synthesis - numerical modelling of the strait of gibraltar.pdf
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SYNTHESIS REPORT
Master Thesis - Civil Engineering
Prof. Schleiss Anton, thesis supervisorMr. J. Franca Mario, thesis coordinator
Mr. Gustav R. Grob, external advisorMr. Zeimetz Fraenz, tutorMr. Smaoui Hassan, tutor
* Corresponding author.Tel.: +41 78 9121076
E-mail address: [email protected]
Numerical modelling of the Strait of Gibraltar for the purpose of a
project to stabilize the level of Mediterranean Sea from the globally
rising ocean levels
Ha-Phong Nguyena*
aLaboratory of Hydraulic Construction, EPFL, 1015 Lausanne, Switzerland
REPORT INFO
Article history:
Received 20 June 2014
Keywords:
Finite difference
Numerical model
Sea level increase
Strait of Gibraltar
Tidal barrage
Tidal simulation
ABSTRACT
In recent year, the threat of the rising ocean level due to global warming endangers coastal area. To solve
flooding problems in the Mediterranean shores, a dam project within the Strait of Gibraltar, called
MEDSHILD, is proposed in order to lower the sea level of the whole region. The objective of this study is
to simulate the water exchange through the Strait by considering the tidal forcing and to determine an
optimal closure that allows keeping the Mediterranean level constant by considering a climate change
scenario of 50 centimetres. A two dimensional general circulation model called MECCA (Model for
Estuarine and Coastal Circulation Assessment) is used. It is a sigma coordinates, time varying free
surface, primitive equation ocean model and uses the implicit finite difference techniques to solve the
hydrodynamic equations. The model works under the hydrostatic and Boussinesq approximations. The
domain incorporates actual bathymetry in very high resolution. Uniform horizontal and vertical grid
spacing of 500 metres is used. The model is forced along the open boundaries (Atlantic Ocean and
Alboran Sea) through the specification of the semidiurnal tidal heights. As first results, computed M 2and
S2amplitudes and phases are in good agreement with data in literature. Model results indicate, also, that a
closed area equal to 90% is sufficient to maintain the Mediterranean constant, coupled with a non-
negligible increase of the Atlantic level. The potential total annual tidal energy that can be extracted from
the barrage is assessed to range between 680 and 1364 GWh.
2014 EPFL. All rights reserved.
1.Introduction
Since decade, the Strait of Gibraltar is an area of great strategic
importance, given its geographical position between Africa and Europe.
Its position at a crossroad between the Atlantic and the Mediterranean
constitue a major corridor for maritime traffic. Over the years, many
projects, like the dam of German architect Srgel or the railway tunnel of
Lombardi Engineering Ltd, were developed in order to make the Western
Mediterranean area a key exchange passage between Africa and Europe.
Nowadays, bridging the gap between the two continents is still relevant,
but for others reasons than economic. Indeed, many surveys (Nicholls and
Hoozemans 1996; Gonella et al. 1998; Brochier and Ramieri 2001;
Nicholls 2002; Snoussi, Ouchani, and Niazi 2008; Vargas Ynez 2010;
Cronin 2012; Jevrejeva, Moore, and Grinsted 2012; Horton et al. 2014)
highlighted the threat of the constantly sea level rise on the coastal area of
the Mediterranean, Black and Red seas. Risk of flooding, erosion, salinity
intrusion, safety of foundations, to name but a few of the most serious
cases currently threatening the coastal population, deltas and islands.
More recently, according to the fifth assessment report on climate change
of the Intergovernmental Panel on Climate Change (Church, J.A. et al.
2013), scientists expect an increase of seal level of 26 cm to 98 cm by
2100 against 18 cm to 59 cm in the Fourth Assessment Report (Meehl,
G.A et al. 2007). As a result, the coastal populations and areas will be
subject to more frequent risk of flooding and erosion, two phenomena
aggravated by the massive urbanization of seashores.
It is in this context that the International Sustainable Energy Organisation
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!! !
!!
!!
!!"!
K is the turbulence energy; l the mixing length defined in Equation (16);
!!the Prandtl number; !! ! !!!!"#the coefficient of friction.
2.4.
