Experimental evaluation of two-layer air bubble curtains to prevent seawater intrusion into rivers

Experimental evaluation of two-layer air bubble curtains to prevent seawater intrusion
into rivers
Ehsan Kahrizia, Seyed Ali Akbar Salehi Neyshabouria,*, Amin Zeynolabedinb, Javad Souria and Hassan Akbaria
a
Department of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran
b
Department of Civil and Environmental Engineering, Tehran University, Tehran, Iran
*Corresponding author. E-mail: salehi@modares.ac.ir
ABSTRACT
The seawater intrusion (SWI) into rivers can lead to many negative consequences, especially on agricultural activities and live ecosystems in
upstream areas of rivers. One solution to prevent SWI is using air bubble curtains (ABCs). The objective of this study is to investigate the
optimal location of ABCs and airflows. To this end, several tests with different flow and salinity rates were performed and effect of ABC
location on SWI investigated. The results show that, when the ratio of seawater to freshwater densities increased from 1.006 to 1.010,
the ratio of saline wedge tip velocity to seawater velocity, airflow to seawater discharge ratio for first and second ABCs are raised 60, 58,
and 70%, respectively. Also, when the Froude number (Fr) . 0.031, seawater density changes do not significantly affect the process of
SWI. Besides, results of the study show that the closer the ABC is to the river downstream, the higher the airflow rates required. In addition,
the optimal value of air bubbles for controlling SWI depends on the density of seawater, where more airflow is required to control denser
flows. Finally, the regression equations to predict the SWI parameters based on flow properties were derived.
Key words: air bubble curtain, density currents, image processing method, river, salinity rate, seawater intrusion
HIGHLIGHTS
• Sustainable solution to solve seawater intrusion.
• Decreasing the negative effect of seawater intrusion on rivers.
• Feasibility to build in different sites.
• Does not have negative effect on the nature.
• It may protect freshwater resources.
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redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/licenses/by-nc-nd/4.0/).
© 2023 The Authors Journal of Water and Climate Change Vol 14 No 2, 543 doi: 10.2166/wcc.2023.384
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GRAPHICAL ABSTRACT
SYMBOLS AND ABBREVIATIONS
BC Bubble column
DO Dissolved oxygen
SCW Sharp-crested weir
SWI Seawater intrusion
ABC Air bubble curtain
Qa Air bubble discharge
Qs Seawater discharge
Qf Freshwater discharge
LOP Length of a river which polluted by seawater
IPM Image processing method
ρs Density of seawater
ρf Density of freshwater
Vfrontal Frontal velocity of saline wedge zone
Vs Velocity of the saline wedge at the beginning of intrusion
KH Kelvin–Helmholtz instability
H Hight of river’s water
I0 Intensity of struck light
I Intensity of light transmitted from material
ɛ Ability to absorb of the absorbing material
b Length of the path in which light is absorbed
C Concentration of the material
Reo Reynolds number of freshwater
Fr Froude number of freshwater
Frd Densimetric Froude number
Journal of Water and Climate Change Vol 14 No 2, 544

