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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 01, January 2019, pp. 1840-1848, Article ID: IJMET_10_01_182
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=01
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
Scopus Indexed
M. Jeyar and E. Chaabelasri
LME, Faculty of sciences, First Mohamed University, Oujda, Morocco
In this work the impact of the tidal wave on pollutant residence time within Nador
lagoon has been computed using an Eulerian approach and a 2D hydrodynamical model.
The model is based on the finite volume method; it solves the shallow water equations on
spatial domain that represents the Nador lagoon. The residence time has been defined
through the remnant function of a passive tracer released inside the lagoon. The renewal
capacity of the Nador Lagoon has been investigated when forced by the astronomic tide.
The influence of tidal wave on residence time has been defined by the return flow, and
computed for two scenarios during winter and spring periods.
Keywords: Tidal wave, Residence time, Hydrodynamical model, Finite Volume method,
Nador Lagoon,
Cite this Article: M. Jeyar and E. Chaabelasri, Tidal Hydrodynamic Wave Impact on
Pollutant Residence Time within Nador Lagoon, International Journal of Mechanical
Engineering and Technology, 10(01), 2019, pp.1840–1848
Semi-enclosed basins such as lagoons, gulfs and lakes are commonly subjected to intensive
anthropogenic inputs that modify both the trophic state and the health of the whole ecosystem.
Most of contaminants and masses of nutrients release in these aquatic systems are carried in a
suspended or dissolved status by the fluid medium. The cleaning capacity of these environments
can be represented by two different types of processes: biogeochemical processes and physical
Advection and diffusion can be reasonably considered the main physical processes that
influence the cleaning capacity of a lagoon ecosystem water compartment. Through the advection
and diffusion mechanisms, the water mass is transported to the open sea where it is mixed with
the sea water. The time spent by each water particle inside the lagoon gives an idea of the
efficiency of this physical cleaning process. To describe this process, the concept of times scales
has been introduced and applied to real coastal waters. One of widely used timescales is the
residence time.
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M. Jeyar and E. Chaabelasri
Several parameters forcing water circulation in the lagoons, gulfs among them swell and tide.
If the tide is the main forcing for the water circulation, such as in the Nador Lagoon case, the
cleaning capacity of the basin is influenced by the characteristic of the tidal exchange. In this
situation, the flushing mechanism is produced through repeated exchange of the intertidal water
volume between the embayment and the receiving water body of the Mediterranean Sea.
In the literature, the residence time is subject of many recent investigations. In 2004, Cucco
et all [1] computed the water residence time of the Venice lagoon using a two dimensional
hydrodynamics model based on advection-diffusion equation. In 2009 Jain et all [2] are modeling
the residence time and exposure time in the Pearl River Estuary in China using a lagrangian
description of particle trajectory. And most recently, Rynne et all [3] analyzed numerically the
residence time within an idealized lagoon that is connected to the ocean via a tidal inlet and
demonstrated that process of tidal exchange is inversely proportional to the residence time.
In this study, we focus on tow objectives, the methodology to investigate the particle
residence time in coastal lagoon with the Eulerian based advection-diffusion approach modeling
[4]. And, the impact of the tidal wave on the residence time in some sub-domains Nador lagoon,
and the influence of the return flow on this basin have to be into account.
The Nador lagoon is among the largest lagoons in North Africa (115km2, 27km long and 7, 5km
wide). It is located in the southern shore of the Mediterranean Sea in a semiarid region (Figure
2). The lagoon complex is divided in three main domains as follows: (1) the continental border
with salt marshes and rivers with irregular torrential runoff, most of the time dry, (2) Nador
lagoon itself, the most extended lagoon in Morocco, (3) the island barrier broken off by one tidal
inlet, Bokhana, through which exchanges with the sea occur.