Model Grid and Bathymetry
Area covered by the model contains the Strait of Gibraltar, and is limited
by the two sub-basins on both sides of the Straits; namely the Gulf of
Cadiz and the Alboran Sea. The model domain extends longitudinally
from 6.241 to 4.567 West and 35 to 36.666 North. Horizontal grid is
made by 306 x 330 grid points. It is characterized by a uniform spacing
and a high spatial resolution of 500 metres in both directions in order to
well resolve the dynamic within the Strait of Gibraltar Sannino (2004).
The model topography was generated by linear interpolation of the depth
data on to each grid point of the model grid. The depth data were obtained
from the EMODnet Bathymetry portal (available at http://www.emodnet-
bathymetry.eu). Model bathymetry is illustrated in Figure (1) with the
main topographic features (from left to right): Spartel sill, Tangier basin,
Camarinal sill, Tarifa narrow.
2.5.Boundary and initial conditions
As shown in Figure 1 the domain is composed of two open boundaries
located at the Eastern and Western end of the computation domain. At
these boundaries, values of surface elevation (!) or mean velocity (!! !)
should be specified. A lot of setting for open boundary conditions exists,
however, in this study, boundaries conditions used are the same as used
by Sannino, Bargagli, and Artale (2002) and Sannino (2004). Indeed, they
are proven to give the best model results for an application in the Strait of
Gibraltar. A description of these boundaries is set forth hereafter. For boundary conditions on either side of the computational domain, they
need to ensure that phenomena (e.g. waves) generated inside the domain
can freely leave it without being reflected at the boundaries and
accordingly contaminate the interior solution (Schot 1992; Blumberg and
Kantha 1985). For the purpose of minimizing the effects due to wave
reflection at the open boundaries, a force Orlansky radiation condition
(Orlanski 1976) is used for the sea surface elevation (!). According to
Bills and Noye (1987), this can be state as follow:
!!
!!!
!!
!!"
!!!
!! !!" !
!"!
!!
!!!
!! !"!
!!!
!
!! !"!
!!"!
Where!!
! is the surface elevation at the i grid point for the open
boundaries at time step n; !" ! !!! !!! the Courant number in x-
direction; !!"
!!!the tidal elevation at grid point i and time step n-1;!!" the
time independent mean sea elevation at grid point i (Bills and Noye 1987;
Sannino 2004).
As explained by Sannino (2004), Equation (20) incorporates a radiation
mechanism that allows the undesired transients to pass through the open
boundaries, going out of the model basin, without contaminating the
desired forced solution . In Equation (20), the sea elevation at the grid
points (!!
! ) situated on the open boundaries should be specified. To
achieve this, values from literature (Candela, Winant, and Ruiz 1990;
Padman and Erofeeva 2005) has been used. Moreover, as suggested bySannino (2004), sea elevation values must be augmented by the time
independent mean sea elevation, !!" , equal to 12 metre at the Western
open boundary and to 0 meter at the Eastern open boundary. These values
were obtained from the model of Sannino (2004) in the following manner:
The time independent mean elevation (!!") value used at the open
boundaries is obtained running the model in barotropic mode. This model,
as the baroclinic version (three dimensional), has at the eastern and
western ends of the computational domain two open boundaries where
values of barotropic velocity and surface elevation must be specified. For
the surface elevation an Orlansky radiation condition (Orlanski 1976) was
used at the western boundary while a clamped to zero condition was used
for the eastern end. For the barotropic velocity a zero gradient condition
was used at both ends. In this way the barotropic model was able to freelyadjust the western surface elevation, after 180 days of simulation, to about
12 cm .
Concerning the velocity, a zero gradient condition is used for the depth
integrated velocity (!!!).
As the most energetic system in the Strait of Gibraltar is the tidal
dynamics, the model is forced at the open boundaries with the tidal
forcing. The main tidal harmonics are shown in Table 1.
Table 1 The main tidal harmonic
Symbol Period [hour] Description
Semidiurnal components
M2 12.42 Main lunar constituent
S2 12.00 Main solar constituent
Diurnal componentsK1 23.93 Soli-lunar constituent
O1 25.82 Main lunar constituent
The semidiurnal tides arise from thegravitational forces of the moon (M2)
and sun (S2) while the diurnal components originates from the declination
in the moons orbit about the earth (O1) and the corresponding solar
declination (K1). In order to study the dynamic of the Strait of Gibraltar to
tidal forcing, the model is forced with the main semidiurnal (M2and S2)
components. M2wave has a period higher than 0.5 day because every day
the moon offset slightly (1/28th turn) whereas the period of S2 is worth
exactly 0.5 day. Consequently, the two waves will angle slightly towards
each another. Note also that the amplitude of M2 is larger than S2 (M2 %
Figure 1 Model bathymetry. The colour levels indicate the water depth in
meter.
