometry variables and the sediment
distribution patterns in a reservoir through a series of numerical
experimentations.
Transportation and deposition of sediment are governed primarily by the
flow velocity. Sediment particles transported by the flow induces
morphodynamic changes on the bed. As a result, in an artificial
reservoir where the flow field of a natural river gets substantially
altered, the modified velocity pattern has a significant influence on
the spatial pattern of the sediment deposited at the reservoir bottom.
This, therefore, intuitively leads to suggest that it may be possible to
identify certain characteristic geometrical parameters defining
reservoirs which, when varied, can result in different patterns of
sedimentation.
The velocity of flow in a reservoir, if idealised as having a
trapezoidal shape in plan, is likely to reduce more if it widens over a
relatively short distance. This may cause the suspended sediment being
brought in by the river to get deposited close to its entry point to the
reservoir. On the other hand, in a narrow reservoir, the velocity may
not reduce significantly along its length and the sediment deposition on
the reservoir floor may get elongated along the downstream direction.
Hence, the average expansion angle of the reservoir walls in plan (\selectlanguage{greek}α\selectlanguage{english}) is
considered here as the first parameter by which a reservoir may be
characterised. On similar reasoning, the average bed slope measured
along the length of a reservoir, that is the longitudinal slope
(\emph{SL}), appears to be another governing parameter since with a
greater slope, the rate of increase of depth would be more along the
flow direction, leading to a rapid decrease in the flow velocity.
Finally, the bottom profile of the reservoir bed also appears to play a
role in the spatial distribution of sediments. Dutta and Sen 2016
indicated that the Ib, smaller of the two rivers contributing flow to
the Hirakud Reservoir, has a relatively flat bottom as compared to that
of the Mahanadi. It may be presumed that the cross slope of the
reservoir bed (which is more in case of the Mahanadi branch) may help in
driving the depositing sediment towards the central spine of the
reservoir, resulting in a single deposition track at the bottom.
Conversely, a flatter reservoir bed may not let this happen (as for the
Ib branch) and the sediment is likely to spread out spatially, more like
an alluvial fan. Hence, the average cross slope of the bed (\emph{SC})
of a reservoir is considered here as the third important characteristic
parameter influencing the deposition pattern of the sediments on the
floor of the reservoir.
Although the above parameters may be estimated approximately for any
reservoir created by a dam across a river, it is difficult to obtain a
direct analytical relation connecting the spatial sediment deposition
patterns in terms of the governing variables. For the present work,
therefore, the validated TELEMAC-2D model {[}as demonstrated in (Dutta
and Sen, 2016){]} is employed in carrying out numerical experimentation
by varying the three parameters (\selectlanguage{greek}α, \selectlanguage{english}\emph{SL} and \emph{SC}) for
different hypothetical reservoir geometries and analysing the features
of the deposited sediments. The generic trends from these series of
numerical experiments are used at the end of this paper for explaining
the unique sedimentation patterns mentioned earlier for the Mahanadi and
Ib River branches of the Hirakud Reservoir. The work presented in this
paper attempts to fill in this gap by proposing a methodology by which
any reservoir that can be approximated by the characteristic parameters
\selectlanguage{greek}α, \selectlanguage{english}\emph{SL} and \emph{SC}, the resulting spatial sediment deposition
pattern on its bed can be predicted
\par\null
\section*{3 MODEL SET-UP}
Numerical simulations of flow characteristics along with sedimentation
are performed on the hypothetical reservoirs with the common
computational mesh for the numerical 2-D flow simulation model TELEMAC
(Desombre, 2013) and the sediment transport model SISYPHE (Tassi, 2014).
