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Ocean Engineering 322 (2025) 120520
Available online 3 February 2025
0029-8018/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-
nc-nd/4.0/).
Research paper
Experimental investigation of tidal bore-like unsteady ow interaction with
solitary spur dike
D. Nandhini
a,b
, Holger Schüttrumpf
b
, S. Harish
b,*
, K. Murali
a
a
Department of Ocean Engineering (DOE), IIT Madras, Chennai, 600036, India
b
Institute of Hydraulic Engineering and Water Resources Management (IWW), RWTH Aachen University, 52074, Aachen, Germany
ARTICLE INFO
Keywords:
Tidal bore
Hydrodynamics
Froude number
Energy dissipation
Backwater effect
ABSTRACT
In a river and estuarine region dominated by strong tidal bores, spur dikes play a crucial role in inuencing both
hydrodynamics and morphodynamics. The present study experimentally quanties the hydrodynamics around a
solitary spur dike during tidal bore-like unsteady ow interaction by varying the ow Froude number (Fr) and
relative dike height (h
d
/h). During the tidal bore interaction with the spur dike, splashing occurred during bore
impact, followed by continuous overow, resulting in a signicant difference in ow characteristics in the spur
dike vicinity during the quasi-steady ow phase. Fr and h
d
/h positively correlated with the upstream water
elevation (backwater rise) and negatively correlated at the downstream region. At the head region, the back-
water upstream and the overtopped ow together dictated the ow characteristics. Empirical equations for
predicting the ow characteristics (bore depth and velocity) around the spur dike during tidal bore interaction
are obtained through the non-linear multivariate regression analysis. At high Fr and high h
d
/h conditions, the
spur dike was found to effectively reduce the tidal bore energy at the downstream region by nearly 25% due to
high turbulence intensity. Overall, the paper provides quantitative and qualitative discussion on tidal bore hy-
drodynamics and the variation in the tidal bore energy around a solitary spur dike for engineering design and
operational appraisal.
1. Introduction
1.1. Tidal bore
A tidal bore is a captivating and regular hydrological event that oc-
curs notably in estuaries and rivers under limited circumstances. Many
rivers in the world experience this periodic event, including the Severn
River (United Kingdom), Qiantang River (China), Alaska River (The
United States of America), Amazon Rivers (Brazil), Styx and Daly Rivers
(Australia), Indus (Pakistan), Hooghly Rivers (India), Bay of Fundy
(Canada) and Mascaret, Garonne and Dordogne Rivers (France)
(Bartsch-Winkler and Lynch, 1988; Chanson, 2008, 2012; Koch and
Chanson, 2008; Mouaze et al., 2010; Reungoat et al., 2015; Roy-Biswas
and Sen, 2023). Tidal bore is dened as a rapid rise in the water ow
inside an estuary and a river which occurs when a rising tide rushes
upstream against the river’s current (Chanson, 2010a, 2011a, 2012).
The narrow and shallow funnel-shaped estuaries with high water levels
often form the tidal bore (Chanson, 2012; Bonneton et al., 2015). There
are also a few unique conditions, such as: The Amazon River, which
originates in Brazil and is the longest river in the world, empties into the
Atlantic Ocean. Despite its wide mouth, the Amazon River has a sig-
nicant tidal bore. A tidal bore occurs here because of the shallow water
depth at the river mouth, which is also littered with a number of
low-lying islands and sandbars (Fricke et al., 2019); Also, in few loca-
tions like Turnagain Arm, Alaska River (America), Qiantang River
(China) and Batang River (Malaysia) the tidal bore can occur almost
every day (Bartsch-Winkler and Lynch, 1988). Henceforth, it is evident
that the tidal bore characteristics are merely location-dependent. Be-
sides, the development of tidal bore depends on a number of factors,
including tide, river discharge, river morphology, and climatology
(Bonneton et al., 2015; Pan et al., 2023). Generally, tidal bore propa-
gating in a river is differentiated into undular and breaking bores based
on the bore front Froude number (Fr
b
) (Chanson, 2011a, 2011b).
Frb=v+C
gd0
(1)
where v =initial ow velocity of the river (m/s), C =bore front celerity
* Corresponding author.
E-mail address: selvam@iww.rwth-aachen.de (S. Harish).
Contents lists available at ScienceDirect
Ocean Engineering
journal homepage: www.elsevier.com/locate/oceaneng
https://doi.org/10.1016/j.oceaneng.2025.120520
Received 17 September 2024; Received in revised form 21 December 2024; Accepted 23 January 2025
Ocean Engineering 322 (2025) 120520
2
for an observer standing on the bank, positive upstream (bore propa-
gation velocity) (m/s), g =gravity acceleration (m/s
2
), and d
0
=water
depth before bore passage (initial ow depth) (m). If the Fr
b
is less than
1.5–1.6, the formed bore is categorized as undular. Whereas if Fr
b
is
greater than 1.5–1.6, it signies a breaking bore (Chanson, 2011b). The
bore front of an undular-type bore trailed a series of well-dened
quasi-periodic undulations. On the other hand, the bore front in
breaking bores has a distinct roller along with turbulent mixing and air
entrainment (Chanson, 2011a, 2011b). The extreme tidal bores in the
autumn season in the Qiantang River are sometimes referred to as
“tsunami-like” tides (Wang et al., 2019). Especially when it comes in
contact with the projecting banks, groins/spur dikes, and other hy-
draulic structures on its path, it induces a large load on those structures;
signicant water level rise occurs upstream of such structures, resulting
in backwater rise (Li and Pan, 2022). The backwater rise is dened as an
increase in water level at the upstream of spur dike or any ow resis-
tance, leading to a reduction in ow velocity and accumulation of water.
Subsequently, the tidal bores can profoundly alter ow patterns and
sediment transport dynamics, which may potentially pose an ecological
impact on aquatic organisms and have a substantial inuence on the
river and estuary ecosystems. Additionally, they can contribute to river
bank erosion, land degradation, vegetation damage, debris accumula-
tion, infrastructure damage, including roads and bridges, and other
topographical changes (Jiyu et al., 1990; Donnelly and Chanson, 2005).
1.1.1. Replication of tidal bore in the laboratory
Previous researchers have employed various bore generation tech-
niques/facilities to replicate the tidal bore phenomenon inside the lab-
oratory environment. However, mimicking the real-time tidal bores in
the laboratory is still challenging. For example, the entire time series of
the bore is not simulated. Hence, the present study calls the laboratory-
generated bore a “tidal bore-like unsteady ow” where abrupt changes
in bore depth and velocity characterize the tidal bore. Several acceptable
techniques, including dam break, vertical release, rapid gate closure,
and pumping, are still utilized to depict the tidal bore. Existing tidal bore
generation methods in the laboratory are illustrated in Table 1. Gose-
berg et al. (2013) demonstrated the pump-driven method as an alter-
native approach to generate long-period bores to replicate tsunamis in
the laboratory. Later, Huang et al. (2013) utilized a combination of
pump and gate (at both upstream and downstream ends) techniques to
create the tidal bore in the laboratory. The multiple pumps (at both
upstream and downstream of the channel) technique was recently
endorsed by a few researchers (Zhang et al., 2022; Fan et al., 2023) for
tidal bore-related studies. Likewise, the present study adopted a
pumping technique to generate the tidal bore-like unsteady ow (Oetjen
et al., 2020; Harish et al., 2021, 2022a, 2022b). Compared to dam break
and rapid gate closure methods, this pumping approach has a major
benet in long-period bores. Nevertheless, creating realistic long-period
unsteady bore requires high-capacity pumps. Plenty of trial experi-
mental cases might be necessary to foresee and depict the required ow
characteristics at a specic location in the laboratory.
1.2. Spur dikes in the river environment
In general, to mitigate bank erosion, river protection structures like
spur dikes are constructed. Such structures facilitate sediment deposi-
tion near the riverbank, contributing to bank stabilization (Teraguchi
et al., 2011; Nakagawa et al., 2013). Beyond erosion protection, spur
dikes serve to enhance river ecosystem health and promote biological
diversity (Pennington et al., 1988; Sparks, 1995; Zhou et al., 2014). In
navigable waterways, these structures redirect the ow towards the
centre of the river, ensuring adequate navigation depth (Duan, 2009)
while effectively managing suspended sediment transport within allu-
vial channels (Duan and Nanda, 2006). Although these spur dikes offer
more benets, poor design and inuence on ow conditions can lead to
detrimental impacts such as backwater rise and increased scour at the
head section (Pinter and Heine, 2005; Wu et al., 2005; Azinfar, 2010).
There have been numerous studies conducted in the past to understand
Table 1
Existing tidal bore generation techniques in the laboratory.
Bore generation
method
Schematics Description References
Dam break
technique
This technique involves the sudden release of
water from a reservoir behind a gate that causes
dam-break ow to propagate as a bore in the
channel.
Nakagawa et al. (1969); Yeh et al. (1989);
Mrokowska et al. (2015); Castro-Orgaz and
Chanson (2017, 2020)
Vertical release
technique
This technique involves the sudden release of a
large volume of water due to gravity, generating
tidal bore-like unsteady ows in the laboratory.
Initially, the rapid release from the upper basin
causes an upward surge in the lower basin, which
then propagates downstream of the ume.
Chanson et al. (2002, 2003); Wüthrich et al.
(2018)
Rapid gate closure
method
(partial/
complete)
This method involves the quick partial or complete
closing of a gate positioned in the extreme channel
downstream. This sudden closure causes a rapid
rise in the water level upstream, generating an
unsteady ow that mimics natural tidal bores.
Koch and Chanson (2009); Chanson (2010a,
2010b; 2011b); Khezri and Chanson (2012);
Huang et al. (2013); Rousseaux et al. (2016); Li
and Chanson (2018); Wüthrich et al. (2020); Shi
et al. (2023a, 2023b)
Pump-type bore
generation
This mechanism involves controlling the pump
openings and bore creation duration (similar to the
vertical release approach), which creates bores
with diverse characteristics in the laboratory.