The external hydrodynamics of this coastal area depends on the tidal regime, the littoral drift
currents, and the prevailing waves. The tidal regime of this Mediterranean region is microtidal
and semidiurnal, increasing toward the eastern inlet [5]. The internal hydrodynamics of the Nador
lagoon is joined to three types of hydrological resources: the marine waters passing through the
artificial inlet, which are always dominant; the hydrogeological contributions margin of the
lagoon (See figure 1) and the surface water inputs with the periodic flows of ten small streams
flow most of these dry out completely in summer, causing freshwater discharges to be negligible
relative to tidal prisms. Among them, the Selouane stream is the most important, bringing the
urban/industrial wastes of the Selouane village into the lagoon during the wet season.
3.1. The hydrodynamic model
For shallow flow domains, such as the Nador Lagoon, where the flow is mainly horizontal the
vertical acceleration can be ignored and hydrostatic pressure is assumed. This implies that all
waves simulated are long waves, whose amplitude is much smaller than both the depth and the
wave length. Moreover, the domain is sufficiently small that the effect of Coriolis acceleration
owing to the Earth’s rotation can also be ignored. In such cases, an adequate mathematical
description of the flow hydrodynamics is provided by the two-dimensional (2D) shallow water
equations. This model can been written as:
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Tidal Hydrodynamic Wave Impact on Pollutant Residence Time within Nador Lagoon
∂h ∂(hu) ∂(hv)
∂y 2
∂(hu 2 +
2 + ∂(huv) = − gh ∂Zb − τ bx + τ wx
∂x ρ
∂(hv +
∂(hv) ∂(hvu)
2 = − gh ∂Zb − τ by + τ wy
∂y ρ
Where h the water depth, u and v are the depth-averaged velocities in the x and y directions,
respectively, g the gravity constant, ρ the water density, τ bx and τ by are the bed shear stress
friction forces in the x and y directions, respectively defined by the depth-averaged velocities:
τ bx = ρ Cb u u 2 + v 2 ; τby = ρCbv u2 + v2
is the bed friction coefficient: τwx = ρACdwx wx + wy ; τ wy = ρACd wy wx + wy
is the coefficient of wind and w = ( wx , w y ) is the velocity of wind.
3.2. The finite volume method
The numerical model used in this study is the Unstructured Finite Volume Shallow Water Model,
or UFV-SWM, is a 2D unstructured-grid coastal ocean model that simulates water surface
elevation, velocity, and transport diffusion of a tracer. The unstructured triangular cells and finite
volume approach employed in the model provides geometric flexibility and computational
efficiency that is well suited to simulating the effect of tidal turbines on a flow field at a fine scale
within in a large domain. The model uses unstructured meshes, incorporates upwinded numerical
fluxes and slope limiters to provide sharp resolution of steep bathymetric gradients that may form
in the approximate solution. The scheme is non-oscillatory and possesses conservation property
that conserves the pollutant mass during the transport process. UFV-SWM has been applied to
simulate many problems of hydraulic flows and coastal waters. For more detailed descriptions
the reader is referred to the works [6, 7, 8, 9].
3.2. The Eulerian-based advection diffusion approach
The Eulerian approach is suitable and convenient to estimate detailed spatial and temporal
distributions of particle concentrations and the particle residence time. This approach is easy to
use; however, it models the particulate phase as a continuum phase, and treats particulate matters
as passive pollutants. Most recent numerical works of the Eulerian approach use the advectiondiffusion equation with the gravitational settling to calculate particle concentrations [10-11] and
the particle residence time [12, 13, 14, and 15].
3.3. Residence time formulation
In this study the Eulerian water residence time, RT, has been defined as the time required for
each element of the lagoon area to replace most of the mass of a conservative tracer, originally
released, with new water. To compute it we refer to the mathematical expression given by
Takeoka [16, 17, 18, and 19] known as the remnant function.