The model TELEMAC-2D solves the depth-averaged Saint-Venant equations
(conservation of mass and momentum) using the finite element formulation
over the computational domain. SISYPHE computes the sediment transport
and predicts the evolution of the reservoir bed by solving the Exner
equation.~ Descriptions of the models in greater details have been
provided in Dutta and Sen, 2016; where these were demonstrated for
simulating the morphological changes in the Hirakud Reservoir due to
sedimentation. Although previous studies reported the use of the coupled
hydrodynamic and sediment transport model (TELEMAC-SISYPHE) for
simulating sedimentation (Villaret et al., 2013; Hostache et al., 2014),
this is a first attempt to apply TELEMAC-SISYPHE numerical 2-D model to
generate some relations in between the reservoir geometry and sediment
distribution pattern.
An idealised reservoir geometry is modelled (Figure 1), defined by the
three characteristic parameters \selectlanguage{greek}α, \selectlanguage{english}\emph{SL} and \emph{SC}. The length
of the reservoir is kept constant at 10 km. The unstructured triangular
mesh was generated with the help of the graphical user interface
BlueKenue (2012). The mesh size used in each of the experiments is in
the order of 50 m. Figures 2(a) to 2(c) illustrate the generated
triangular mesh for the entire computational area of a typical idealised
reservoir geometry, along with the bottom elevations. The same domain
has been replicated for different parameters, permitting the evaluation
of the hydrodynamic response of idealised reservoir having different
configurations.~
The geometric and hydraulic conditions of the simulations are initially
set up to schematize the sediment flow into the reservoir domain. Since
the primary objective of this study focuses on the influence of the
reservoir geometry (expansion angle, longitudinal slope and cross
slope), the characteristics of flow and sediment are kept constant for
all the simulations. The mean diameter of sediment is set as 30 \selectlanguage{greek}µ\selectlanguage{english}m and
uniform sediment gradation is assumed. Non-uniform sediments are not
assumed in the present study since the sedimentation characteristics of
such particles is likely to vary widely over the extent of the
reservoir. The inflow rate of sediment in the domain is chosen in such a
way that the volumetric concentration corresponds to those observed in
the field. SSC (Suspended sediment concentration) is set equilibrium to
avoid unwanted erosion and deposition. The vertical variations of SSC
are considered negligible in comparison to its horizontal equivalents.
The reservoir depths in the experiments have been kept an order of
magnitude smaller than the lateral dimensions as generally encountered
in wide reservoirs, ensuring that the vertical velocity component
remains negligible and the flow may reasonably be represented by the
shallow water equations.
Two open boundaries for the domain are defined, one on the upstream and
the other on the downstream. The width of the inlet and outlet of the
domain are kept equal. Following the monsoon period of 4 months, the
simulations were also continued for 4 months, which generate maximum
amount of annual sediment load. A constant inflow discharge is
prescribed as the upstream boundary condition for all the cases
considered and a constant water depth, corresponding to normal operating
water level, is specified at the downstream boundary. The rest of the
points along the periphery of the closed domain are considered as a
closed boundary. Figure 3 shows the inlet and outlet boundaries
respectively of a typical domain.
The simulations for each case are carried out until a steady state is
reached and no meandering jet is observable within the domain. The
initial sediment concentration of water is assumed to be zero, that is,
clear water. As discussed in some of the previous studies like Dufresne
et al. (2011) and Dewals et al. (2012), a steady flow may be reached
depending upon the initial condition used for running the simulation.
Therefore, in all simulations, a constant value of free surface
elevation is prescribed as an initial condition such that the steady
state condition is achieved promptly. At each node, the water depth is
calculated as the difference between the free surface elevation and
bottom elevation. The frictional resistance, represented by the
Strickler's roughness coefficient, is considered same for all the runs
with different geometries. The constant viscosity turbulence model is
considered here since it requires a lower refinement level of the mesh
in comparison to the others, resulting reduced CPU time. The mass
balance check is performed over the entire domain for each simulation in
order to ensure physically viable result. The time step chosen,
considering the optimum computation time and Courant condition, is
around 4 seconds. This helps to ensure the numerical stability and
convergence.