Huang et al. (2013); Zhang et al. (2022); Fan
et al. (2023);
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
3
the regular river ow interaction with single spur dike (Rajaratnam and
Nwachukwu, 1983; Yeo et al., 2005; Ho et al., 2007; Zhang and Naka-
gawa, 2008; Kang and Yeo, 2011; Kang et al., 2011) and multiple spur
dikes (Uijttewaal et al., 2001; Uijttewaal, 2005; Yossef and de Vriend,
2010, 2011). The studies mainly focused on regular river ow interac-
tion with the spur dike, sediment exchange and scour around the spur
dike. The research efforts in these regards have been summarized in
detail by Nandhini et al. (2024).
Despite the emphasis being mainly on the impact of spur dikes in the
riverine environment during the regular river ow, few researchers also
focused on the effect of unsteady ow (replication of ood) (Iqbal and
Tanaka, 2023; Moghispour and Kouchakzadeh, 2024), tidal bore (Xu
et al., 2016; Wang et al., 2022a; Zhang et al., 2022, 2023) and landslide
induced surges (Wang et al., 2022b) interaction with spur dikes. Ac-
cording to the U.S. Army Corps of Engineers (USACE), spur dikes reduce
ow elevations under minimal ow circumstances by deecting the ow
into the main channel. However, when submerged during ood events
(unsteady ow), no signicant inuence was observed (USGAO, 2011).
Huthoff et al. (2013) demonstrated that spur dikes may decrease water
levels during in-bank ows but rise them during ood events, based on
theoretical research. Moghispour and Kouchakzadeh (2024) also
discovered that higher ow discharge causes a rise in water height up-
stream of the spur dike.
1.3. Tidal bore interaction with spur dikes
Limited research exists on the tidal bore interaction with the spur
dike despite their occurrence in various river and estuarine regions. Xu
et al. (2016) conducted a comprehensive study involving eld mea-
surements and numerical simulations to analyze the temporal and
spatial distribution of bore-induced pressures on sheet pile spur dike in
the Qiantang River. The study ndings revealed a linear increase in
Fig. 1. Photographs of tidal bore interaction with spur dike in Qiantang River, China near Yanguan (left) (Photograph: H. Schüttrumpf, 2024) and at IWW laboratory
(right) (Photograph: D. Nandhini, 2024) (a) before interaction, (b) initial impact stage, (c) during interaction, (d) after interaction with spur dike.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
4
impact pressure with depth, peaking at the still water level, and followed
a trapezoidal distribution below that level. Building on this work, Cai
et al. (2018) investigated the inuence of perviousness on sheet pile spur
dike response to tidal bore impacts through a combination of experi-
mental and numerical analyses. A signicant reduction in pressure on
sheet pile spur dikes was observed with increased perviousness. Pan and
Li (2022) focused on scour characteristics around sheet pile spur dikes,
conducting eld measurements and experimental modelling of single
sheet pile spur dike. Beyond scouring and bore-induced impact studies,
other research efforts have aimed to understand the dynamic response of
sheet pile spur dikes and provide analytical solutions for their vibration
behaviour during tidal bore events in the Qiantang River (Wu et al.,
2022, 2023a, 2023b). The dynamic impedance of sheet-pile spur dikes
was examined in these studies in relation to water depth, sheet pile
length, pile radius, and soil–pile modulus ratio (ratio between stiffness
of soil and the stiffness of pile). In light of the results, suggestions are
made to direct the design of sheet-pile spur dikes with the goal of
enhancing impedance and avoiding resonant frequencies.
Moreover, existing studies have primarily concentrated on sheet pile
spur dikes in the Qiantang River (Xu et al., 2016; Cai et al., 2018; Pan
and Li, 2022; Wu et al., 2022, 2023a, 2023b). Zhang et al. (2022) were
perhaps the pioneers in investigating the hydrodynamics of tidal bore
overow on the spur dike (impermeable solitary vertical spur dike, not
the sheet pile spur dike) and quantifying the scour around the spur dike.
When a tidal bore hits a spur dike, it induces an intense impact followed
by signicant scour damage surrounding the spur dike (Khezri and
Chanson, 2012; Zhang et al., 2022). The scour behind the spur dike is
identied to be a function of tidal bore depth, velocity, and spur dike
height (Zhang et al., 2022). Further, the study observed an increase in
the water level at the upstream of the spur dike during the interaction
process, as can also be observed in Fig. 1. Fig. 1 presents the photograph
of the tidal bore interaction with a spur dike at Qiantang River, China,
near Yanguan (left[a-d]), renowned for its signicant tidal bore phe-
nomenon and a generated bore interaction with a spur dike at the IWW
laboratory (right[a-d]).
From the literature, it is clear that the limited existing studies on
tidal-bore interaction with spur dikes primarily focused on sheet-pile
type spur dikes and evaluated the impulsive pressure the tidal bores
induce on the spur dikes and the scour around such spur dikes. Despite
the recent study of Zhang et al. (2022) pointed out the backwater rise at
the spur dike front, the spur dike was represented as a vertical wall
(caisson) in their study. Vertical caissons can result in a signicant water
level variation in the vicinity of spur dikes compared to the conventional
trapezoidal cross-sectioned spur dikes, which are also common in
several inland rivers, exhibiting uncertainty even in the prediction of
backwater rise in such a case. Fig. 2(a) and (b) present the case studies of
round-headed trapezoidal spur dikes from the Gironde River (France)
and Severn River (United Kingdom), respectively, similar to those used
in this study. Furthermore, there is a limited understanding of the ow
characteristics at the head and the downstream, which are the locations
of signicant bed shear stresses that induce scouring (Khezri and
Chanson, 2012; Zhang et al., 2022, 2023). This study addressed this
limitation by experimentally understanding the tidal bore interaction
with the trapezoidal-shaped spur dike with a round head, which resulted
in improved ndings.
1.4. Objective, novelty, and framework of the study
The objective of the present study is to quantify the ow character-
istics in the vicinity of the spur dike when the tidal bore interacts with a
spur dike. More specically, this research.
•presents and discusses the hydrodynamics of the wet bed tidal bores
generated using the pump-driven technique in the laboratory.
•quanties the ow hydrodynamics around a solitary trapezoidal-
shaped spur dike with a round head (actual shape to replicate the
reality) during the tidal bore.
•addresses the variation of bore depth, ow velocity, and energy
dissipation by varying the incoming tidal bore Froude number and
the relative dike height.
While previous studies have explored tidal bores and spur dikes
separately, the present study addresses the tidal-bore interaction with
the trapezoidal-shaped spur dike with a round head by conducting a
detailed experimental campaign. The study utilizes a pump-driven
technique to generate wet bed tidal bores in a laboratory setting that
allows for a controlled and precise analysis of hydrodynamics.
Furthermore, the study compares ow characteristics in the presence
and absence of the spur dike, providing new insights into the local
changes in hydrodynamics caused by the dike’s interaction with the
tidal bore. Empirical equations are proposed to predict the ow char-
acteristics at the spur dike vicinity. The ndings from this study high-
light the shape of the spur dike has a greater inuence on local
hydrodynamics.
The outline of the paper is as follows: Initially, the physical model-
ling setup, spur dike model design, dimensions and the experimental
cases conducted are elucidated. Subsequently, the generated tidal bore
characteristics are presented in the absence of the spur dike and
compared with those observed in the presence of spur dike. Finally, the
variations in the ow properties, such as water elevation, ow velocity,
Fr, and ow energy around the spur dike, are examined, leading to
conclusions regarding the tidal bore interaction with the solitary spur
dike. The present study contributes to a deeper understanding of the
ow features in the vicinity of the spur dike during tidal bore-like un-
steady ow events.
Fig. 2. Trapezoidal spur dike with round head at (a)Gironde River, France (source: Google Earth) and (b)Severn River, United Kingdom [the small yellow circles
represent the spur dike eld] (source: Google Earth).
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
5
2. Physical modelling
2.1. Experimental facility and instrumentation
The experiments were conducted in the large tilting ume (25.5 m
usable length and 1m width) at the Institute of Hydraulic Engineering
and Water Resources Management (IWW), RWTH Aachen University in
Germany (Fig. 3). The controlled generation of tidal bore-like unsteady
ow was achieved using a bore generation facility at IWW equipped
with two underground pumps. The bore of varying discharges (up to 0.4
m
3
/s) can be produced by regulating the valve positions of two pumps.
Additionally, the duration of bore generation could be adjusted within
the existing experimental setup, allowing for the creation of a wide
range of ow features. Once the pumping is started, the water ows via
the perforated plate and ow straighteners at the entrance of the ume,
creating a two-dimensional ow characteristic in the ume. A similar
type of controlled bore generation facility has been utilized in previous
tidal bore research (Huang et al., 2013; Zhang et al., 2022) (Table 1).
Detailed information about the present bore generation facility can be
found in Harish et al. (2021, 2022a, 2022b).
Experiments were carried out with and without the spur dike model
(free-ow experiments) to quantify the variation in the ow character-
istics in the presence of the spur dike model. For both experiments, the
generated bore characteristics were probed through ow depth (h) and
depth-averaged velocity (u) measurements. Flow depth measurements
were conducted at eight locations along the length of the ume using
ultrasonic depth sensors (US) (microsonic pico +35/l), and velocity
measurements were taken at three locations using an Acoustic Doppler
Velocimeter (ADV) (Nortek Vectrino Plus - side-looking probe), as
indicated in Fig. 4. In the case of free-ow experiments, all the ow
measurements were carried out at the ume centre. The ADV probes
were kept at three different depths in the still water depth from the
ume bottom to arrive at depth-averaged velocity (u). All the mea-
surements were carried out at 100 Hz frequency. Fig. 4 illustrates the
experimental plan layout and instrumentation positions and the detailed
illustration of the bore generation mechanism at IWW. The study mainly
focuses on the ow characteristics in the vicinity of the spur dike (up-
stream, downstream, and at the dike head). Further, throughout the
results and discussion sections, the terms upstream, downstream, and at
the dike head are used to denote specic instrument positions in the
vicinity of the spur dike, as indicated in Fig. 4. These correspond to the
locations of ADV1, ADV3, and ADV2, respectively.