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2.7 S2). Consequently, M2 imposes the period with a small perturbation
from S2. The choice to limit the simulation to the semidiurnal component
is justify because 90% of the total kinetic energy in the Strait of Gibraltar
stem from the semidiurnal components M2 and Ss (Kinder and Bryden
1987; Kinder and Bryden 1988; Candela, Winant, and Ruiz 1990).
Finally, the resulting two major semidiurnal surface tidal elevations
forcing at the open boundaries of the domain is defined as:
! !!! ! !! ! !"# !
!! ! !
! ! !!"!
!
!!!
Where!! ! and !
! ! are the surface elevation amplitude and phase of
the nthharmonic of the tidal signal; !!its frequency. The semidiurnal tidal
elevation amplitude (!! ! ) and phase (!
! ! ) are obtained from the
TPXO 7.1 global model of ocean tides (Padman and Erofeeva 2005). At
the Western and Eastern boundaries, four and three points are specified in
MECCA respectively (Table 2). Linear interpolation from these points is
made for the entire boundaries with satisfactory results as the variation in
regional amplitude and phase are relatively small.
Table 2 Semidiurnal tidal elevation amplitude and phase enter at
the Western and Eastern end of the computational domain for the
interpolation in MECCA.
Latitud
e [N]
Longitude
[W]
M2 S2
Amplitude
[m]
Phase
[]
Amplitude
[m]
Phase
[]
36.6667 -6.2410 1.0092 54.61 0.3653 79.15
36.5000 -6.2410 1.0104 54.46 0.3658 78.32
35.5000 -6.2410 0.9705 56.29 0.3529 82.2
35.0000 -6.2410 0.9992 54.97 0.3609 80.83
36.1467 -4.5670 0.2075 53.82 0.0777 81.9
35.9067 -4.5670 0.2099 55.96 0.0788 83.65
35.2800 -4.5670 0.2084 59.15 0.0791 86.48
For example, the tidal signal forced at the middle of the Western
computational domain is shown in Figure 2. The combination of M2and
S2, known as beating, has a fortnightly modulation with a period of 14.79
days.
Time step is fixed to 10 seconds according to the CourantFriedrichs
Lewy (CFL) condition.
2.6.Model experiments
The model is initially run separately for the M2and S2constituent forcing
over 123 hours and 131 hours respectively in order to compare the results
(amplitude and phase) with observed data (Candela, Winant, and Ruiz
1990; Tsimplis, Proctor, and Flather 1995; Sannino 2004). Once
validated, the model simulation is integrated for a fortnight period by
considering the combination of the semidiurnal component.
Three closures (70%, 85% and 95%) from both side of the Strait and two
(50% and 70%) starting from the Moroccan side representing the dam are
considered. The dam site is chosen according to previous geological study
from Lombardi Engineering Ltd. The five alternatives differ above all in
terms of the dam closure and site. The dam is 500 metres wide (this
choice is based on the grid resolution of 500 metres in each direction)
with a maximum length of 27 kilometres (Figure (3)). Total area
computed according to the so-called Rectangle Method equals 4025865
square meters. The model is run again for these configurations.
In this study, based on these forecast, a climate scenario of 50 centimetres
is considered. It is implemented in the model by adding a height of 50
centimetres to the semidiurnal tidal elevation forcing applied at the
Western open boundary (Atlantic). The simulations were extended for this
climate scenario by considering the different closures defined previously.
Figure 2 Semidiurnal tidal elevation forcing applied at the middle of the
Western end.
27km
0.5 km
Figure 3 (top) Dam site with the main characteristics. (bottom) Cross section
(b) corresponding to the dam site showing the bottom topography.
Area = 4025865 m2
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3.Model validation
A harmonic analysis is made for the tidal elevations and currents in order
to compare the obtained results with measured data (Candela, Winant, and
Ruiz 1990; Tsimplis, Proctor, and Flather 1995; Sannino 2004).