~
\section*{4 ANALYSIS OF RESULTS}
{\label{211922}}
The bed morphological process of a reservoir due to flow and
sedimentation is a complex dynamic process as several factors such as
development of vegetation in the river bed, presence of different
hydraulic structures, etc. influence the flow velocity, which ultimately
affects the morphological characteristics. Hence, this study aims at
determining the morphological changes of the bed due to sedimentation in
idealised trapezoidal shaped reservoir configurations. In all, 64
different configurations are run by varying the three characteristic
parameters, as indicated in Table 1.
~
\textbf{4.1 Velocity distribution}
Figures 4(a) to 4(c) show the typical contours of (depth averaged)
velocity and bed shear stress for simulations with various
configurations. Both the velocity contours and shear stresses show
similar trends across different sections for a particular configuration.
It is evident that the bed shear stress increases with increasing flow
velocity resulting in an excess stress that is required to initialize
the sediment motion. The flow direction is normal to the cross section
of the reservoir domain and the velocity varies significantly across the
channel width. The flow field remains essentially symmetric, as expected
from the symmetric geometry of the models, and steady throughout all the
simulations. For all the configurations, the average velocity was found
to be in the range of 0.3-0.7 m/s. Initially the simulation time was set
to 1 month to achieve a steady state flow condition in the reservoir. As
the inlet and outlet channels are located on the opposite sides of the
reservoir centreline, the flow pattern is mainly controlled by the inlet
channel. The flow passes straight from the inlet to the outlet of the
reservoir. Recirculation of flow {[}Figures 5(a) to 5(c){]} is observed
in the computational domain along the banks of the trapezoidal
reservoir, as the outflow width is restricted symmetrically in the
middle part of the downstream boundary. The width of the recirculation
zones on either bank is observed to decrease with an increase in the
longitudinal and cross slopes of the reservoir. The intensity of
recirculation is mainly observed towards the outlet end of the domain.
However, the zone increases significantly for the simulations with
higher values of expansion angle due to the limited width of the outlet
boundary with respect to the total downstream boundary width. As the
velocity governs the mechanism of transport of sediment, the knowledge
of its pattern is important to determine the spatial distribution of
sediment in the reservoir.
The figures show that the maximum velocity along the centre line of the
domain increases with the increase of the cross and longitudinal slope.
However, the effect of expansion angle is insignificant on the magnitude
of maximum velocity.
\textbf{4.2 Morphological changes}
Morphological variation within the computational domain is not uniform.
Hence, it is interesting to visualize its evolution along the
longitudinal profiles. Figures 6(a) to 6(c) show the morphological
evolution of the bed within the domain. The entire domain is
characterised mostly by a positive value of deposition. Only a small
fraction of sediment is driven towards the outlet due to the turbulence
and most of them settle down before reaching the outlet. On the other
hand, erosion is visible at the entry point due to the high flow
velocities generated by the narrow entrance. At the downstream, no
significant change of the river bed was found due to the presence of low
velocity which is not strong enough to transport the sediments towards
the outlet end. Narrow peaks with decreasing heights are evident, which
form closer to the inlet with the increase of the cross slope. As
discussed in the previous section, the expansion angle is not found to
have any effect either on the velocity distribution or on the bed
evolution. This is due to the fact that the outlet and inlet widths were
kept same in the simulations. Nevertheless, the maximum height of
evolution of the bed marginally increases with the increase of the
expansion angle. The variations are explained further in the following
sections.