2.2. Spur dike model
The modelled spur dike in the experiments resembled the conven-
tional trapezoidal spur dike with the circular head (plan view). The spur
dike model is made with concrete and is xed rigidly at 14.6 m from the
start of the barrier (indicated in Fig. 4). The height (h
d
) and length of the
model were kept at 15 cm and 30 cm, respectively. The side slopes at the
head and trunk portion of the spur dike were kept at 1:1.25 to represent
a more realistic dike model. Fig. 5shows the photograph of the spur dike
model with dimensions. The GoPro Hero4 camera was kept at the side of
the ume to capture the bore interaction process throughout the
experiment. The camera was operated at 24 fps with 1080p resolution.
2.3. Experimental test conditions
Experiments were conducted with four different wet bed conditions,
i.e., initial still water depth ‘d
0
’ (5 cm, 8 cm, 10 cm, and 15 cm), in the
laboratory to simulate a wide range of tidal bores by adjusting the height
of barriers at the front and rear end of the ume (Fig. 4a). Also, these still
water levels were chosen to correspond approximately to one-third, two-
thirds, and the full height of the spur dike model. Throughout the study,
the spur dike dimensions were kept constant, and only ow discharge
was varied between 0.1 and 0.36 m
3
/s by regulating the pump openings.
Table 2 presents the details of the experimental program along with the
generated bore characteristics that were tested. The generated bore
ranged from undular and broken bores with the generated discharge and
still water depth conditions. As no opposing ow (only unidirectional
ow) was considered in the study, the initial velocity remains constant
at zero during the course of the experiment, similar to Zhang et al.
(2022).
3. Bore characteristics with and without spur dike
3.1. Free ow hydrodynamics
Dening the bore generation period is essential before conducting
experiments in a pump-type bore generation facility. Harish et al. (2021)
reported that the bore properties remained stable when the bore gen-
eration period was extended beyond 15 s in the present experimental
facility. Hence, for all the generated test conditions, the bore generation
period was maintained at 30 s or above to enhance the comprehension of
both the initial aerated bore front and the quasi-steady condition of the
bore. The generated bore in this experimental facility is highly repeat-
able, as can be found in Appendix A. The details of the bore generation
period of each test case are listed in Table 2. Fig. 6a–b depict the bore
depth variations for low discharge and high discharge conditions in all
four wet bed cases. Shi et al. (2014) highlighted that the initial still
water depth is considered to have a more signicant inuence on the
generation of tidal bore. The bore front steepness increases with the
increase in initial still water depth (Wüthrich et al., 2018). Especially for
the low-discharge and larger still water depth conditions, the bore front
propagated completely as an undular bore, as can be seen in Fig. 6a.
Flow velocity decreased as the initial still water depth increased
(Fig. 7) since it induced resistance to the ow, resulting in a reduced
ow velocity and aerated ow at the bore front. Such effects are even
more pronounced when a low discharge ows over a higher still water
depth, resulting in an undular wave-type bore front (Ramsden, 1996;
Wüthrich et al., 2018). After the pumping period ends, both the bore
depth and velocity decrease signicantly. Also, alterations in discharge
and wed bed conditions resulted in the formation of distinct bore front
characteristics.
Fig. 3. Bore generation facility available in IWW, RWTH Aachen University.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
6
Further, for the low wet bed conditions (d
0
=0.05m and 0.08m), the
generated bore front resulted in a super-critical ow (Fr
b
>1) with
relatively higher Fr
b
ranges from 1.8 to 2.6 (Refer Table 2). The broken
bore was spotted due to a subtle balance of energy at the bore front. It is
noticed that when the initial still water level is low, the bore front is
more susceptible to surface instabilities and turbulence. These in-
stabilities might cause the front to break, leading to a “broken” bore type
instead of a smooth, undular bore. Further, due to large h/d
0
, the ow
became unstable when it entered the ume and formed a broken bore, as
can also be observed in Fig. 1. On the contrary, in the case of a high wet
bed (d
0
=0.15m), undular bore fronts were observed (Fr
b
between 1.3
and 1.6), and specically, an evident waveform can be spotted during
the high discharge scenarios (Fig. 6b). h/d
0
observed in this d
0
=0.15m
case was between 1.5 and 2. These observations agree with the tidal bore
observed in different rivers around the world, as Pelinovsky et al. (2015)
reported. For d
0
=0.1 m, depending on the discharge conditions, h/d
0
varied, and accordingly, the generated bore was undular (during low
discharge conditions) and broken (during high discharge conditions)
bores. Thus, during the low discharge conditions, small undulations in
the bore front prole were clearly observed (Fig. 6a).
Despite the fact that the bore front took undular or broken bore
shapes depending on the discharge and the wet-bed conditions, the
continuous ingress of the ow resembled a quasi-steady ow condition
with nearly no signicant oscillations (Figs. 6 and 7). Subcritical ow is
the most commonly observed ow regime behind tidal bores in natural
systems (Pelinovsky et al., 2015). This is due to the natural dissipation of
energy and the typical hydraulic conditions of estuarine and riverine
environments. Critical ow is less common and usually transient, while
super-critical ow is rare and typically requires specic conditions that
are not commonly found in nature (Chanson, 2009). Consequently, in
the present study, discharge and wet bed conditions were considered to
have aided the generation of subcritical and critical ows. From Table 2
and it is evident that in the quasi-steady ow state, the generated bore is
subcritical in a higher still water level (d
0
=0.15m), irrespective of
discharge conditions. And close to critical for other lesser still water
levels (d
0
=0.05m, 0.08m and 0.1m).
While the initial impact of the bore front presents a dynamic water
level oscillation with an aerated bore front, it represents only a short
phase (<3 s) in the tidal bore event. Quasi-steady state analysis can offer
insights into sustained ow conditions over extended time periods,
which are responsible for continuous loading on the structure and long-
term impacts like scour. This approach allows for a deeper under-
standing of the structural stability of spur dikes under sustained tidal
bore inuences. By focusing on quasi-steady ow conditions, engineers
can better predict long-term hydraulic performance and design resilient
spur dike capable of withstanding the complex and varying dynamics of
tidal bores. Therefore, this study emphasizes further quasi-steady ow
interaction with the spur dike and understands the ow characteristics
in the vicinity of the spur dike.
3.2. Tidal bore ow interaction with spur dike
With the presence of spur dike, there is a signicant variation at the
upstream and downstream of the spur dike for different discharge and
wet bed conditions. During the quasi-steady ow phase, the water level
upstream of the spur dike increases during the bore interaction
depending on the energy associated with the incoming bore. The spur
dike acts as a vertical obstruction, resulting in the reection of the part
of the incoming bore depending on the incoming bore energy. As the
bore inundation progresses, it pushes more water upstream and against
the spur dike, causing an escalation in the water level upstream. Fig. 8
depicts the visual observation during bore interaction with the spur dike
in the laboratory for different wet bed conditions in the quasi-steady
ow conditions (at t =4.5 s after the bore impacted the spur dike). It
can be observed that with the increase in the still water depth (i.e.,
decrease in the Fr), the difference in elevation between the upstream and
the downstream reduces. Fig. 9 compares the water depth upstream,
head and downstream of the spur dike for two different discharge con-
ditions for the different still water depths tested. The water depth up-
stream (h
us
) of the spur dike increases with discharge, as expected.
However, h
us
– d
0
exhibits a decrease as d
0
increases, which indicates a
clear inverse relationship between h
us
– d
0
and d
0
. Further, in the case of
d
0
=15 cm, the water just slides over the spur dike since the spur dike
height equals the d
0
, thereby resulting in insignicant vertical obstruc-
tion to the ow. It is noticed that h
us
– d
0
is larger in d
0
=0.05m when
compared to other still water depths considered in the study (Fig. 9a). At
the spur dike head (h
dh
), a nearly similar water depth pattern like the
water depth upstream for different d
0
(Fig. 9b) was observed with a
slightly reduced magnitude. At the spur dike downstream, h
ds
– d
0
Fig. 4. Sectional view (top) and plan view (bottom) of the experimental ume along with the sensor locations in the experiments with spur dike.
Fig. 5. Photograph showing the spur dike model dimensions (a) front view and
(b) side view.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
7
Table 2
Experimental program and bore characteristics tested in the laboratory. The presented data is from free-ow experiments.