3.1.Tidal elevation
Compilation from these data of the two semidiurnal components for the
observed amplitudes and phases are summarized in Table 3 and 4. Also,
the simulated amplitudes and phases of the semidiurnal tide computed by
the model are given in order to compare them with the observed values at
some relevant points (Figure 4) in the Strait of Gibraltar.
Table 3 Comparison between observed and computed amplitudes
(A) and phases (P) of M2 tidal elevation.
Table 4 Comparison between observed and computed amplitudes
(A) and phases (P) of S2 tidal elevation.
As it can be observed, a general good agreement between observed and
Figure 4 Chart of the computational domain showing the geographic
features referred to in the text. Blue points are the relevant points used forthe comparison between observed and predicted values (exception at
Tangier and Sebta). Shaded red line represents the dam site.
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computed values of amplitudes and phases for the semidiurnal component
is found. Indeed, the maximum difference do not exceed 8.6 centimetres
in amplitude and 8.24 in phase for M2constituent and 4.6 centimetres in
amplitude and 8.47 in phase for S2constituent. The maximum differences
(in relative units) are concentrated in coastal regions (e.g. Tarifa, SN, SS)
since the model grid is not coastal-fitted Sannino (2004).
Figures (5) and (6) show the computed amplitude and phase contours of
the simulated M2and S2tidal waves respectively. For the M2chart (Figure
5.2), it is in good qualitative and quantitative agreement with those
presented in literature (Candela, Winant, and Ruiz 1990; Tejedor et al.
1999; Tsimplis 2000). However, the cotidal lines (lines of constant phase)
of M2differ slightly at the Camarinal sill area causing a deviation toward
North. This deformation can be explained by the irregularities of the
topography in this area.
From Figure (5) two information can be highlighted: (i) the unchangeable
of the amplitude in the cross-Strait direction except the Eastern part of the
Tarifa narrow and (ii) a decline of more than two-fold in the M2amplitude
in the along-Strait direction. Concerning the M2phase, it is characterized
by a southwestward propagation. For the S2 tidal wave (Figure (6)), the
same features are observed. The amplitude and phase ratios differences
between M2 and S2 constituents remain constant throughout the Strait of
Gibraltar as predicted by Candela, Winant, and Ruiz (1990). The
amplitude and phase ratios range from 2.5 to 2.8 and from 23.8 to 27.5
respectively.
Figure 5 Amplitude (left), in meters, and Phase (right), in degrees, contours of the M 2tidal wave
Figure 6 Amplitude (left), in meters, and Phase (right), in degrees, contours of the S 2tidal wave.
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3.2.Tidal currents
In order to describe the motion of fluids within the Strait of Gibraltar, the
depth integrated velocity (!!!) is computed for the M2and S2constituent
as well as for the semidiurnal M2S2constituents. Appendix G (refer to the
report) shows the direction of the velocity field during an entire M 2period
(12.42 hours) simulation with the module in background for the high
water at Gibraltar harbour. As expected, the direction of the velocity
reverses periodically. The velocity is the highest in the area of Camarinal
sill section. Figure (7) shows a semidiurnal tidal cycle during spring tide
at Gibraltar (top) and Pt5 (bottom).
Tidal currents value during the spring tide ranges from 0.06 m s-1 at
Gibraltar to 1.85 m s-1at the cross section of Camarinal sill. For the neap
tide (Figure (8)), the currents range from 0.02 m s-1at Gibraltar to 1.02 m
s-1 at the cross section of Camarinal sill. These values are in quite good
agreement with Sannino (2004). The fact that the Camarinal sill exhibits
the highest current was an expected result. Consequently, at the Camarinal
sill, due to the interaction of the strong tidal flow with the complex
bathymetry, the currents are not always reverse which means that the
water column can flow in the same direction twice per day. This result
should be confirmed with a three dimensional model (Sannino 2004) in
order to highlight outflow and inflow currents at the Camarinal sill.
4.Results
4.1.Basic scenario
The sea elevation for the semidiurnal tidal cycle during spring tide for a
closure of 70% (Figure 9) compared to the normal case (without closure)at some relevant point is computed. Only results for spring tide are
presented as it is the regime with the higher surface elevation. The major
sea elevation change is at Pt5 with a decrease of 12.6 centimetres
compared to the normal case. The maximum increase in sea level is at Pt4,
with an increase of 9.4 centimetres. These points are located to the right
(Mediterranean) and left (Atlantic) side of the dam respectively. The
change in sea elevation at other location is: Tanger (+2.8 cm), Sebta (-0.6
cm), Gibraltar (-1cm), Tarifa (-2.9 cm), Pt1 (-0.3 cm), Pt2 (-1.5 cm), Pt3
(+1.5 cm).