~
\textbf{4.3 Maximum evolution}
The following sections describe the maximum evolution of the bed within
the trapezoidal reservoir:
~
\textbf{4.3.1 Longitudinal distance of maximum evolution}
Figure 7 plots the longitudinal distances (\emph{xd}) at which the
maximum evolution occurs against longitudinal slope for different
expansion angles and cross slopes. In all simulations, because of
symmetry, the maximum deposits appear along the path of the main stream
of flow. The patterns of deposited sediment at various sections depend
on the velocity of flow at those sections. The location of maximum
values in the pattern of sediment deposits coincides with the lowest
values of the velocity field. The low value of flow velocity leads to an
increased value of settling velocity resulting in significantly
decreasing the sediment transport capacity. Thicknesses of the deposits
are represented with respect to the bed level. As evident from the
graphs, \emph{xd} appears to bear an inverse relationship with both
longitudinal and cross slope.
~
\textbf{4.3.2 Height of maximum evolution}
Figure 8 shows the maximum height of evolutions (\emph{hd}) for
different configurations versus longitudinal slopes for variations of
expansion angles and cross slopes. The graphs show that for the flat
bottom (\emph{SC} = 0) the velocities are significantly less to sustain
sediment movement. The peak value of sediment deposition increases with
the increase in longitudinal slope for flat bottom configurations only.
However, velocities become significant to sustain continous sediment
movement for configurations with steeper cross slope (\emph{SC} = 0.01),
that is the reservoirs with a V-shaped bottom. The dunes formed due to
the deposition of sediment disintegrates due to higher velocities and
consequently propelled towards the downstream of the reservoir. Thus,
the peak height of the deposited mound decreases with an increase in the
longitudinal and cross slope.
\par\null
\textbf{4.4 Minimum and maximum isolines of bed evolution}
The minimum and maximum isolines within the reservoir for different
longitudinal slopes and expansion angles are plotted in Figures 9(a) to
9(d). Evidently, the maximum height of evolution moves upstream of the
reservoir, while the minimum isoline moves downstream towards the outlet
with an increase of longitudinal slope for any given expansion angle and
cross slope. This may be explained due to the phenomenon of sediments
sliding along the bed, driven by gravity, since the downward component
of its weight increases with an increase in the longitudinal slope.
Here, too, it is visible that for any given expansion angle and
longitudinal slope, the sediment gets restricted and accumulates more
towards the upstream of the reservoir with the increase of the cross
slope. However, the expansion angle doesn't seem to have any significant
impact on the sediment deposits for higher value of cross slope. The
pattern of maximum isoline is especially noticeable in case of the flat
bottom reservoirs, where a horse-shoe shaped formation is observed for
lower values of longitudinal slope.
Further, the isolines (value of 0.75 m) of sediment deposits at the end
of 4 months are drawn for different configurations to compare the
lateral and longitudinal expansion of the bed evolution (Figures 10 and
11). It is evident that for a given expansion angle, for both flat and
V-shaped bottomed configurations, the 0.75 m evolution isolines move
downstream towards the outlet, due to the larger sediment slides
occurring at higher values of longitudinal slopes. Also, for a given
longitudinal slope in a flat-bottomed reservoir, as the expansion angle
increases, the 0.75 m isoline moves upstream due to increased
recirculation, causing increased lateral flow of sediment. This effect
is more pronounced for configurations with flat bottoms in comparison to
those with V-shaped bottoms, due to an increased intensity of the flow
in the central region of the reservoir.
~
\textbf{4.5 Distribution of sediment in the transverse direction}
Figure 12 shows the distribution of sediment across the transverse
direction of the reservoir. The extent of transverse spread of the
deposited sediment decreases and the sediment moves towards the centre
of the channel due to the effect of flow with the increase of the cross
slope for any given expansion angle and longitudinal slope. Here too,
gravity plays an important role on attaining the threshold bed shear
stress responsible for the initiation of motion of the sediment
particles. For any given cross and longitudinal slope of the reservoir
bottom, the transverse spread of the sediments increases with an
increase in the expansion angle and shifts towards the outer edges of
the reservoir.
For a reservoir with a flat bottom and having a relatively small
expansion angle, there is insignificant recirculation to cause lateral
spread of sediment. In contrast, for higher expansion angles, the
velocities and recirculation zones significantly increase with the
increase in longitudinal slope resulting in the lateral spread of
sediment.