Initial water
level (d
0
)
[m]
Bore
depth (h)
[m]
Bore generation
period (t) [s]
Dimensionless water
level (h/d
0
) [-]
Relative dike
height (h
d
/h)
[-]
Bore celerity
(C) [m/s]
Bore front
Froude number
(Fr
b
) [-]
Froude number (Fr)
in the Quasi-steady
state [-]
Reynolds number
(Re) in Quasi -steady
state [-]
0.05 0.148 40 2.960 1.014 1.33 1.899 0.808 144562.7
0.05 0.161 40 3.220 0.932 1.45 2.070 0.824 166307.9
0.05 0.182 30 3.640 0.824 1.52 2.170 0.915 222752.3
0.05 0.191 30 3.820 0.785 1.54 2.199 0.925 242196.2
0.05 0.195 30 3.900 0.769 1.61 2.299 1.014 274148.7
0.05 0.191 30 3.820 0.785 1.72 2.456 0.997 261020.5
0.05 0.205 30 4.100 0.732 1.64 2.342 0.997 290369.3
0.05 0.212 30 4.240 0.708 1.79 2.556 1.047 319665.8
0.05 0.217 30 4.340 0.691 1.67 2.384 1.058 335362.2
0.08 0.209 30 2.613 0.718 1.59 1.795 0.719 214648.4
0.08 0.213 30 2.663 0.704 1.59 1.795 0.738 227684.4
0.08 0.225 30 2.813 0.667 1.69 1.908 0.797 265861.3
0.08 0.22 30 2.750 0.682 1.56 1.761 0.796 257615.5
0.08 0.234 30 2.925 0.641 1.56 1.761 0.824 292986.7
0.08 0.243 30 3.038 0.617 1.72 1.942 0.817 306733.9
0.08 0.247 30 3.088 0.607 1.79 2.021 0.847 325834.5
0.1 0.18 40 1.800 0.833 1.28 1.292 0.485 116554.1
0.1 0.206 40 2.060 0.728 1.37 1.383 0.583 170308.5
0.1 0.221 30 2.210 0.679 1.49 1.504 0.665 216319.2
0.1 0.236 30 2.360 0.636 1.52 1.535 0.687 246394.5
0.1 0.243 30 2.430 0.617 1.67 1.686 0.701 262590.1
0.1 0.241 30 2.410 0.622 1.56 1.575 0.717 265968.6
0.1 0.246 30 2.460 0.610 1.56 1.575 0.759 290536.4
0.1 0.256 30 2.560 0.586 1.72 1.737 0.758 307876.8
0.1 0.265 30 2.650 0.566 1.82 1.838 0.789 337542.6
0.1 0.249 30 2.490 0.602 1.67 1.686 0.74 287647.0
0.1 0.267 30 2.670 0.562 1.89 1.908 0.811 351044.8
0.1 0.273 30 2.730 0.549 1.85 1.868 0.805 359454.0
0.15 0.237 40 1.580 0.633 1.59 1.311 0.398 144378.4
0.15 0.26 30 1.733 0.577 1.72 1.418 0.451 187688.5
0.15 0.267 30 1.780 0.562 1.67 1.377 0.505 217608.6
0.15 0.277 30 1.847 0.542 1.64 1.352 0.513 233847.9
0.15 0.277 30 1.847 0.542 1.85 1.525 0.526 240158.2
0.15 0.289 30 1.927 0.519 1.69 1.393 0.548 266842.9
0.15 0.297 30 1.980 0.505 1.82 1.500 0.568 287451.7
0.15 0.309 30 2.060 0.485 2.00 1.649 0.588 316308.5
*h
d
=dike height; Fr
b
=C
gd0
, where d
0
=initial still water depth; g=acceleration due to gravity; C=the speed in which the bore front travels (calculated based on the
time taken for the bore front to reach from US3 to US4); Fr =u
gh
, where u=depth-averaged bore velocity; h=representative bore depth in the quasi-steady state (the
chosen bore depth and velocity are discussed in section 3.1), Re=
ρ
uh/
μ
;
μ
=dynamic viscosity of the uid.
Fig. 6. Bore depth variation with respect to initial wet bed variations for different discharge conditions (a) Q =0.16 m
3
/s; (b) Q =0.26 m
3
/s. Herein, the discharge
Q, is calculated by averaging the discharge calculated for the four still water depths by multiplying bore depth and bore velocity.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
8
increases as d
0
increases, showing a contrary observation compared to
the upstream (Fig. 9c). The water depth downstream is critical since
higher d
0
tends to reduce scouring action downstream of structures like
spur dikes (Zhang et al., 2022). Thus, h
us
/h
ds
decreases with the increase
in the still water depth. This can also be related to the decrease in Fr and
increase in the dike submergence (d
0
/h
d
) with the increase in the still
water depth, as discussed in section 4.1.
4. Results and discussion
4.1. Hydrodynamics around spur dike
4.1.1. Dependence of water depth and ow velocity in the vicinity of spur
dike on Fr
Understanding the relationship between Fr and relative water
elevation and relative velocity is important for understanding the ow
behaviour in the presence of a spur dike. Fig. 10 shows the water depth
and ow velocity at the upstream, head and downstream of the spur dike
compared against the free-ow Fr. Herein, the water depth and ow
velocity are non-dimensionalized with free-ow parameters (h and u) to
appreciate the variation in the ow characteristics. The data presented
in this section are time-averaged between t =3s and 6s, where t =0s
represents the time instant when the bore front crosses the particular
instrument location. Within this time instant, the bore was already in the
quasi-steady phase. Further, the time-averaging approach was found to
sufciently represent the bore characteristics in the quasi-steady phase,
as Harish et al. (2021, 2022a and 2022b) pointed out, and hence the
same has been adopted in this study.
One could observe that as Fr increases, indicating the higher ow
velocities, the spur dike obstructs the ow more signicantly. This ow
blockage creates a backwater effect, raising the water levels upstream of
the spur dike (h
us
) (Fig. 10a). Increased h
us
is due to the incoming ow
kinetic energy partially converted into potential energy due to
obstruction, resulting in elevating the water elevation upstream. Thus,
the ow velocity upstream of the spur dike (u
us
) decreased with the
increase in Fr. It can also be observed that even for low Fr, u
us
/u <0.8 in
most of the tested cases. At the head section, both the accumulated ow
at the spur dike front diverted around the head section and the over-
topped ow characteristics decide the ow characteristics. In the case of
high Fr, the bore depth at the head section (h
dh
) is slightly greater than h,
with ow velocity at the head (u
dh
) approximately equal to or slightly
lesser than the free ow velocity. Contrarily, in the case of low Fr, the h
dh
is approximately equal to h; however, the ow velocity at the head (u
dh
)
is slightly higher than the free ow velocity. Nevertheless, both h
dh
/h
and u
dh
/u ranged between 0.95 and 1.2, showing only an insignicant
variation compared to the free-ow characteristics (Fig. 10b). Immedi-
ately downstream of the spur dike, the ow characteristics are just
opposite to the upstream ow characteristics. The bore depth at the
downstream of the spur dike (h
ds
) is lesser than the free-ow bore depth
(Fig. 10c), and the ow velocity increased with increasing Fr. Especially
in the case of high Fr, the thickness of the overtopping ow decreased
(Fig. 8), resulting in high ow velocity, and hence, resulting in low h
ds
and high u
ds
. Also, the ow downstream is highly turbulent and expe-
riences ow separation, resulting in vortex formation in the vertical
plane and thereby dissipating ow energy; the energy dissipation is
discussed in section 4.3.
4.1.2. Dependence of water depth and ow velocity in the vicinity of spur
dike on relative dike height (h
d
/h)
The bore depth and velocity upstream, head, and downstream also
depend on the relative height of the dike (h
d
/h). Fig. 11 presents the bore
depth and velocity variations with respect to h
d
/h. Higher h
d
/h results in
more signicant ow obstruction and rise in backwater upstream of the
spur dike. At lower relative dike heights (h
d
/h =0.5 to 0.6), minor
variations in the ow characteristics are observed compared to the free-
ow characteristics. As h
d
/h increases from 0.7 to 0.8, the impact on
bore depth and velocity becomes more pronounced. The spur dike
signicantly affected the ow regime, resulting in higher h
us
/h (lower
u
us/u
) and lower h
ds
/h (higher u
ds/u
). When h
d
/h ≈1, the dike almost
completely obstructs the ow, leading to maximum upstream water
accumulation and increased h
us
/h. Thus, as a general trend, increased
dike heights (h
d
) lead to increased water elevations upstream (h
us
) due to
the backwater effect, while downstream water levels (h
ds
) decreased due
to ow acceleration. Correspondingly, ow velocities decreased up-
stream (u
us
) due to obstruction. A complicated downstream u
ds
was
observed since the overtopping ow accelerates downstream the dike,
and the ow passing around the dike together inuences the ow
characteristics downstream. At the head section, since the accumulated
ow at the upstream and the overtopped ow decide the ow features, it
is hard to understand a clear pattern. Thus, both h
d
/h and Fr together
inuence the ow characteristics at the spur dike vicinity.
4.1.3. Spur dike impact on ow Froude number
The relationship between free-ow Fr and the Fr at the upstream
(Fr
us
), head (Fr
dh
) and downstream (Fr
ds
) of the spur dike is shown in
Fig. 12. In the low Fr regime, Fr
us
, Fr
dh
and Fr
ds
did not vary signicantly
compared to the free ow conditions, indicating that at low Fr, the
impact of the spur dike on the ow remains minimal. Nevertheless, the
upstream Froude number (Fr
us
) was consistently less than the free-ow
Froude number (Fr). With the further increase in the free-ow Fr, it can
be observed that the ow Fr
us
did not increase but rather reached an
equilibrium state. At the spur dike head, it is noticed that Fr
dh
is not
signicantly inuenced by the presence of spur dike up to Fr <0.8. With
the further increase in the free-ow Fr, Fr
dh
started to reach an equi-
librium, with nearly a gradual rise in Fr
dh
with an increase in Fr. These
equilibrium conditions indicate that once the free-ow Fr reaches a
specic value, the inuence of the spur dike on the Fr regime becomes
more consistent. Conversely, at the spur dike downstream (Fr
ds
), there is
a signicant increase up to 1.8. This steep increase indicates that at
higher Fr, the obstruction caused by the spur dike exerts a substantial
impact on the ow velocity and bore depth, resulting in a much higher
Fr with the spur dike than in conditions without the spur dike.
Furthermore, it can also be realized from Fig. 8 that with the increase in
the ow Fr (i.e., decrease in the still water depth), the hydraulic jump
moves farther downstream the dike crest, also indicating the reason for
the large increase in Fr
ds
. Overall, these observations suggest that the
ow upstream and at the head of the spur dike tends to be sub-critical
and close to critical, respectively, whereas downstream of the spur
dike, the regime shifts to super-critical conditions at Fr >0.8. This
characterization highlights the inuence of the spur dike on ow char-
acteristics across different ow regimes.
4.2. Dimensionless relationship and prediction formulae
It is necessary to arrive at a relationship between the free-ow pa-
Fig. 7. Depth averaged freeow bore velocity variation at x =14.725m (at spur
dike head location) with respect to initial wet bed conditions Q =0.26 m
3
/s.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
9
rameters and the ow parameter in the vicinity of the spur dike to es-
timate the backwater rise and expected scour depth using analytical
formulas (Zhang and Nakagawa, 2008; Azinfar, 2010; Zhang et al.,
2022, 2023). The ow parameters in the spur dike vicinity are mainly
affected by hydrodynamic factors, mainly Fr and the relative dike height
(h
d
/h). The dimensionless relationship is found as follows:
hus
h=hdh
h=hds
h=uus
u=udh
u=uds
u=fFr,hd
h(1)
From the discussions in section 4.1, it is concluded that the Fr and h
d
/
h have a positive correlation with h
us
/h and h
dh
/h and a negative cor-
relation with h
ds
/h. Therefore, eqn. (2) is assumed as:
Fig. 8. Picture showing ow interaction with spur dike at t =4.5s during different wet bed conditions (a) d
0
=0.05m; (b) d
0
=0.08m; (c) d
0
=0.10m; (d) d
0
=
0.15m; green dotted lines indicate the upper and lower limits of turbulence zone observed. Q =0.26 m
3
/s.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
10
hus
h=hdh
h=hds
h=uus
u=udh
u=uds
u=a(Fr)bhd
hc
(2)
where a, b and c are tting coefcients. A non-linear multivariate
regression analysis was carried out using the experimental data. The
regression analysis yielded the empirical equations to determine the
ow characteristics at the upstream, dike head, and downstream, as
listed in Table 3.