Figure 7 Semidirunal (M2S2) tidal cycle during spring tide at Gibraltar(top) and Pt5 (bottom) (see location in Figure 4). Blue line indicates the
tidal height, green line the corresponding velocity in absolute value.
Figure 8 Semidirunal (M2S2) tidal cycle during neap tide at Gibraltar (top)
and Pt5 (bottom) (see location in Figure 4). Blue line indicates the tidal
height, green line the corresponding velocity in absolute value.
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For a closure of 85% (Figure (10)), the change in sea elevation at the
locations is: Tanger (+5.9 cm), Sebta (-1.3 cm), Gibraltar (-2.2cm), Tarifa
(-6.5 cm), Pt1 (-0.5 cm), Pt2 (-2.1 cm), Pt3 (+2.7 cm), Pt4 (+12.1 cm), Pt5
(-17.2 cm). The same trend is observed with an amplification of the
increase or decrease in sea level at each location.
For a closure of 95% (Figure (11)), the change in sea elevation at the
locations is: Tanger (+21.5 cm), Sebta (-4.2 cm), Gibraltar (-8.2cm),
Tarifa (-22.5 cm), Pt1 (-1.8 cm), Pt2 (+1.1 cm), Pt3 (+8.2 cm), Pt4 (+24.9
cm), Pt5 (-34.2 cm). It can be seen that the sea surface variation follow the
same trend than the two previous cases except for Pt2 who undergoes an
increase of sea level instead of a decrease as previously observed. This is
certainly caused by the high degree of obstruction or numerical noise in
the computation of surface elevation at this point.
For the closure of 95%, the phase shift is most pronounced with the higher
closure. Indeed, the signal is perturbed and distorted. This effect is more
pronounced at Tarifa (Figure 12), Pt3, 4 and 5. This can be explained by
plotting the stream function corresponding to this closure (Figure (13)).
The disturbance stems from the fact that eddies and recirculation zones
appear on both sides of the closure. As the latter points are in this area,
their signals are deformed. Indeed, water coming from the Atlantic (and
respectively the Mediterranean) through the closure will form an eddy just
behind it creating a stagnant region. The streamlines (tangent curve to the
velocity vector field) form an arc just after passing through the opening.
At this location, the water is stagnant with small tides. As Tarifa is veryclose, the signal at Tarifa is completely disturbed.
Total Area = 4025865 m2
Close Area = 1229670 m2
Open Area = 2796195 m2
9.5 km 9.5 km8 km
Figure 9 Cross section corresponding to the dam site showing the bottom
topography where shaded blue represents the area closes by the dam. In
this case, 30% area closed.
Total Area = 4025865 m2
Close Area = 2449500 m2
Open Area = 1576365 m2
4 km11.5 km 11.5 km
Figure 10 Cross section corresponding to the dam site showing the
ottom topography where shaded blue represents the area closes by the
dam. In this case, 60% area closed.
Figure 11 Cross section corresponding to the dam site showing the
ottom topography where shaded blue represents the area closes by thedam. In this case, 90% area closed.
Total Area = 4025865 m2
Close Area = 3608600 m2
Open Area = 417265 m2
12.5 km12.5 km
1 km
Figure 12 Semidirunal (M2S2) tidal cycle during spring tide at Tarifa. Blue
line indicates the sea elevation for the normal case, green line the sea
elevation for a closure of 95% of the Strait.
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Figure (14) shows surface elevation difference (maximum absolute sea
elevation for normal situation minus maximum absolute sea elevation for
closure situation) for the closure of 70%, 85% and 95% at different
locations for a semidiurnal (M2S2) tidal cycle during spring tide. The
closure is expressed in term of percentage closed area (closed area divided
by total area), which corresponds to 30%, 60% and 90% respectively
(markers in Figure (14)). Positive values indicate an increase in surface
elevation and negative value a decrease of sea level. As expected, a
correlation between the closed area and the increase or decrease of sea
level difference is established. When the surface elevation increases (at
Tanger, Pt3 and Pt4), the larger the closed area, the greater the increase.