1. INTRODUCTION
Due to the population growth, the water resources are in danger of overuse and contamination (Karamouz et al. 2016). In
coastal areas, a significant portion of the water consumption is supplied by groundwater resources (Erostate et al. 2020).
Burgan et al. (2017) conducted a statistical study about extreme events in some rivers that indicated the frequency of extreme
events like drought increased from 1981 to 2000 which can cause destructive results. Chebana & Ouarda (2021) studied
hydrological events like floods and droughts in Iran. They developed a model that considers the non-stationary new risk
assessment framework. The final model constitutes a lognormal distribution for the margins with a linear trend in the
peak series, stationary for the volume series, and a quadratic trend in the logistic Gumbel copula parameter for the depen-
dence structure (Chebana & Ouarda 2021). Overexploitation of groundwater resources, sea-level rise (SLR) due to climate
changes, extreme conditions such as drought and floods lead to seawater intrusion (SWI) in coastal zones. SLR could directly
affect the serviceability of infrastructures of coastal regions; effects may include intrusion of seawater into drinking water
resources (Nazarnia et al. 2020). Soil may solute by infiltrating water, and its chemical contents affect the environment
(Ekeleme et al. 2021). Sharp differences between fresh and seawater densities result in the formation of density currents
and lead to intrusion of the tip of the seawater into the freshwater in rivers and estuaries (Zhang & Savenije 2019). SWI
could damage water bodies and the neighbouring regions along rivers. Currently, more than 100 counties and locals world-
wide are endangered by SWI (Barlow & Reichard 2010; Abd-Elhamid et al. 2016; Han & Currell 2018; Palacios et al. 2020;
Bhagat et al. 2021). This issue has received more attention than ever, fostering several developments. The increasing SLR and
salination of groundwater resources in coastal areas and rivers has made researchers study this phenomenon (van der Ven
et al. 2018; Zeynolabedin et al. 2021a, 2021b).
It is necessary to characterize the coastal aquifer and the SWI to evaluate and mitigate the environmental risks of this
phenomenon. Different approaches are applied by researchers in this regard. Zheng et al. (2021) studied the optimal location
of cut-off walls for SWI using the Kriging surrogate model simulation and optimization model. The results show that the out-
puts of the Kriging surrogate model and the variable density groundwater simulation model for the same cut-off wall design fit
well, and the average relative error of the two outputs is only 2.2% which proves that it is feasible to apply the Kriging surro-
gate model to this problem. Yusuf et al. (2022) provide a physical simulation to demonstrate the sand column performance of
a recharge reservoir to control seawater. The results revealed a reasonably close match between physical and computational
modelling. It was also found that the more sand columns and higher the reservoir water level resulted in decreased seawater
penetration length. In a numerical simulation, Panpan et al. (2021) studied the controlling of SWI by using hydraulic and
physical barriers. The results show that when the recharge well is located near the toe of the seawater wedge of 40 cm
from the coastline and 5 cm from the surface, the optimal performance of the recharge scheme is achieved with a repulsion
rate of up to 21.5%. When the physical barrier is located 10 cm from the coastline, and the penetration depth is 35 cm, the toe
of the seawater wedge is effectively driven to the coastline with a repulsion rate of up to 81.8%. Llopis-Albert & Pulido-
Velazquez (2015) used the numerical models to investigate SWI. They showed that the sharp interface approach can provide
accurate results in modelling SWI when applied to transient problems. Chun et al. (2018) assessed the impacts of climate
change and SLR on SWI in a coastal aquifer by using the Saturated-Unsaturated Transport (SUTRA) model. The results
showed that the largest increase in salinity occurred (40.3%) from the scenario of 57 cm in SLR. Abd-Elhamid et al.
(2019) evaluated the impact of reservoir dam on SWI in the Nile Delta Aquifer, Egypt using a numerical method. They con-
cluded that the maximum groundwater drawdown will reach 2.65 m and seawater will advance significantly by constructing
the new dam. Torres-Martinez et al. (2019) developed a geophysical model to assess SWI in a coastal aquifer in Mexico. This
model was based on a density-dependent flow model to simulate groundwater flow and SWI. The results indicated that due to
the high rate of pumping for agricultural use in the past decade, a large cone of depression had formed, leading to the SWI
advancement on the order of 6–8 km inland in the northern-central part of the aquifer. Zeynolabedin et al. (2021a, 2021b)
assessed the uncertainty of geoelectrical models in modelling SWI in the coastal aquifer of Chaouia, Morocco. The general
results indicated that the seawater has intruded about 2 km into the shore. The uncertainty analysis showed that there was a
sensible difference between the maximum and minimum extent of SWI (maximum 9% variation in the area of SWI) which
should be noted when doing water research management studies.
Besides modelling SWI and assessing the current status of coastal aquifers, researchers proposed different appropriate miti-
gation strategies in previous studies. One of the common alternatives to solving or reducing this negative effect is to decrease
the intrusion length of the saline wedge (Nakai & Arita 2002; Zeynolabedin & Ghiassi 2019). The initial solution to cutting