Fig. 13 depicts the comparison of the observed and predicted ow
characteristics around the spur dike. The present study data t well with
the regression analysis and the proposed equations in Table 3 at all three
locations (upstream, dike head, and downstream), showing a goodness-
of-t in regression analysis. Despite the R
2
value being lesser for the ow
velocity, the present study results were predicted reasonably, consid-
ering the strong turbulence, especially at the head and downstream
(Fig. 1). Further, the predicted results from Zhang et al. (2023)’s
equation on the water depth upstream are compared with the current
experimental results (‘x’ symbol). Herein, the values are predicted using
the Fr and h
d
/h from the present study. As can be seen in Fig. 13(a)–
Zhang et al. (2022) overpredict the current results by nearly 50%. The
probable reason could be the vertical caisson-type spur dike in their
study, which could maximize the backwater rise, minimize the down-
stream ow depth, and accordingly change the ow characteristics in
the vicinity. Thus, by incorporating the conventional shape, these
ndings provide a more reliable and accurate representation of the
hydrodynamic interactions, leading to better predictions of ow
behaviour. Therefore, the conventional round-headed trapezoidal spur
dike shape has a greater inuence on the local hydrodynamics. Further,
it is attempted to check whether the B´
elanger equation for conjugate
depth (hus
/h=−0.5+0.5
1+8Fr2
can predict the h
us
for Fr >1
since the water level increase at the upstream of the spur dike can be
related to a hydraulic jump scenario. In our study, only a few test cases
in d
0
=5 cm had Fr >1, and hence, only limited comparisons exist. The
comparison showed that the hydraulic jump theory could not predict the
h
us.
This is primarily due to the reection of the incoming bore by the
spur dike, which was not taken into account in the B´
elanger’s conjugate
depth equation.
From Table 3 and it is also clear that at the upstream, h
us
increased
with the increase in Fr and h
d
. Contrarily, u
us
decreased with the increase
in Fr and h
d
, conrming the accumulation of ow due to the reection
from the spur dike. At the head, h
dh
and u
dh
are partially affected by the
Fr and h
d
. This can be evidenced by the scatter of data points predom-
inantly between 0.9 and 1.2. (see Fig. 13b and e). Nevertheless, the trend
shows that h
dh
increased insignicantly with the increase in Fr and h
d
,
while a contrary behaviour is observed for u
dh
. At the downstream, h
ds
consistently decreased with the increase in Fr and h
d
, while the empirical
equation shows that u
ds
increased with the increase in Fr and slightly
decreased with the decrease in h
d
, although a complicated ow velocity
pattern was observed (Fig. 11c).
4.3. Energy
Tidal bore energy is the driving force behind its formation, behav-
iour, and environmental impact. It governs the bore’s propagation, its
ability to transport sediment, and its inuence on riverbed morphology.
Additionally, the energy dynamics are crucial in determining the extent
of saltwater intrusion and the overall lifespan of a tidal bore (Pelinovsky
Fig. 9. Schematic gure of ow spur dike interaction observed with the inuence of initial wet bed variations (a) upstream (b) head (c) downstream; Q =0.2 m
3
/s
(left) Q =0.33 m
3
/s (right).
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
11
et al., 2015; Qiushun et al., 2024).
Fig. 14compares the energy calculated in the vicinity of the spur dike
and the energy calculated under free-ow conditions. Herein, the energy
is presented as the energy head. The energy of the free-ow, E, is
calculated as
Efree flow =h+u2
2g(3)
Where h and u are the ow depth (m) and velocity (m/s), respectively,
and g is the acceleration due to gravity (m/s
2
). Similarly, the energy at
any location near the spur dike (E
spur dike
) is calculated utilizing the ow
depth and velocity at that location in the presence of the spur dike.
Upstream, it can be observed that the energy at the spur dike presence
did not signicantly change compared to the free-ow conditions.
However, the energy was reduced to a maximum of −9% for a few of the
tested cases. The negative sign indicates energy reduction. Herein, the
energy reduction is calculated as
ΔEspur dike
E=Espur dike −Efree flow
Efree flow
×100% (4)
The probable reasons could be that the reection could have created
additional ow circulation at the dike front, which increases the ow
friction and the ow separation occurring upstream when the ow
passes around the dike. Fig. 15 presents the turbulence intensity at the
upstream, head and downstream of the spur dike. As could be observed,
the intensity is higher at the downstream location due to downstream
hydraulic instabilities and mixing due to the presence of the spur dike.
While at the spur dike head, higher intensity than the upstream location
is observed due to higher velocities. Nevertheless, the turbulence still
exists even at the upstream of the spur dike, although it is low. Turbu-
lence intensity is lower at the upstream of the spur dike because the ow
is relatively stagnant, with less velocity uctuation. Further, the shape of
the dike can also inuence these processes happening upstream. At the
dike head, the energy head was not signicantly inuenced by the
presence of the dike. The energy reduction expected by the local tur-
bulences and ow separation would be compensated by the energy fed
by the ow passing around the spur dike. As expected, at the spur dike
downstream, the spur dike induces signicant energy reduction since
these are the regions of high turbulences and vertical eddy formation,
especially true for submerged spur dike. The turbulent intensity was also
signicantly higher in the downstream compared to the upstream and
head location due to the chaotic ow structure (Fig. 8). In the present
study, for the range of ow conditions tested, the spur dike reduced the
energy head by nearly −25%, hence showcasing that the presence of the
spur dike increases the ow energy dissipation and hence can reduce the
Fig. 10. Variation of relative water elevation and relative velocity with Fr. (a)
upstream (b) at head and (c) downstream of the spur dike. Fig. 11. Variation of relative water elevation and relative velocity with relative
dike height (h
d
/h). (a) upstream (b) at head and (c) downstream of the
spur dike.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
12
extent of tidal bore propagation in the ow direction.
Further, to understand the effect of Fr and h
d
/h, the interpolated 3D
colour map (right) and 2D projection curve (left) showing the percent-
age of energy reduction variation in the dike vicinity are presented in
Fig. 16. Despite signicant scattering, it can be observed the reduction in
the ow energy upstream is more pronounced for high Fr cases (i.e., for
d
0
=5 cm). The overall energy reduction varied between +3% and
−10%. At the dike head, the energy reduction was insignicantly
inuenced by Fr and h
d
/h. The overall reduction percentage varied be-
tween +5% and −5%, and hence, it can be safely concluded that the
presence of spur dike did not inuence the energy at the head section. At
the downstream, the results show that the spur dike reduced the ow
energy, and the reduction is more pronounced, especially at high Fr (Fr
>0.6) and high h
d
/h (h
d
/h >0.7) since high Fr increases the overow
velocity while high h
d
/h decreases the thickness of overow and hence
together increasing strength of the vertical vortices formed resulting in
signicant energy losses. In specic, the experimental results showed
that h
d
/h was found to play a predominant role in energy reduction.
Thus, spur dike could efciently reduce the tidal bore energy under high
Fr and high h
d
/h conditions. Nevertheless, high Fr and high h
d
/h can
increase the water level upstream (backwater rise), hence necessitating
higher river bank heights to avoid the tidal bore overowing the banks.
4.4. Discussions and perspectives on practical applications
The present experimental study attempted to understand the tidal
bore interaction with the trapezoidal-shaped spur dike with the round
head in the quasi-steady ow phase. The experiments were conducted
on the geometric scale of 1:15 and Froude similitude. Considering the
ow depth without spur dike, the experimental results in the real scale
represent a tidal bore height without considering the still water depth, i.
e., h -d
0
, between 1.2 m and 2.6 m. Including the still water depth, the
ow depth (h) ranged between 2.2 m and 4.6 m, while the bore front
celerity of such incoming tidal bore was in the order of 4.95 m/s – 7.5 m/
s in the real scale, which is in the ranges of observed tidal bore heights
and front celerity in several rivers (Pelinovsky et al., 2015; Zhang et al.,
2022; Roy-Biswas and Sen, 2023), and hence the simulated ow con-
ditions replicate the real eld scenario.
In regards to the spur dike design, generally, the dimensions of the
spur dike (more specically, the length of the dike and dike head shape)
have been found to be highly correlated with the scour, as reviewed by
Nandhini et al. (2024). Kuhnle et al. (1999, 2002, 2008), Kuhnle and
Alonso (2013) and Han et al. (2022) utilized the trapezoidal spur dike of
similar dimensions. Mainly, Kuhnle et al. (1999) varied the spur dike
length between 0.35m and 0.5m and highlighted that 0.35 m length
performs better in terms of volume of scour in a 1.2 m tank. With the
larger length of the spur dike, the side wall effect could play a pre-
dominant role, as was also indicated by Kuhnle et al. (1999). Hence, we
chose a spur dike of length 0.3 m for a 1 m wide ume. Further, the
height of the spur dike is carefully selected so that it simulates a wider
range of overtopping conditions (0.48 ≤h
d
/h ≤1). Besides, the ow
parameters and the spur dikes are non-dimensionalized, and hence, the
results can be easily transferred to any location provided the spur dike
height, the ow depth and Fr are known, the ow characteristics in the
vicinity of the spur dike can be easily calculated using the equations
proposed. The Fr ranges have been chosen based on the recent study by
Zhang et al. (2022). Overall, the present study is a parametric study
covering a wider range of submergence and ow conditions and, hence,
can be applied to any eld within the range of tested conditions.