Same pattern is observed when the surface elevation decreases (at
Gibraltar, Sebta, Tarifa, Pt1 and Pt5); the larger the closed area, thegreater the decrease. Sea elevation of points situated to the left of the dam
tend to increase while it decrease for the points located to the right side.
Moreover, the closer to the dam the points, the higher the increase (Pt4) or
decrease (Pt5).
In order to confirm these results, two others simulations with a closure
from the Moroccan side is made. Results are presented in the following.
Figure (15) shows the sea elevation for the semidiurnal tidal cycle during
spring tide for a closure of 95% compared to the normal case at some
relevant point. The change in sea elevation at the locations is: Tanger
(+6.8 cm), Sebta (-1.3 cm), Gibraltar (-2.2cm), Tarifa (-5.7 cm), Pt1 (-0.5
cm), Pt2 (+3.0 cm), Pt3 (+2.0 cm), Pt4 (+0.3 cm), Pt5 (-18.5 cm). These
results are in good agreement with the closure of 85% from both sides,
except at Pt4 where the difference in sea level does not change much
because of the opening on the Spanish side (contrary to the closure of
85% on both sides).
For a closure of 95% (Figure (16)), the change in sea elevation at the
locations is: Tanger (+30.2 cm), Sebta (-7.4 cm), Gibraltar (-12cm), Tarifa
(-34.5 cm), Pt1 (-2.8 cm), Pt2 (+14.1 cm), Pt3 (+15.5 cm), Pt4 (+10.3
cm), Pt5 (-50.5 cm). Same pattern are observed with the important
deformation of the tidal signal and can be explained as before by plotting
the streamlines (Figure (17)).
Figure 13 Stream function for the M2constituent for a closure of 95%.
Figure 14 Difference in sea elevation of the closures compared to the
normal case at different location for a semidiurnal tidal cycle (M 2S2)
during spring tide. Positive value means an increase sea level compared to
the normal case, negative value a decrease in seal level. X-axis shows the
closed area (30%, 60%, 90%) corresponding to the closure 70%, 85% and
95% respectively.
Total Area = 4025865 m2
Close Area = 2064500 m2
Open Area = 1961365 m2
13.5 km 13.5 km
Figure 15 Cross section corresponding to the dam site showing the bottom
topography where shaded blue represents the area closes by the dam. In
this case, 50% area closed on Moroccan side.
Figure 16 Cross section corresponding to the dam site showing the
ottom topography where shaded blue represents the area closes by the
dam. In this case, 95% area closed on Moroccan side.
Total Area = 4025865 m2
Close Area = 3818100 m2
Open Area = 207765 m2
8 km 19 km
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Finally, the trend of Figure (14) is confirmed by Figure (18). The higher
area closed, the higher the increase or decrease in surface elevation
compared to the normal case. The dam site (closure on both sides or on
Moroccan side) does not affect the trend for points located far from the
dam (Sebta, Gibraltar, Tarifa, Pt1, Pt3). This means that for a constant
closed area, the result is the same no matter where the dam is positioned
(same longitude but different latitude). Concerning points situated near
the dam (Pt4, Pt5), different behaviours are observed. For Pt4, when the
closure is only on the Moroccan side, there is almost no increase in sea
elevation which is logical since it is an open area. For Pt5, the fact to close
only the Moroccan side seems to accentuate the decrease of sea level
compared to the closure on both side. This suggests that the dam site has
an area of influence on the flow regardless of area closed. From these
results, it can be seen that a closure of the Strait of Gibraltar can reducethe sea level on the Mediterranean side. However, with counterpart an
increase of the surface elevation on the Atlantic side.
4.2.Climate scenario
Results of simulations by modifying the signal at the Western open
boundaries (+50 centimetres) and with different closures are presented.
The increase in sea level is taken into account by increasing the signal at
the Western end of the computational domain. Figure (19) shows how the
signal is modified. The rise is not exactly equal to 50 centimetres as linear
interpolation from four points is made for the Western boundary.
Figure 19 Semidiurnal (M2S2) tidal cycle during spring tide applied at the
middle of the Western computational domain.