down the SWI length is creating a mound or a weir on the bottom of the channels, which also has side effects such as redu-
cing the flood run-off capability of the channels. A superior alternative for narrow rivers is using air bubble curtains (ABCs).
Not only is this solution easy to build but also it does not decrease the flood run-off capability (Nakai & Arita 2002). More-
over, it increases the dissolved oxygen (DO) by injecting bubbles into the water, which is notable in enhancing water quality
(Larsen et al. 2019). Most of the studies carried out on the application of ABCs have focused on the density current in lock
exchanges (Sasaki & Asaeda 1993; Asaeda et al. 1997; Oldeman et al. 2020). Nakai & Arita (2002) investigated steady saline
wedge behaviour with the addition of ABC to find out more about the flow mechanism around an air curtain. Based on the
findings, ABCs can significantly prevent SWI in different scenarios. Recently, Talebi & Salehi Neyshabouri (2021) studied the
effect of ABCs on SWI in a numerical assessment with various seawater density rates and with river water levels as the main
variable. The results showed that the ABC method is a good solution for SWI challenges. Bacot et al. (2022) established a
formal analogy between bubble curtains and air curtains and unified the two frameworks. By means of small-scale laboratory
experiments conducted in a channel with freshwater and brine solutions, they studied how effectively a bubble curtain acts as
a separation barrier for a wide range of density differences as well as different air fluxes and water depths. The results showed
high applicability of this approach. Talebi et al. (2022) investigated the effect of seawater density and air bubbles discharge on
the performance of the air bubbles curtain using a numerical model. The results showed that the ABCs can prevent salinity
intrusion by forming a vertical flow. Also, they concluded that there is an optimal discharge that discharges greater than it has
insignificant effects on ABCs performance.
Reviewing the literature revealed that most previous studies focused on a single linear ABC, while ignoring the optimal
location of ABC installation along a polluted river. This is important in terms of economic approaches because the length
of the intrusion in actual conditions sometimes exceeds tens of kilometres. The cost of providing airflow in ABC in different
locations vary since intrusion fluxes might decrease by moving in the upstream direction. Also, the minimum value of airflow
to prevent SWI in different scenarios is another question that directly affects the feasibility of such ideas in field projects. In
order to fill these gaps, this experimental study is focused on investigation of the optimal location of ABC regarding the
changes in the density of seawater, velocity, and depth of the river by using two different linear ABCs. Also, this study
attempts to investigate the optimal air bubble flow for controlling SWI.
2. MATERIALS AND METHODS
2.1. Experimental set-up and test cases
A 2D straight flume of 200 cm in length, 5 cm in width, and 50 cm in height was used in this experiment (Figure 1). The
freshwater flowed from upstream (right side) to downstream (left side), and the depth of the river was controlled by a
sharp-crested weir (SCW) installed at the end of the reservoir. Saline wedge intrusion was created in the flume by releasing
seawater from the outlet installed at the end of the downstream edge to the upstream side.
Figure 1 | Experimental set-up’s side view.