In the experimental analysis, we have chosen a time-averaged
analysis to derive the ow characteristics since the variation in bore
characteristics in the quasi-steady ow phase over the selected analysis
frame (from t =3s to t =6s) is closely linear despite some local oscil-
lations. This linear behaviour minimizes the need for other analysis (for
example, ensemble averaging or median analysis for general bore height
analysis, which Chanson (2020) suggested). Harish et al. (2021)
compared three analytical approaches—time-averaged, median, and
ensemble analysis—using the same experimental facility and reported
only minor negligible discrepancies between the methods in the
quasi-steady ow phase. The present study did not capture the intricate
dynamics of the splash-up during the initial impact of the tidal bore. For
such highly transient conditions, alternative analysis techniques like
ensemble analysis are required, which demands many repetitions of the
same experimental run as Chanson (2020) depicted.
The study successfully captured the dynamics of tidal bore in-
teractions within a controlled experimental range of Froude numbers
(0.4 ≤Fr ≤1.05). The present study was carried out under very high Re
(1.2 ×10
5
≤Re ≤3.6 ×10
5
), which is sufciently high to minimize the
effect of viscosity for both aerated and non-aerated ow regime (i.e.,
both at the bore tip and quasi-steady phase of tidal bore) (Heller, 2011;
Pster and Chanson, 2012). Heller (2011) and Le M´
ehaut´
e and Le
M´
ehaut´
e (1976) recommended a minimum wave height of 2 cm to
minimize the scaling effect due to surface tension. In our study, as listed
in Table 2, the studied ow depths are signicantly higher. Hence, it can
be safely concluded that the present study can be considered devoid of
scale effects. Nevertheless, the aeration inuence on turbulence and the
corresponding energy dissipation, especially at the downstream of spur
dike, can induce a certain level of inaccuracy when scaled, demanding
future studies using large-scale facilities.
Fig. 12. Relationship between Froude number calculated with (Fr Spur dike)
and without (Fr) spur dike; Fr
us
, Fr
dh
and Fr
ds
represent the Froude number at
spur dike upstream, head and downstream regions, respectively.
Table 3
Empirical equations to estimate the local ow characteristics during tidal bore
interaction with a spur dike. The presented equations are valid for 0.48 ≤hd/h
≤1 and 0.4 ≤Fr ≤1.05
Flow depth Flow velocity
Upstream hus
h=1+0.44 (Fr)2.22hd
h1.45 uus
u=1−0.68 (Fr)0.785hd
h1.03
R
2
=0.97;
σ
=0.016 R
2
=0.76;
σ
=0.060
At head hdh
h=1.12 (Fr)0.18hd
h0.1udh
u=0.93 (Fr)−0.22hd
h−0.035
R
2
=0.72;
σ
=0.033 R
2
=0.44;
σ
=0.067
Downstream hds
h=0.56 (Fr)−0.51hd
h−0.45 uds
u=1.15 (Fr)0.48hd
h−0.21
R
2
=0.87;
σ
=0.053 R
2
=0.58;
σ
=0.098
**
σ
– standard deviation.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
13
5. Conclusions and future outlook
The present experimental study aimed to investigate the hydrody-
namics in the vicinity of the trapezoidal shaped round-headed spur dike
during the tidal bore-like unsteady ow events. During the interaction
with the spur dike, the tidal bore splashed and overowed, creating a
signicant water level difference (in the quasi-steady phase) observed
between the upstream and downstream of the spur dike, thereby varying
the ow characteristics in the spur dike vicinity. Specically, the effect
of the tidal bore Froude number (Fr) and the relative dike height (h
d
/h)
on the bore characteristics around the spur dike are addressed during the
quasi-steady ow phase.
The main conclusions of the paper are as follows:
1) Increasing h
d
/h and Fr increased the backwater rise upstream of the
dike (h
us
) (reduced the ow velocity, u
us
) and decreased the water
level (h
ds
) (increased the ow velocity, u
ds
) downstream. At the
highest Fr tested case (i.e., Fr =1.05, the corresponding h
d
/h =0.7)
and h
d
/h tested case (i.e., h
d
/h =1, the corresponding Fr =0.8), h
us
was nearly 30% higher than the free ow bore depth (h). Therefore,
higher river bank heights are required to prevent the tidal bore from
overowing the banks due to backwater rise.
2) A distinct pattern in the ow characteristic variation with h
d
/h and
Fr is difcult to comprehend at the head section due to the fact that
the accumulated ow at the upstream and the overtopped ow
dene the ow features. The bore depth and ow velocity at the head
did not signicantly change compared to the free-ow conditions for
the tested ow conditions. The variation of bore depth and ow
velocity was in the range of −5% to +20% compared to the free-ow
conditions.
Fig. 13. Comparison of observed and predicted ow characteristics (based on Table 3) in the vicinity of the spur dike. a, b, and c are the water levels upstream, at the
head, and downstream, respectively. Similarly, d, e, f are the ow velocities upstream, at the head and downstream, respectively. The predicted results of Zhang et al.
(2022) are included for upstream water level (h
us
). CI denotes the condence interval.
Fig. 14. Energy head in the vicinity of the spur dike (E
spur dike
) compared
against the free ow energy head (E
free ow
). Fig. 15. Turbulence intensity (uʹ
rms
/|¯
u | %) at the vicinity of the spur dike. The
turbulent intensity is calculated following the approach of (Arnason, 2005).
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
14
3) The observations show that the ow tends to be sub-critical up-
stream, near critical at the head of the spur dike and super-critical
conditions downstream of the spur dike with the increase in free-
ow Fr. With the increase in the Fr (Fr between 0.8 and 1.05[-]),
the Froude number downstream of the spur dike (Fr
ds
) increased
rapidly from 1.0 to 1.8 [-] due to decrease in ow depth and increase
in ow velocity. The change in the ow characteristics at the
downstream can have a signicant effect on scour, as Zhang et al.
(2022) pointed out.
4) Empirical equations for calculating the local ow characteristics
(bore depth and velocity) during tidal bore interaction with a spur
dike are proposed. The presented equations are valid for 0.48 ≤h
d
/h
≤1 and 0.4 ≤Fr ≤1.05.
5) The energy reduction downstream of the dike was pronounced for Fr
>0.6 and h
d
/h >0.7, as conrmed by the high turbulence intensity
observed in the downstream region.
Overall, this study depicts the ow features and energy reduction
around the solitary spur dike during the tidal bore interaction. The
future outlook based on the present study is listed as follows:
➢ The presented equations are valid for 0.48 ≤h
d
/h ≤1 and 0.4 ≤Fr ≤
1.05. Extrapolation beyond these limits is not recommended without
further validation, as the empirical equations were derived under the
assumptions valid only within these specied conditions. For h
d
/h >
1 or Fr >1.05, additional experiments or numerical modelling would
be needed to verify their applicability.
➢ In this study, the downstream measurements were carried out at a
single location, and hence, the location of the hydraulic jump could
have partially inuenced the results. Future research could benet
from spatial measurement, especially at the downstream. Besides, a
detailed three-dimensional investigation of turbulent structures,
such as vortices, and their contribution to energy dissipation would
Fig. 16. Inuence of Froude number and spur dike height on the reduction of the energy head in the vicinity of the spur dike. a) upstream, b) at head, and c)
downstream of the spur dike. Left: 2D projection curve and Right: 3D colourmaps; Black dotted points are the experimentally calculated energy reduction, and the
colour map is arrived at by spline interpolation of the data points.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
15
be particularly valuable, especially in the downstream region of the
spur dike.
➢ This study primarily focused on the quasi-steady ow state of the
tidal bore, excluding the impacts of the bore front, such as short-
duration impulsive pressure effects. Future research could investi-
gate the interaction between the tidal bore front and various types of
spur dikes, considering that the bore front may be either undular or
broken. Further, the study didn’t simulate the full-time scale of the
tidal bore inundating the channel since our focus was primarily on
the hydrodynamic changes in the vicinity of the spur dikes. Espe-
cially for studies related to morphodynamics, we recommend the
full-time range simulation of tidal bore event in order to capture the
equilibrium scour depth precisely.
➢ The present study is conducted in a rectangular channel in which the
bank slopes and meandering channels are not considered. Such
studies could further improve the prediction equations we proposed
in this study. Besides, the tidal bore interaction with rubble mound
structures would be interesting since such high-energy bore impact
can dislodge the armour layers. Further, the hydrodynamic evolution
of tidal bore is expected to vary due to the growing climate change
and sea level rise (Wang et al., 2018), necessitating further studies
also on tidal-bore spur dike interaction and complex morphody-
namic changes.
CRediT authorship contribution statement
D. Nandhini: Writing – original draft, Visualization, Validation,
Software, Methodology, Investigation, Formal analysis, Data curation,
Conceptualization. Holger Schüttrumpf: Writing – review & editing,
Visualization, Supervision, Resources, Project administration, Funding
acquisition. S. Harish: Writing – review & editing, Visualization, Su-
pervision, Project administration, Conceptualization. K. Murali:
Writing – review & editing, Supervision, Project administration,
Conceptualization.
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgments
The authors would like to express their kind gratitude to the labo-
ratory technicians at IWW, RWTH Aachen University, for their support
in model construction, installation, and instrumentation. The rst
author extends sincere gratitude to Prof. S. A. Sannasiraj (Department of
Ocean Engineering, IIT Madras, India) for the recommendation to the
laboratory facility. The rst author is thankful to ABCD Future Envi-
ronmental Leaders Scholarship 2022 awarded by the DAAD-funded
“Global Water and Climate Adaptation Centre- Aachen, Bangkok,
Chennai, Dresden (ABCD-Centre),” Indo-German Centre for Sustain-
ability (IGCS), International Immersion Experience (IIE) travel award
and RWTH-IIT Madras Junior Research Fellowship (JRF) for the nan-
cial support to the research stay in RWTH Aachen University. The au-
thors would like to thank the two anonymous reviewers for their
valuable feedback to improve the quality of the manuscript.