The increase in sea level introduced at the Western boundary did not
spread everywhere throughout the domain in the similar manner. Thesignal decrease as moving away from the Western boundary. For example,
at Tanger, the climate scenario is still strong (+46 centimetres). But at
Gibraltar, as the signal passes through rugged bathymetry, friction and
other phenomena, it decreases in intensity (+8 centimetres).
The goal with the closure is to ensure that the sea level in the
Mediterranean stay constant, meaning that the difference between the sea
level in the normal case (without climate and closure) and the climate
scenario with closure must be as close as possible to zero for points
located in the Mediterranean side. If this difference is greater than zero,
this means that the closure is too much. On the contrary, if the difference
is below zero, this means that the closure is not enough to keep the level
constant (equal to the normal case). For example, Figure (20) shows thesurface elevation at Tarifa. If the difference (in term of maximum absolute
value) between the normal case (in blue in Figure (20)) and the climate
with closure is positive, this means that the corresponding closure (95%
and 70% Moroccan side in this case) is enough to ensure the sea level to
stay constant (in purple and black in Figure (20)). If the difference is
negative, the closure is not enough (70%, 85% and 50% Moroccan side in
this case).
Figure 17 Stream function for the M2constituent for a closure of 70% on
the Moroccan side.
Figure 18 Difference in sea elevation of the closures compared to the
normal case at different location for a semidiurnal tidal cycle (M 2S2)
during spring tide. Positive value means an increase sea level compared to
the normal case, negative value a decrease in seal level. X-axis shows the
closed area (30%, 60%, 90%, 50%, 95%) corresponding to the closure
70%, 85%, 95% on both side and 50%, 70% on the Moroccan side
respectively. Pt 2 is not presented for the closure 50% (50% area closed)and 70% (95% are closed) on Moroccan side.
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Figure 20 Semidirunal (M2S2) sea elevation during spring tide at Tarifa for
different configuration.
In Figure (21), the difference between the sea level in normal case and the
climate scenario with different closure is shown for point located in the
Mediterranean side. A closed area equal to 90% allows maintaining the
sea level constant at these locations and even reduces the surface elevation
compared to the actual situation.
Figure 21 Difference in sea elevation of the closures with climate change
compared to the normal case at Mediterranean points for a semidiurnal
tidal cycle (M2S2) during spring tide. Positive value means a decrease in
sea level compared to the normal case, negative value an increase in sea
level. X-axis shows the closed area (30%, 60%, 90%, 50%, 95%)
corresponding to the closure 70%, 85%, 95% on both side and 50%, 70%
on the Moroccan side respectively.
Taking a look at the other side of the dam is necessary. Figure (22) shows
the difference between the sea level in normal case and the climate
scenario with different closure is shown for point located in the Atlantic
side. As expected, the more the closure, the more the increase of surface
elevation at the Atlantic. This important counterpart cannot be neglected.
Indeed, Moroccan and Spanish coastal area would be flooded due to the
important increase of surface elevation.
Figure 22 Difference in sea elevation of the closures with climate change
compared to the normal case at Atlantic points for a semidiurnal tidal
cycle (M2S2) during spring tide. Positive value means a decrease in sea
level compared to the normal case, negative value an increase in sea level.
X-axis shows the closed area (30%, 60%, 90%, 50%, 95%) corresponding
to the closure 70%, 85%, 95% on both side and 50%, 70% on the
Moroccan side respectively.
4.3.Estimation of annual energy output
In order to estimate the annual energy that can be extracted from a dam
exploiting the tidal power through the Strait of Gibraltar, a method based
on the principle of tidal hydrodynamic is used (Xia et al. 2012). The
principle is to block the entry and exit tides to create a water level
differential. As suggested by Charlier and Finkl (2009), the most efficient
way to operate for tidal barrage is to generate power during ebb tide asshown in Figure (23).
Figure 23 Sketch of ebb generation mode. Image from Xia et al. (2012).
The principle described by Xia et al. (2012) is as follows: First, the basin
(upstream) is filled through the sluice of the barrage until it achieves the
high tide level. From there, the sluices are closed (filling C-D in Figure
(23)). The turbines and sluices stay closed until the sea level downstream
decreases sufficiently to create a water level differential (called starting
head) across the dam (holding D-A in Figure (23)). Therefore, the turbines
gate are spun to create electricity (generating A-B in Figure (23)) until the
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estimated annual tidal energy of 1364 GWh is found by using an
operating efficiency of 0.4.