The tracer, initially released inside the lagoon with a concentration of 100%, is subject to the
action of the tide forcing that drives it out through the one inlet. This leads to a decay of its
concentration. The remnant function r(t) of the concentration is given at each position of the
domain as r(t)=C(t)/C0where C(t) is the concentration at time t of the passive tracer S in the x, y
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M. Jeyar and E. Chaabelasri
position, and C0=C(t=0) is it initial value. The residence time τ can then be defined according to
Takeoka [16,17], For every position x, y of the domain:
τ (x, y) = ∫ ∞ r(x, y,t )dt
The decay of the concentration C is exponential i.e.
C (t ) = C0
−α t
Then, the residence time can be computed as τ = 1/ e that is the time it takes to lower the
concentration to 1/ e of its initial value. A complete description of the model may be found in [20].
To compute the water residence time in the Nador Lagoon, a passive tracer C was released
in the lagoon basin with an initial concentration corresponding to 100%. To simulate the behavior
of tracer concentration the model solves the diffusion and advection equation that, in the
vertically integrated from, is given as:
∂C + u ∂C + v ∂C = ∂ ( D ∂C ) + ∂ (D ∂C )
∂y ∂x x ∂x ∂y y ∂y
Where C is pollutant concentration, and Dx and D are pollutant diffusion coefficient in
the and direction.
3.3. Return flow
When the tide forces the circulation, the lagoon water mass is carried out of the embayment
during the ebb phase. Some fraction of the discharged water is lost by exchange and mixing
within the receiving water body, the remainder returns back to the lagoon basin on the subsequent
flood phase. The return flow has a significant effect on the increase of the residence time and it
depends on three important factors: the phase of the tidal flow in the connecting channel relative
to the flow along the coast, the amount of mixing that occurs once the water is outside the
embayment and the strength of the inlet flow relative to the strength of the coastal current [16].
3.4. Numerical setup
The numerical computation has been carried out on a spatial domain that represents the lagoon
of Nador through a finite volume grid which consists of 8075 triangular elements and 14042
nodes. The bathymetry of the lagoon, obtained combining several dataset, has been interpolated
onto the grid. The finite volume method allows for high flexibility with its subdivision of the
numerical domain in triangles varying in form and size. It is especially suited to reproduce the
geometry and the hydrodynamics of complex shallow water basins such as the Nador lagoon. The
principal hydraulic forcing of the Nador lagoon is the tide. The water depth is set so that it is
invariably positive, with mean value h0 and fluctuating-free surface elevation h f such that:
h( t) =h0 + hf
. Initially, the tracer is distributed uniformly throughout the lagoon; that is:
C0 (x,y) = C(x,y,t=0) = 1.
The lagoon hydrodynamic at inlet is mainly governed by tide which in the sea, is composed by
three main harmonic constituents semi-diurnal M 2 , N 2 a n d K 2 Figure 2, shows the variation of
observed sea surface level inside lagoon, caused by tide.
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Tidal Hydrodynamic Wave Impact on Pollutant Residence Time within Nador Lagoon
Figure 1: Sea surface elevation (SSE) of Nador lagoon observed during year of 2014.
According to figure 1 the spectrum varies between a maximum 0.38m and minimum -0.38m
values receptively.
The maximum correspond of the spring tide, the minimum correspond of the neap tide. In
order to better understand the impact of the tide on the residence time in the Nador lagoon, The
values of the harmonic constituents semi-diurnal tide are chosen to reach the maximum tide range
in winter and spring periods. The model was integrated for a period 30 days, which includes three
tidal periods as time to reach a stable hydrodynamic behaviors, with time step interval of 3
seconds. For the time integration, an explicit Euler method is used. The time step interval is
restricted to 3s in accord with the Courante-Friendriche-Levy (CFL) critical number (0.6) in all
computational cells. No flooding and drying fronts are taken in account in this study. The table 1
summarizes some parameters used in the simulation scenarios.
Table 3: Parameters of the hydrodynamic model.