Appendix A. Repeatability Check of Experimental Data
The repeatability of the measured bore depth at the spur dike upstream is veried since experiments were conducted with an unsteady bore
generated by a pumping-type bore generation mechanism. To ensure measurement repeatability, the bore depth comparison for d
0
=0.1m and Q =
0.33 m
3
/s at the spur dike upstream (for at least six trials) is presented in Fig. A.1. The comparison demonstrates that, in the quasi-steady state, the
bore depth measured at the spur dike upstream is highly reproducible with a negligible time delay. Because of the intricate air-water mix, the bore
depth during the initial bore front interaction with the structure cannot be replicated precisely.
Fig. A.1. Verifying the repeatability of the generated bore depth at the upstream of spur dike (h
us
) for d
0
=0.1m and Q =0.33 m
3
/s.
NOTATION
Cbore celerity
d
0
initial undisturbed still water level
d
0
/h
d
spur dike submergence
Eenergy of the freeow
E
us
energy at spur dike upstream
E
dh
energy at spur dike head
E
ds
energy at spur dike downstream
Fr Froude number in Quasi-steady state
Fr
b
tidal bore front Froude number
Fr
us
Froude number at spur dike upstream
Fr
dh
Froude number at spur dike head
(continued on next page)
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
16
(continued)
Fr
ds
Froude number at spur dike downstream
hbore depth
h
d
spur dike height
h
us
water level at spur dike upstream
h
dh
water level at spur dike head
h
ds
water level at spur dike downstream
h/d
0
dimensionless water level
h
d
/d
0
relative dike height
Qdischarge
Re Reynolds number
udepth averaged velocity
¯
umean velocity in the x-direction
u
ʹ
rms
root-mean-square average of velocity deviations
u
us
ow velocity at spur dike upstream
u
dh
ow velocity at spur dike head
u
ds
ow velocity at spur dike downstream
Data availability
Data will be made available on request.
References
Arnason, H., 2005. Interactions Between an Incident Bore and a Free-standing Coastal
Structure. University of Washington.
Azinfar, H., 2010. Flow Resistance and Associated Backwater Effect Due to Spur Dikes in
Open Channels. University of Saskatchewan. Doctoral dissertation.
Bartsch-Winkler, S., Lynch, D.K., 1988. Catalog of Worldwide Tidal Bore Occurrences
and Characteristics, vol. 1022. US Government Printing Ofce.
Bonneton, P., Bonneton, N., Parisot, J.P., Castelle, B., 2015. Tidal bore dynamics in
funnel-shaped estuaries. J. Geophys. Res.: Oceans 120 (2), 923–941.
Cai, Y., Cao, Z., Wang, Y., Guo, Z., Chen, R., 2018. Experimental and numerical study of
the tidal bore impact on a newly-developed sheet-pile groin in Qiantang river. Appl.
Ocean Res. 81, 106–115.
Castro-Orgaz, O., Chanson, H., 2017. Ritter’s dry-bed dam-break ows: positive and
negative wave dynamics. Environ. Fluid Mech. 17, 665–694.
Castro-Orgaz, O., Chanson, H., 2020. Undular and broken surges in dam-break ows: a
review of wave breaking strategies in a Boussinesq-type framework. Environ. Fluid
Mech. 20, 1383–1416.
Chanson, H., Aoki, S.I., Maruyama, M., 2002. Unsteady air bubble entrainment and
detrainment at a plunging breaker: dominant time scales and similarity of water
level variations. Coast. Eng. 46 (2), 139–157.
Chanson, H., Aoki, S.I., Maruyama, M., 2003. An experimental study of tsunami runup on
dry and wet horizontal coastlines. Sci. Tsunami Hazards 20 (5), 278–293.
Chanson, H., 2008. Photographic Observations of Tidal Bores (Mascarets) in France,
pp. 1–104.
Chanson, H., 2009. Current knowledge in hydraulic jumps and related phenomena. A
survey of experimental results. Eur. J. Mech. B Fluid 28 (2), 191–210.
Chanson, H., 2010a. Undular tidal bores: basic theory and free-surface characteristics.
J. Hydraul. Eng. 136 (11), 940–944.
Chanson, H., 2010b. Unsteady turbulence in tidal bores: effects of bed roughness.
J. Waterw. Port, Coast. Ocean Eng. 136 (5), 247–256.
Chanson, H., 2011a. Current knowledge in tidal bores and their environmental,
ecological and cultural impacts. Environ. Fluid Mech. 11, 77–98.
Chanson, H., 2011b. Undular tidal bores: effect of channel constriction and bridge piers.
Environ. Fluid Mech. 11, 385–404.
Chanson, H., 2012. Tidal Bores, Aegir, Eagre, Mascaret, Pororoca: Theory and
Observations. World Scientic. https://doi.org/10.1142/8035.
Chanson, H., 2020. Statistical analysis methods for transient ows–the dam-break case.
J. Hydraul. Res. 58 (6), 1001–1004.
Donnelly, C., Chanson, H., 2005. Environmental impact of undular tidal bores in tropical
rivers. Environ. Fluid Mech. 5, 481–494.
Duan, J.G., Nanda, S.K., 2006. Two-dimensional depth-averaged model simulation of
suspended sediment concentration distribution in a groyne eld. J. Hydrol. 327
(3–4), 426–437.
Duan, J.G., 2009. Mean ow and turbulence around a laboratory spur dike. J. Hydraul.
Eng. 135 (10), 803–811.
Fan, J., Tao, A.F., Shi, M.Q., Li, Y., Peng, J., 2023. Flume experiment investigation on
propagation characteristics of tidal bore in a curved channel. China Ocean Eng. 37
(1), 131–144.
Fricke, A.T., Nittrouer, C.A., Ogston, A.S., Nowacki, D.J., Asp, N.E., Souza Filho, P.W.,
2019. Morphology and dynamics of the intertidal oodplain along the Amazon tidal
river. Earth Surf. Process. Landforms 44 (1), 204–218.
Goseberg, N., Wurpts, A., Schlurmann, T., 2013. Laboratory-scale generation of tsunami
and long waves. Coast. Eng. 79, 57–74.
Han, X., Lin, P., Parker, G., 2022. Numerical modelling of local scour around a spur dike
with porous media method. J. Hydraul. Res. 60 (6), 970–995.
Harish, S., Sriram, V., Schuettrumpf, H., Sannasiraj, S.A., 2021. Tsunami-like ow
induced force on the structure: prediction formulae for the horizontal force in quasi-
steady ow phase. Coast. Eng. 168, 103938.
Harish, S., Sriram, V., Schüttrumpf, H., Sannasiraj, S.A., 2022a. Tsunami-like ow
induced forces on the structure: dependence of the hydrodynamic force coefcients
on Froude number and ow channel width in quasi-steady ow phase. Coast. Eng.
172, 104078.
Harish, S., Sriram, V., Schuettrumpf, H., Sannasiraj, S.A., 2022b. Flow-structure
interference effects with the surrounding structure in the choked quasi-steady
condition of tsunami: comparison with traditional obstruction approach. Appl.
Ocean Res. 126, 103255.
Heller, V., 2011. Scale effects in physical hydraulic engineering models. J. Hydraul. Res.
49 (3), 293–306.
Ho, J., Yeo, H.K., Coonrod, J., Ahn, W., 2007. Numerical modeling study for ow pattern
changes induced by single groyne. Proceedings of the Congress International
Association for Hydraulic Research, vol. 32. IAHR, p. 662.
Huang, J., Pan, C.H., Kuang, C.P., Zeng, J., Chen, G., 2013. Experimental hydrodynamic
study of the Qiantang River tidal bore. J. Hydrodyn. 25 (3), 481–490.
Huthoff, F., Pinter, N., Remo, J.W., 2013. Theoretical analysis of wing dike impact on
river ood stages. J. Hydraul. Eng. 139 (5), 550–556.
Iqbal, S., Tanaka, N., 2023. Experimental study on ow characteristics and energy
reduction around a hybrid dike. Int. J. Civ. Eng. 21 (7), 1045–1059.
Jiyu, C., Cangzi, L., Chongle, Z., Walker, H.J., 1990. Geomorphological development and
sedimentation in Qiantang estuary and hangzhou Bay. J. Coast Res. 559–572.
Kang, J., Yeo, H., 2011. Experimental study on the ow characteristics of type groyne.
Engineering 3, 1002.
Kang, J., Yeo, H., Kim, S., Ji, U., 2011. Permeability effects of single groin on ow
characteristics. J. Hydraul. Res. 49 (6), 728–735.
Khezri, N., Chanson, H., 2012. Undular and breaking bores on xed and movable gravel
beds. J. Hydraul. Res. 50 (4), 353–363.
Koch, C., Chanson, H., 2008. Turbulent mixing beneath an undular bore front. J. Coast
Res. 24 (4), 999–1007.
Koch, C., Chanson, H., 2009. Turbulence measurements in positive surges and bores.
J. Hydraul. Res. 47 (1), 29–40.
Kuhnle, R.A., Alonso, C.V., Shields, F.D., 1999. Geometry of scour holes associated with
90 spur dikes. J. Hydraul. Eng. 125 (9), 972–978.
Kuhnle, R.A., Alonso, C.V., Shields Jr, F.D., 2002. Local scour associated with angled spur
dikes. J. Hydraul. Eng. 128 (12), 1087–1093.
Kuhnle, R.A., Jia, Y., Alonso, C.V., 2008. Measured and simulated ow near a submerged
spur dike. J. Hydraul. Eng. 134 (7), 916–924.
Kuhnle, R., Alonso, C., 2013. Flow near a model spur dike with a xed scoured bed. Int.
J. Sediment Res. 28 (3), 349–357.
Le M´
ehaut´
e, B., Le M´
ehaut´
e, B., 1976. An introduction to water waves. An Introduction
to Hydrodynamics and Water Waves, pp. 197–211.
Li, Y., Chanson, H., 2018. Decelerating bores in channels and estuaries. Coast Eng. J. 60
(4), 449–465.