Two linear air curtains were separately installed perpendicularly to the stream-wise direction at the bottom of the flume to
create air. The distance from the first ABC (ABC-I) and the second ABC (ABC-II) to the downstream edge was 50 and 100 cm,
respectively. The curtains had five circular holes. The distance between the holes was 1 cm with each hole 1 mm in diameter.
An air compressor was used to create bubbles in the flume. A flowmeter measured the airflow rate (see Figure 1).
The experimental conditions are shown in Table 1. The variables of the study included freshwater discharge per unit width
(qf), river depth (H ), and seawater density (ρs). Some experimental assumptions made are as follows:
• The slope of the flume is zero.
• The cross-section is rectangular.
• There is no friction between the flume and water.
• The injected air pressure is 1 atm and the water temperature is around 25 °C.
The air bubble discharge per unit of width under standard atmospheric pressure (qa) was measured as the response par-
ameter. Reo, Frd, and Fr are the channel Reynolds number, channel densiometric Froude number, and channel Froude
Table 1 | Test cases
Test case Qf-LPM Qs-LPM H (cm) ρs (g/cm3
) Frd Fr Reo
T1 32 1.67 23 1.006 0.380 0.0309 10614
T2 32 1.67 23 1.008 0.333 0.0309 10614
T3 32 1.67 23 1.010 0.300 0.0309 10614
T4 32 1.67 24 1.006 0.356 0.0290 10614
T5 32 1.67 24 1.008 0.312 0.0290 10614
T6 32 1.67 24 1.010 0.281 0.0290 10614
T7 32 1.67 25 1.006 0.335 0.0272 10614
T8 32 1.67 25 1.008 0.294 0.0272 10614
T9 32 1.67 25 1.010 0.265 0.0272 10614
T10 34 1.67 23 1.006 0.404 0.0328 11277
T11 34 1.67 23 1.008 0.354 0.0328 11277
T12 34 1.67 23 1.010 0.319 0.0328 11277
T13 34 1.67 24 1.006 0.379 0.0308 11277
T14 34 1.67 24 1.008 0.332 0.0308 11277
T15 34 1.67 24 1.010 0.299 0.0308 11277
T16 34 1.67 25 1.006 0.356 0.0289 11277
T17 34 1.67 25 1.008 0.312 0.0289 11277
T18 34 1.67 25 1.010 0.281 0.0289 11277
T19 36 1.67 23 1.006 0.427 0.0347 11940
T20 36 1.67 23 1.008 0.374 0.0347 11940
T21 36 1.67 23 1.010 0.337 0.0347 11940
T22 36 1.67 24 1.006 0.401 0.0326 11940
T23 36 1.67 24 1.008 0.351 0.0326 11940
T24 36 1.67 24 1.010 0.316 0.0326 11940
T25 36 1.67 25 1.006 0.377 0.0307 11940
T26 36 1.67 25 1.008 0.330 0.0307 11940
T27 36 1.67 25 1.010 0.298 0.0307 11940

number, respectively, which are obtained as follows (Equations (1)–(3):
Reo ¼
qf
n
(1)
Frd ¼
qf
(g0H3)
1=2
, g0
¼
rs rf
rf

g (2)
Fr ¼
V
(gH)1=2
(3)
where g0
, V, g, and ν denote the buoyancy acceleration, freshwater velocity, gravitational acceleration, and the kinematic vis-
cosity, respectively.
Two-dimensional analyses were performed to investigate the flow characteristics (Equations (4) and (5):
Qa
Qs
:f
rs
rf
, Frd

(4)
Vfrontal
Vs
:f
rs
rf
, Fr

(5)
where Qa, Qs, Vs, and Vfrontal denote discharge of the air bubbles, discharge of the seawater, velocity of the seawater, and tip
velocity of the saline wedge, respectively.
2.2. Method
In the experiment, a steady salt wedge without any ABC was produced in the flume (Figure 2). Then, an ABC was produced
by releasing bubbles from the linear ABC. ABC-I and ABC-II were placed in different locations. Once the salt wedge was
steadily formed, ABC-I was opened, gradually increasing the air flow rate as all the seawater mass returned downstream
by the effect of the bubble curtain (Figure 2(b)). Next, the optimal amount of the air discharge required to control the seawater
was obtained for ABC-I. Also, the flow characteristics around ABC-I was observed and photographed. Then, the air flow of
ABC-I was closed, after which the salt wedge gradually formed again. Subsequently, ABC-II was gradually opened and all the
previous steps were repeated to find the optimal air flow discharge of ABC-II (Figure 2(c)). With this procedure, the effect of
ABC location on SWI was considered. Figure 3 presents the flowchart of the research methodology.
The image processing method (IPM) was used to trace the flow concentration and distribution of SWI. IPM provides an un-
intrusive technique for generating high-resolution concentration data in experimental studies. Quantifying the mixing level in
SWI by IPM requires establishing a link between pixel intensity and dye concentration which is provided by Beer–Lambert
Law (BLL). BLL was used to determine concentration profiles in flows through porous media by Ghisalberti Nepf (2005).
Also, potassium permanganate was used as a tracer to investigate the salt concentration of seawater wedges in a flume
(Figure 4).
Based on this law, when light reaches material that absorbs light, the relationship between the intensity of the impact light
(I0) and the intensity of the light transmitted from material (I) is as follows (Equation (6)) (Ghisalberti Nepf 2005):
Log
I0
I