As observed from the pattern of sediment distributions, it is seen that
the sediment accumulates mostly in the central region. In case of
V-shaped bottom, the increase in velocities due to increase in
longitudinal slope causes the sediment to move downstream rather than in
the lateral direction. The rate of decrease of lateral spread of
sediment distribution also changes with an increase of cross slope.
~
\textbf{4.6 Bed morphology in the longitudinal direction}
The following sections represent the change in bed morphology along the
longitudinal direction for the reservoirs with flat and V-shaped
bottoms.
~
\textbf{4.6.1 Reservoirs with flat versus V-shaped bottom}
The variation of the pattern of deposition with respect to the
longitudinal distance for various longitudinal slopes, expansion angles
and cross slopes are plotted in Figure 13. For reservoirs with V-shaped
bottom cross sections, the reaches are narrow, resulting in higher flow
velocities. Consequently, a significantly higher sediment transport rate
is noticed in comparison to sediment deposition, whereas the opposite is
observed for the flat bottomed reservoirs. Hence, it may be said that
sedimentation is predominant in flat bottom reservoirs mainly during the
floods due to flow with higher sediment concentration. However, sediment
deposited at the bottom of V-shaped reservoirs is likely to be eroded
during floods due to the higher velocity occurring along the centreline.
Figure 13 also shows that the expansion angle has no significant impact
on the longitudinal sediment distribution, especially for V-shaped
bottoms, with other parameters remaining constant. Some abnormality,
however, is observed for flat bottomed reservoirs at very low expansion
angles. This can be attributed to the fact that there is less
recirculation in the transverse direction and more flow towards the
centre compared to other flat bottom configurations, which causes the
peak of the deposited sediment mound to move in the downstream
direction.
One more observation that can be made is that for a given expansion
angle of a flat bottomed reservoir, the longitudinal slope doesn't have
any significant effect on the longitudinal distribution of the
sedimentation pattern. The lateral flow of sediment from the sides
towards the centre of the reservoir increases with the increase in cross
slope. For a given cross slope, the dunes become increasingly unstable
with the increase of longitudinal slope. Further, the sediment slides
from the dune results in a larger foot-print in the longitudinal
direction while the peak of the mound moves upstream.
~
\textbf{4.6.2 Varying cross slope, fixed longitudinal slope and
expansion angle}
For a fixed value of longitudinal slope and expansion angle, the
sediment gets accumulated and forms higher peak due to the reduced
lateral movement with the increase in the cross slope, as shown in
Figure 14. It is also observed that the dunes get steeper with an
increase of cross slope. However, with the increase in sediment
deposition, the cross sectional area of flow reduces, which affects the
movement of the incoming sediment resulting in deposition at the bottom
of the reservoir.
~
\section*{5 SEDIMENT DEPOSITION FEATURES IN THE HIRAKUD
RESERVOIR}
{\label{368833}}
The generic trends from the previous sections are compared with the
sedimentation features in the Hirakud Reservoir. The Rivers Mahanadi and
Ib contribute the reservoirs flow and also bring in sediment from the
respective catchments. However, the deposited sediment in the two river
valleys exhibit different spatial distribution patterns. While the
Mahanadi portion shows a single central meridional formation, that in
the valley of the Ib appears to follow two branches separated some
distance away from the central meridional axis. It is hypothesized that
this difference is due to the variation in the physical features of the
two valleys. Accordingly, measurements are taken from the river bed
contours and the features, expressed in terms of the geometric variables
considered in developing the generic depositional patterns, are
summarized in Table 2.