Li, Y., Pan, D., 2022. Tidal bore impact pressures on a trestle pier in the Qiantang River
Estuary, China. Adv. Mech. Eng. 14 (10), 16878132221131435.
Moghispour, S., Kouchakzadeh, S., 2024. Spur dike layouts impact on upstream ow
conditions during ood wave movement. J. Hydro-environ. Res. 53, 44–57.
Mouaze, D., Chanson, H., Simon, B., 2010. Field Measurements in the Tidal Bore of the
S´
elune River in the Bay of Mont Saint Michel, pp. 1–72. September 2010.
Mrokowska, M.M., Rowi´
nski, P.M., Kalinowska, M.B., 2015. Evaluation of friction
velocity in unsteady ow experiments. J. Hydraul. Res. 53 (5), 659–669.
Nakagawa, H., Nakamura, S., Ichihashi, K., 1969. Generation and development of a
hydraulic bore due to the breaking of a dam (1). Bull. Disaster Prev. Res. Inst. 19 (2),
1–17.
Nakagawa, H., Zhang, H., Baba, Y., Kawaike, K., Teraguchi, H., 2013. Hydraulic
characteristics of typical bank-protection works along the Brahmaputra/Jamuna R
iver, B Bangladesh. J. Flood Risk Manag. 6 (4), 345–359.
D. Nandhini et al.
Ocean Engineering 322 (2025) 120520
17
Nandhini, D., Murali, K., Harish, S., Schüttrumpf, H., Heins, K., Gries, T., 2024. A state-
of-the-art review of normal and extreme ow interaction with spur dikes and its
failure mechanism. Phys. Fluids 36 (5).
Oetjen, J., Engel, M., Pudasaini, S.P., Schuettrumpf, H., 2020. Signicance of boulder
shape, shoreline conguration and pre-transport setting for the transport of boulders
by tsunamis. Earth Surf. Process. Landforms 45 (9), 2118–2133.
Pan, D., Li, Y., 2022. Tidal bore scour around a spur dike. J. Mar. Sci. Eng. 10 (8), 1086.
Pan, C., Wang, Q., Pan, D., Hu, C., 2023. Characteristics of river discharge and its indirect
effect on the tidal bore in the Qiantang River, China. Int. J. Sediment Res. 38 (2),
253–264.
Pelinovsky, E.N., Shurgalina, E.G., Rodin, A.A., 2015. Criteria for the transition from a
breaking bore to an undular bore. Izvestiya Atmos. Ocean. Phys. 51, 530–533.
Pennington, C.H., Shields Jr, F.D., Sjostrom, J.W., Myers, K.A., 1988. Biological and
Physical Effects of Missouri River Spur Dike Notching (No. WES/MP/EL-88-11).
Army Engineer Waterways Experiment Station Environmental Lab, Vicksburg, MS.
Pster, M., Chanson, H., 2012. Scale effects in physical hydraulic engineering models by
VALENTIN HELLER. J. Hydraul. Res. 49 (3), 293–306. Journal of Hydraulic
Research, 50(2), 244-246.
Pinter, N., Heine, R.A., 2005. Hydrodynamic and morphodynamic response to river
engineering documented by xed-discharge analysis, Lower Missouri River, USA.
J. Hydrol. 302 (1–4), 70–91.
Qiushun, W., Cunhong, P., Fuyuan, C., 2024. Study on the tidal bore energy along the
Qiantang River estuary, China. Water Resour. 51 (1), 27–37.
Rajaratnam, N., Nwachukwu, B.A., 1983. Flow near groin-like structures. J. Hydraul.
Eng. 109 (3), 463–480.
Ramsden, J.D., 1996. Forces on a vertical wall due to long waves, bores, and dry-bed
surges. J. Waterw. Port Coast. Ocean Eng. 122 (3), 134–141.
Reungoat, D., Chanson, H., Keevil, C.E., 2015. Field measurements of unsteady
turbulence in a tidal bore: the Garonne River in October 2013. J. Hydraul. Res. 53
(3), 291–301.
Rousseaux, G., Mougenot, J.M., Chatellier, L., David, L., Calluaud, D., 2016. A novel
method to generate tidal-like bores in the laboratory. Eur. J. Mech. B Fluid 55,
31–38.
Roy-Biswas, T., Sen, D., 2023. Tidal bore dynamics of a mixed estuary: the hooghly river,
India. J. Waterw. Port, Coast. Ocean Eng. 149 (1), 05022005.
Shi, J., Tong, C., Yan, Y., Luo, X., 2014. Inuence of varying shape and depth on the
generation of tidal bores. Environ. Earth Sci. 72, 2489–2496.
Shi, R., Wüthrich, D., Chanson, H., 2023a. Air–water properties of unsteady breaking
bores part 1: novel Eulerian and Lagrangian velocity measurements using intrusive
and non-intrusive techniques. Int. J. Multiphas. Flow 159, 104338.
Shi, R., Wüthrich, D., Chanson, H., 2023b. Air–water properties of unsteady breaking
bore part 2: void fraction and bubble statistics. Int. J. Multiphas. Flow 159, 104337.
Sparks, R.E., 1995. Need for ecosystem management of large rivers and their oodplains.
Bioscience 45 (3), 168–182.
Teraguchi, H., Nakagawa, H., Kawaike, K., Yasuyuki, B.A.B.A., Zhang, H., 2011. Effects
of hydraulic structures on river morphological processes. Int. J. Sediment Res. 26
(3), 283–303.
Uijttewaal, W.S.J., Lehmann, D.V., Mazijk, A.V., 2001. Exchange processes between a
river and its groyne elds: model experiments. J. Hydraul. Eng. 127 (11), 928–936.
Uijttewaal, W.S., 2005. Effects of groyne layout on the ow in groyne elds: laboratory
experiments. J. Hydraul. Eng. 131 (9), 782–791.
United States Government Accountability Ofce (USGAO), 2011. Mississippi River :
Actions Are Needed to Help Resolve Environmental and Flooding Concerns about the
Use of River Training Structures. GAO-12-41, 59.
Wang, Q.S., Pan, C.H., Zhang, G.Z., 2018. Impact of and adaptation strategies for sea-
level rise on Yangtze River Delta. Adv. Clim. Change Res. 9 (2), 154–160.
Wang, J., Liu-Lastres, B., Ritchie, B.W., Pan, D.Z., 2019. Risk reduction and adventure
tourism safety: an extension of the risk perception attitude framework (RPAF).
Tourism Manag. 74, 247–257.
Wang, Q.S., Pan, C.H., Chen, F.Y., 2022a. Tidal bore dynamics around the similar right-
angle shoreline in the Qiantang Estuary, China. China Ocean Eng. 36 (5), 827–838.
Wang, M., Tian, Y., Li, X., 2022b. Experimental study on pressure distribution of spur
dike under the combined action of landslide surge and water ow. AIP Adv. 12 (7).
Wu, B., Wang, G., Ma, J., Zhang, R., 2005. Case study: river training and its effects on
uvial processes in the Lower Yellow River, China. J. Hydraul. Eng. 131 (2), 85–96.
Wüthrich, D., Pster, M., Nistor, I., Schleiss, A.J., 2018. Experimental study of tsunami-
like waves generated with a vertical release technique on dry and wet beds.
J. Waterw. Port, Coast. Ocean Eng. 144 (4), 04018006.
Wüthrich, D., Shi, R., Chanson, H., 2020. Physical study of the 3-dimensional
characteristics and free-surface properties of a breaking roller in bores and surges.
Exp. Therm. Fluid Sci. 112, 109980.
Wu, T., Sun, H., Aires, R.G., Cai, Y., Wu, J., Zhang, Y., 2022. Analytical solution for sheet-
pile groin vibrations under tidal bore excitation. Mar. Georesour. Geotechnol. 1–16.
Wu, T., Zhang, Y., Sun, H., Galindo, R., Wu, W., Cai, Y., 2023a. Dynamic response of
sheet‒pile groin under tidal bore considering pile‒pile mutual interaction and
hydrodynamic pressure. Soil Dynam. Earthq. Eng. 164, 107568.
Wu, T., Galindo, R., Sun, H., Cai, Y., 2023b. Dynamic responses of the sheet–pile groin
under tidal bore considering the soil–structure–water interaction. Ships Offshore
Struct. 1–17.
Xu, C.J., Yin, M., Pan, X.D., 2016. Field test and numerical simulation of tidal bore
pressures on sheet-pile groin in Qiantang River. Mar. Georesour. Geotechnol. 34 (4),
303–312.
Yeh, H.H., Ghazali, A., Marton, I., 1989. Experimental study of bore run-up. J. Fluid
Mech. 206, 563–578.
Yeo, H.K., Kang, J.G., Kim, S.J., 2005. An experimental study on tip velocity and
downstream recirculation zone of single groynes of permeability change. KSCE J.
Civ. Eng. 9 (1), 29–38.
Yossef, M.F., de Vriend, H.J., 2010. Sediment exchange between a river and its groyne
elds: mobile-bed experiment. J. Hydraul. Eng. 136 (9), 610–625.
Yossef, M.F., de Vriend, H.J., 2011. Flow details near river groynes: experimental
investigation. J. Hydraul. Eng. 137 (5), 504–516.
Zhang, H., Nakagawa, H., 2008. Scour Around Spur Dyke: Recent Advances and Future
Researches (Annuals of the Disaster Prevention Research Institute, vol. 51. Kyoto
University, pp. 633–652.
Zhang, Z., Pan, C., Zeng, J., Chen, F., Qin, H., He, K. Zhu, Zhao, E., 2022. Hydrodynamics
of tidal bore overow on the spur dike and its inuence on the local scour. Ocean
Eng. 266, 113140.
Zhang, Z., Du, S., Guo, Y., Yang, Y., Zeng, J., Sui, T., et al., 2023. Field study of local
scour around bridge foundations on silty seabed under irregular tidal ow. Coast.
Eng. 185, 104382.
Zhou, Y.J., Qian, S., Sun, N.N., 2014. Application of permeable spur dike in mountain
river training. Appl. Mech. Mater. 641, 236–240.
D. Nandhini et al.