¼ 1bc (6)
where ɛ is the ability to absorb light from materials, b represents the length of the path in which the light is absorbed, and C
denotes the concentration of the material.
3. RESULTS
3.1. Velocity of frontal wedge
The effects of Frd, ρs/ρf, and Fr on Vfrontal/Vs ratio are shown in Figure 5. Based on Figure 5(a), Frd number increases by
almost 65%, as the Vfrontal/Vs ratio is reduced by about 66%. Also, the line trend will be constant when the Frd number
increases. The R2
of the model for the Frd equation is 0.89, indicating that the model is significant. Figure 5(b) demonstrates

that the Vfrontal/Vs ratio in all cases increases by about 60.6% (average) by a growth in the ρs/ρf ratio. Also, the effect of ρs/ρf
ratio on the lower range of the Fr number slope of the variation increases shows an active role in the frontal velocity com-
pared with the upper range. In addition, there is an inverse relationship between the Fr number and the Vfrontal/Vs ratio, i.e.,
the Vfrontal/Vs ratio is the highest when the Fr number value is the lowest. The trend of the cases is linear, in the higher range
of the Fr number and vice versa. For example, when the Fr number is 0.035 (for cases in which ρs/ρf ratio is 1.006), the
Vfrontal/Vs ratio is 0.15, while for the cases in which Fr is 0.027, it is 0.34. This indicates about 67% growth for Vfrontal/Vs ratio
when the Fr is decreased by 0.008. For the cases in which ρs/ρf ratio is 1.010, the changes rate of this value (Vfrontal/Vs ratio) is
about 92%.
The regression equation for the forehead velocity ratio affected by the Froude number and ρs/ρf is as follows (Equation (7)):
Vfrontal
Vs
¼ 37:61917
rs
rf
24:99835Fr 36:82937, R2
¼ 0:89 (7)
3.2. First ABC equation
Figure 6 indicates the test result for the ﬁrst ABC, including the effects of Frd, Fr, and ρs/ρf on Qa/Qs. Figure 6(a) shows the
effect of the Frd number on the Qa/Qs ratio. The Qa/Qs ratio reduces by a rise in Frd. The results show that when the Frd
Figure 2 | (a) SWI progress, (b) the ﬁrst air bubble curtain (Gate I), (c) the second air bubble curtain (Gate II).

number increases by about 65%, the Qa/Qs ratio reduces, and this ratio reduces to 59%. When the Frd number is low, the Qa/
Qs ratio is high, and vice versa. Similarly, as reported above, the slope of the changes decreases when the Frd number grows.
Figure 6(b) demonstrates that the Fr number and ρs/ρf ratios affect the Qa/Qs ratio. When seawater density rises from 1.006 to
1.010, the Qa/Qs ratio increases by almost 58% (on average for all cases). Also, the ρs/ρf ratio grows sharply in the lower
ranges of the Fr cases. The graph trend is linear where Fr is higher, and it becomes semi-linear when the Fr is reduced.
Also, when the Fr number is 0.035, the Qa/Qs ratio is 0.1 (for cases in which ρs/ρf ratio is 1.006), while for the cases in
which Fr is 0.027, it is 0.24. This indicates about 40% growth for Qa/Qs ratio when the Fr is decreased by 0.008 units (for
cases in which ρs/ρf ratio is 1.006). Also, this value (Qa/Qs ratio) for the cases in which ρs/ρf ratio is 1.010, the change
rate is about 68%.
Figure 3 | Flowchart of the research methodology.