From Table 2, it is evident that for the River Ib, the average values of
cross slope (\emph{SC} = 0.0035) is flatter than that of the Mahanadi
(\emph{SC} = 0.007) and at the same time, the average expansion angle (\selectlanguage{greek}α
\selectlanguage{english}= 20\selectlanguage{ngerman}°) is comparatively larger than Mahanadi (\selectlanguage{greek}α \selectlanguage{english}= 10\selectlanguage{ngerman}°). Though the
longitudinal slope for the Ib (\emph{SL} = 0.0011) is somewhat greater
than Mahanadi (\emph{SL} = 0.00073), the first two parameters dictate
the depositional pattern in this case and cause the sedimentation
formation in the Ib valley to spread out and tend towards a horse-shoe
shape. However, the formation in the Ib appears with two side branches
of deposition and does not display a complete hose-shoe shaped
geometrical pattern. This can be explained with the layout of the two
rivers -- Mahanadi and Ib -- which shows that a flow component of the
former strikes the latter within the reservoir, causing the front bar of
the horse-shoe deposition to become dispersed leaving the two side
branches intact along the walls of the Ib valley. Thus the deposition
pattern in the Ib valley is a degenerated horse-shoe formation.
The above hypothesis is also checked with the graphs developed in this
section as shown in Figures 15 to 16, respectively for the Rivers
Mahanadi and Ib. The three graphs used in each case relate the height of
sedimentation around (\emph{hd}, expressed in m), longitudinal distance
along the reservoir (\emph{xd}, expressed in m) and lateral spread to
the expansion angle (\selectlanguage{greek}α\selectlanguage{english}), longitudinal slope (\emph{SL}) and cross slope
(\emph{SC}). Though \emph{hd} and \emph{xd} are approximately the same
in either case, the lateral spread is much larger for the Ib than for
Mahanadi confirming the horse-shoe nature of the sedimentation in the Ib
valley. The same is also confirmed by the plots of the isolines in
Figure 17 respectively for the two rivers.
~
\section*{6 CONCLUDING REMARKS}
{\label{593533}}
Prediction of sediment deposition and erosion as a function of reservoir
geometry, a question that has apparently not been addressed so far, is
explored in this work as it is intuitively understood that the shape of
a reservoir controls the velocity distribution, which in turn, affects
the sedimentation process. The study made use of a numerical flow and
sediment transport simulation model in analysing the deposition patterns
in idealised reservoir configurations. Rather than considering a complex
geometry, this study proposes representing a prototype reservoir by a
few simple but quantifiable geometric parameters and assuming a regular
and symmetric flow. The results of the numerical experiments, conducted
on a series of 64 geometric configurations with different longitudinal
slopes, expansion angles and cross slopes for fixed hydraulic conditions
(Froude number, Strickler's roughness coefficient, etc.), presents
several critical findings, as enumerated in the paragraphs below.
The reservoir geometry and bathymetry significantly influence the flow
velocity which, in turn, dictates the conditions of sediment transport
and deposition within the reservoir. The lateral spread of sediment
increases with the increase of expansion angle resulting in lower peaks
of sediment dunes. Increasing cross slope increases the velocity of
flow, thereby causing significantly higher movement of sediments.
Further, the cross slope also has a direct influence in increasing the
inward (transverse) movement of sediment towards the central dip
resulting in a narrower sediment footprint across the reservoir
section.~
The findings of this study contribute to the understanding of bed
morphological processes in shallow trapezoidal reservoirs. However,
secondary turbulent flow, which is often generated in a reservoir, has
not been considered in the present depth-averaged model and therefore,
the investigations of 3-D models are required.
~
\section*{ACKNOWLEDGEMENTS}
{\label{576630}}
The authors gratefully acknowledge the Department of Science and
Technology, Government of India, for funding the research project.
Thanks are also due to the Water Resources Department, Government of
Odisha for providing the sedimentation reports of the Hirakud reservoir
and to the Central Water Commission, Bhubaneswar, for providing relevant
discharge and sediment data.
~
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~
\textbf{Data Availability Statement}
Data derived from public domain resources:
\url{http://indiawris.gov.in/wris/\#/riverPoint}
\textbf{Hosted file}
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