Time step
Water Density
Max Triangle area
Min Triangle area
Max tide range (winter/springer)
Average period(winter/springer)
4.1. Impacts of the tide on residence time.
Figure 2, shows the nodes in which the residence time is calculated in the various simulations,
tide of spring and winter periods. We try to choose the nodes in such a way to sample the parts
of the lagoon. In this way it is possible to see the impact of tide on the residence time. Another
aspect that we considered in the choice of the nodes is that they need to have a depth such that
they do not emerge during the various tides.
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Figure 2: Nador lagoon area and residence time measured nodes of the two confined region.
To calculate the residence time in the case of no return flow, two different boundary
conditions are taken in inlet nodes. For water exiting in the lagoon, the tracer concentration is
treated as having a transmissive boundary
condition, and for water entering the lagoon, the concentration at the open boundary nodes is
set to zero, assuming that the incoming tide contains clean water.
The investigation of different tidal wave impart on residence time in two selected scenarios
are summarised in figure 3 and 4. These results shows a good correlation between the two
different residence time in spring and neap tide, during the tow seasons, the results are well
distributed along a straight lane inclined of 45 degrees with respect to the horizontal axis for
almost all the considered nodes, it is possible to note that the residence time in the axis with spring
tide is always a little bit higher that the other one.
Figure 3: Calculated residence time in north region nodes of the lagoon during winter and spring
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Tidal Hydrodynamic Wave Impact on Pollutant Residence Time within Nador Lagoon
Figure 4: Calculated residence time in south region nodes of the lagoon during winter and spring
4.2. Impacts of the return flow on residence time
In order to investigate the return flow notion in the Nador lagoon, residence time is calculated
over all meshing elements of the lagoon. To satisfy the physical condition of return tracer through
the inlet from sea to lagoon the tracer concentration is treated as having a transmissive boundary
condition in all inlet nodes ∂X / inletnodes = 0 ; for both cases entering and exiting water.
The temporal variation of remnant functions of return and no return flow is illustrated in
figure 5, it is shown that the remnant function of no return flow decreases monotonically, while
that of return flow decreases in an oscillatory manner due to the tidal fluctuation. The value of
remnant function of no return flow is always larger than that of return flow, since the fraction of
re-entering water has been taken into account.
Figure 5: Residence time values comparison between return and no return flows cases.
The spatial distribution of residence time in the cases of return and no return flow are plotted
in figure 6. The residence time distribution is heterogeneous and mainly gives high values. Range
between values less than 20 days has been observed for the whole lagoon, except the regions
confined in north depending its distance from the Boukhana inlet. The average value computed
for the whole basin can be divided in three ranges;
During the case of return flow, the residence time are still greater than 15 days, these parts cover
a small area of the lagoon, while most of the area the residence time no exceed 8 days, in the
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M. Jeyar and E. Chaabelasri
other hand for the no return flow the residence time range between value great than 17 and 11 in
the north and south respectively, and 5 days for most of the lagoon.
Figure 6: Residence times distribution in Nador lagoon in two cases: Return and non-Return flow.
The obtained results indicate that the return flow does influence the residence time in the
lagoon much more than in the case of no return flow, which is approved by the results comparison
of the figure 7. Except some nodes, most have a residence time much better in the case of no
return flow, this result can trigger a reflection on a tool that can stop the return pollution once
leave the lagoon.
Figure 7: Residence time values comparison between return and no return flows cases.
This paper has described application of a depth-integrated 2D shallow flow model to predict and
investigate the pollutant residence time due to two tidal forcing in the Nador Lagoon. A remnant
function method was employed to quantify the spatially varying transport mechanism of a
dissolved substance and hence compute the mean residence time of the Nador lagoon. The
residence times, as computed, do not provide an exact value that characterizes the water of a
pollutant specific location, but can be considered a valid time scale that characterizes the transport
processes in the lagoon basin, and also an estimate of the relative efficiency of the renewal
capacity of the basin.
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Tidal Hydrodynamic Wave Impact on Pollutant Residence Time within Nador Lagoon
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