The regression equation for the first ABC, affected by the Fr number and ρs/ρf ratio, is presented in the following
(Equation (8)):
Qa
Qs
¼ 30:83333
rs
rf
17:07294Fr 30:32099, R2
¼ 0:85 (8)
3.3. Second ABC equation
Figure 7 indicates the test result for the second ABC, including the effects of Frd, Fr, and ρs/ρf on Qa/Qs. As expressed in the
previous section, the Frd number has an inverse relationship with the ratio (Qa/Qs), which is also true for ABC-II (according
to Figure 7(a)). The rate of the Qa/Qs is reduced by about 150% when the Frd number is increased by about 65%. The value of
the airflow, which is needed to prevent SWI, in the high range of the Frd number significantly, is low. Increasing the Fr
number inversely affects the Qa/Qs ratio. Contrary to ABC-I, there were multiple behaviours in ABC-II, which can be
observed in Figure 7(b). For the Fr numbers greater than 0.03, the ρs/ρf slope gets close to a constant rate, while for Fr num-
bers smaller than 0.03, the graph is semi-linear. Also, for the lowest Fr number case, Qa/Qs sharply increase. This ratio has
increased linearly by rising in the ρs/ρf ratio. Also, increasing the ρs/ρf raises the airflow needed to prevent SWI (Qa/Qs ratio).
When the ρs/ρf ratio is increased from the lowest to the highest range, the Qa/Qs ratio is raised by about 70% (average of all
cases). Also, when the Fr number is 0.035, the Qa/Qs ratio is 0.07 (for cases in which ρs/ρf ratio is 1.006), while for the cases in
which Fr is 0.027, it is 0.23. This value (Qa/Qs ratio) is 0.17 and 0.33 (for the cases in which ρs/ρf ratio is 1.010), respectively,
for the cases where Fr is 0.035 and 0.027.
The regression equation for the second ABC-II, which is affected by Fr number and ρs/ρf, is as follows (Equation (9)):
Qa
Qs
¼ 27:33333
rs
rf
15:91913Fr 26:85654, R2
¼ 0:92 (9)
As Figure 8(a) shows, there is shear stress between seawater and freshwater at the interface (boundary layer). The boundary
layer is formed, and Kelvin–Helmholtz (KH) is also observed in the boundary layer. As is visible, the mass of the seawater
above the green line is returned downstream by the force of the freshwater. At the top of the saline wedge’s green line,
Figure 4 | Plan view of the calibration used to determine the validity of Beer–Lambert Law in the experiments (17).

entrainment causes seawater and freshwater to mix. Mixing at the interface helps the density of seawater reduce when it
advances upstream. Figure 8(b) illustrates the distribution of seawater concentration along with the saline wedge shown
by IPM. It demonstrates that salinity distribution along the channel occurred both horizontally and vertically. As shown
in Figure 8(b), the seawater column in the ABC-II is shorter than the ABC-I, and the concentration of seawater in the
ABC-II region is lower than ABC-I (about a third of ABC-I).
The prediction chart of Vfrontal=Vs, Qa=Qs for the ABC-I, and Qa=Qs for the ABC-II are respectively shown in Figure 8. As
shown showed on these graphs, the regression equations are significant to predict the values. Based on Figure 9(b) and 9(c),
the prediction of the equation of the ABC-II is more accurate than the ABC-I. The R2
for ABC-II (Equation (9)) is also higher
than ABC-I (Equation (8)).
4. DISCUSSION
The present study explored optimum airflow and suitable location of ABC as a sustainable solution in narrow rivers. Different
parameters like seawater density, power of freshwater, power of seawater, and airflow rate directly affect SWI issues. So,
analysis of the presented results in the previous section is present in this section.
Figure 5 | (a) Ratio of frontal velocity to the Froude number graph; (b) Ratio of frontal velocity to the density ratio graph.

The optimum ABC airflow for preventing SWI in different ABC locations depends on the seawater density. As shown in
Figures 5(b) and 6(b), the seawater density directly affects the value of airflow for preventing SWI at both ABC-I and ABC-II.
As indicated, when the ρs/ρf ratio increased from 1.006 to 1.010, the Vfrontal/Vs ratio, Qa/Qs for the ABC-I, and Qa/Qs for the
ABC-II are raised 60, 58, and 70%, respectively. An increase in saline water density leads to more SWI, which was also
reported by Talebi Salehi Neyshabouri (2021). This may be related to an increase in the momentum and convection of
the saline water, as a result of which a higher volume of saline water is shaped around the ABC location, requiring more air-
flow to prevent SWI. Also, the inertia of the saline wedge rises with an increase in seawater density. All the above-mentioned
causes some environmental phenomena like KH and Entrainment could not mix the fresh and seawater in their interface (in
the higher range of seawater density), so more airflow is required to prevent SWI.
Besides the seawater density, the power of the seawater affects the SWI at the tip of the saline wedge. As reported in
Figure 5(b) in the ABC-I, the effect of seawater density in low Fr ranges plays a significant role. This is related to the lack
of freshwater power and the high power of seawater. So, both the density and power of the seawater have a direct interaction:
seawater power exponentially increases with a rise in seawater density. Contrary to ABC-I, the ABC-II scenario is reverse
behaviour. As shown in Figure 6(b), in the greatest Fr cases (Fr . 0.031), seawater density changes do not significantly
Figure 6 | (a) Ratio of Qa/Qs to the densimetric Froude number graph; (b) Ratio of Qa/Qs to the density ratio graph in the ABC-I.

affect the process of SWI. It means that a rise in the seawater density does not increase the power of the seawater. The reason
for this behaviour is KH in the tip of the saline wedge, which caused seawater to be mixed with freshwater. In other words,
the rate of the entrainment and KH are higher than in other regions of the saline wedge. So, an increase in seawater density in
the ABC-II does not considerably affect seawater power.
Another factor affecting the optimum ABC airflow value in preventing SWI is the power of freshwater. Mainly, the fresh-
water power depends on freshwater discharge, velocity, river level, and Fr number. As shown in Figures 5(b) and 6(b),
increasing the Fr number in both gates caused the rate of the airflow (Qa/Qs) to decrease. As mentioned, when the Fr
number changes from 0.035 to 0.027, the Vfrontal/Vs ratio increases 92%, 67% in cases where ρs/ρf is 1.010 and 1.006, respect-
ively. These values for the ABC-I raise about 40 and 68%, respectively. Raising the Fr number of the freshwater boosts the
freshwater advection; as a result, a higher shear stress rate is exchanged at the interface between the freshwater and seawater.
This helps the seawater mass at the boundary layer return downstream by the KH phenomenon and entrainment, which is in
line with the finding of Nakai and Arita (2002) and Talebi et al. (2022). Also, based on Figure 4(b), increasing in Fr number
leads to a decrease in the saline wedge’s frontal velocity. Increasing in Fr number accelerates the rate of the KH and entrain-
ment, so the velocity of the saline wedge tip reduces. All the mentioned scenarios indicate that an increase in the freshwater
Figure 7 | (a) Ratio of Qa/Qs to the densimetric Froude number graph; (b) Ratio of Qa/Qs to the density ratio graph in the ABC-II.

power leads to a decrease in the intrusion rate. So, these scenarios subsequently led to less SWI intrusion and less demand for
ABC airﬂow. This is in line with the study by Talebi Salehi Neyshabouri (2021).
The other important parameter, i.e., determining a suitable location for ABC, depends on some hydrodynamics processes
that change the seawater concentration. Based on Figure 7(b), concentration of the saline wedge is decreased when it intrudes
Figure 8 | (a) Boundary layer and KH instability; (b) Distribution graph of saline water concentration along with the saline wedge by IPM.
Please refer to the online version of this paper to see this ﬁgure in colour: https://dx.doi.org/10.2166/wcc.2023.384.
Figure 9 | (a) The predicted value to the actual value chart of Vfrontal=Vs; (b) The predicted value to the actual value of Qa=Qs for ABC-I; (c) The
predicted value to the actual value chart of Qa=Qs in the ABC-II.

upstream along a river. This means that the seawater movement would balance the seawater gradient due to the exchange
between seawater and freshwater. So, it can be clarified that if the ABC is installed in zones near the upstream, less airflow
is needed to prevent SWI, while the seawater would pollute more areas of the rivers, and vice versa. Figure 10 presents the
performance metrics for the ABC solution for preventing SWI in rivers. According to Figure 10, ABC-1 is a more sustainable
solution to prevent SWI because the lowest length of the river is polluted by the seawater, while the height of the seawater on
the location of the ABC-1 is higher; consequently cost of running ABC is high. In contrast, the running cost of the ABC in the
ABC-II is lower, while the seawater pollutes longer reaches of the river. Also, in the field project, finding a suitable location
for the ABC depends on the maximum salinity concentration allowed in a river regarding the consumption (drinking, agri-
culture, factory, etc.). So, a good location for installing ABC in any field project is different, and the mentioned factors must be
considered in the design of an ABC project to be cost-effective.
In summary, the optimum location of the ABC and optimum value of the airflow to control the SWI is affected by some
parameters like seawater density, power of the freshwater, and power of the seawater, which are studied in this section.
5. SUMMARY AND CONCLUSION
Many countries worldwide have been endangered because of SLR and climate change in recent years. SWI, as a result of SLR
and climate change, can damage freshwater resources along rivers. Developing a sustainable solution to alleviate this concern
has attracted a lot of attention. In the same line, the present study explored optimum airflow and suitable location of ABC as a
sustainable solution in narrow rivers.
In conclusion, the present study investigated the effect of ABC location and airflow demand on SWI. To this end, several
experimental tests were performed by assuming different values for the river and airflow discharges as well as for the salinity.
Figure 10 | Performance metrics of air bubble curtain.

In addition, two ABCs were located near and far from the downstream. The results showed that the optimal value of the air
bubbles required to control SWI depends mostly on the density of seawater, with more airflow required to control denser
flows. In other words, when the ρs/ρf ratio increased from 1.006 to 1.010, the Vfrontal/Vs ratio, Qa/Qs for the ABC-I, and
Qa/Qs for the ABC-II are raised by 60, 58, and 70%, respectively. Also, when the Fr . 0.031, seawater density changes do
not significantly affect the process of SWI.
Another important parameter is the freshwater discharge and its corresponding Froude number. In the experiments, Fr num-
bers were chosen based on a low velocity of freshwater under estuaries and laboratory limitations. Results indicate that when
the Fr number changes from 0.035 to 0.027, the Vfrontal/Vs ratio increases by 92 and 67% in cases where ρs/ρf is 1.010 and 1.006,
respectively. These values for the ABC-I raise about 40 and 68%, respectively. The results show that as the Froude number of
freshwater increases, the SWI value and the airflow required to control it decrease. In addition, the ABC closer to the river
downstream requires higher airflow rates to completely control the SWI and decrease the pollution extension.
Eventually, the regression equations for predicting the SWI parameters were derived based on the flow properties. Clearly, the
equations have been derived based on some general assumptions and laboratory limitations, for example, flume geometry, Froude
number, etc., yet they can be utilized efficiently for the initial design and for predicting the required range of the airflow and approxi-
mate location of the ABCs to control unwanted SWI properly. It goes without saying that the exact design of the optimal point in a
real case and its corresponding airflow parameters depend on local conditions such as river geometry, water quality, financial costs for
ABC construction, environmental issues, etc. This system may only be applicable to narrow rivers in some specific ranges.
Finally, this study has some limitations. All the tests studied the SWI in a limited density range of the sweater. At the same
time, the seawater concentration in an actual condition is sometimes four times greater than the studied density. For this
study, NaCl is considered for seawater synthesis, while natural seawater may have different properties in the field. Also, exper-
iments were conducted in a specific range of the Fr number of freshwater. In addition, some physical assumption considered
in this investigation includes: (1) the slope of the flume is zero, (2) the cross-section is rectangular, (3) there is no friction
between the flume and water, (4) the injected air pressure is 1 atm, and (5) the water temperature is around 25 °C. Future
studies are recommended to investigate other unknown parameters, including the effects of vegetation as a natural barrier
against SWI prevention. Besides, investigation on the cross variation of airflow and its effect on SWI patterns can be inter-
esting due to the unbalanced seawater and river velocity profile distribution.
ACKNOWLEDGEMENT
This study was supported by the Tarbiat Modares University, Tehran, Iran.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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