5.Summary and Conclusions
The aim of this project has been the developing of a numerical model able
to reproduce the circulation through the Strait of Gibraltar by considering
the tidal forcing. Then, the paper is devoted to determine the size of the
closure needed to ensure a constant level of the Mediterranean to solve
flooding problems due to global warming.
The GCM used in this study is the two dimensional vertically integrated
tidal model MECCA initially developed by Hess (1986) to study costal,
estuarine and open ocean circulation. The version used has already been
successfully implemented for the Strait of Gibraltar by Smaoui andOuahsine (2006). Study domain extends longitudinally from 6.241 to
4.567 West and 35 to 36.666 North. The model grid has a uniform
horizontal and vertical spacing of 500 metres. A significant aspect of this
model is that it solves a prognostic equation for the turbulent kinetic
energy and uses a semi-empirical expression for the mixing length(Davies, Luyten, and Deleersnijder 1995). At the two open boundaries, the
model is forced with the semidiurnal M2 and S2 surface elevation. The
model is run for a complete fortnightly period and a harmonic analysis is
performed to compare results with observed data. Computed amplitudes
and phases for the two semidiurnal constituent are in good agreement with
observed values. Also, results show that the model is able to reproduce
some major features of the tidal flow in this region: a decline of more than
two-fold in the M2 amplitude in the along-Strait direction, a general
invariability of the amplitude in the cross-Strait direction, a
southwestward propagation of the phases, and a constant amplitude and
phase ratios differences between M2 and S2 constituents throughout the
Strait of Gibraltar. However, the two dimensional model has proved its
limitations concerning the simulation of tidal current and cannot substitutea global modelling of the water circulation in this area (a three
dimensional model is needed). Since the flow within the Strait is done at
least in two layers, it is evident that a two dimensional model is not able
to describe all the exchange and hydraulics circulation aspect due to the
complex physics present in one of the most complicated region of the
world.
Once the model validated, simulations are performed for three closures
(70%, 85%, 95% corresponding to 30%, 60%, 90% are closed
respectively) starting both sides of the Strait and two closures (50%, 70%
corresponding to 50%, 95% area closed respectively) starting from the
Moroccan side supposed to represent the dam. The location of the latter it
determined by previous geological reconnaissance. The dam is 500 metres
wide with a maximum length of 27 kilometres. As a first step, simulationsare made for the basic scenario, i.e. with the actual surface elevation
specified at the two open boundaries. Sea elevations at some relevant
points are compared in order to assess the impact of the closure on tidal
height. For the basic scenario, results show a clear correlation between the
percentage area closed and the increase or decrease of sea level compare
to the normal case (without dam): the larger the closed area, the greater
the increase for points situated to the left of the dam, the greater the
decrease for points situated to the right side. Also, for points located
sufficiently far away from either side of the barrage, the dam
configuration (closure on both side or on Moroccan side only) does not
affect the increase/decrease trend. Consequently, a closure of the Strait of
Gibraltar can reduce the sea level on the Mediterranean side. However,
with counterpart an increase of the surface elevation on the Atlantic side.
The second step consisted to add 50 centimetres to the semidiurnal tidal
elevation signal at the Western open boundary supposed to reproduce the
sea level increase due to global warming. As expected, due to the rugged
bathymetry and friction, the signal did not spread everywhere throughout
the domain in the similar manner. By considering the sea level increase of
50 centimetres, it was found that a closed area equal to 90% allows
maintaining the sea level constant at points located on the Mediterranean
side. However, with such closure, the sea level on the Atlantic side
dramatically increased.
In the final part of this paper, a first assessment of the annual energy
output from a barrage within the Strait of Gibraltar is done using a
theoretical estimation method (Xia et al. 2012). The result indicates that
the magnitude of the annual energy output from the barrage would range
between 680 and 1364 GWh depending on the power conversion
efficiency considered. These values are relative with regard to the surface
area being considered. Moreover, as these predictions are based on
simplifying assumptions, a more accurate estimation of the annual energy
output should be conducted with more detailed information on the dam,
sluices, turbines and tidal ranges.
The objective of this study is reached, since its principal aim is the
understanding of tidal flow in the Strait of Gibraltar for a dam project. In
the future, a three dimensional version of MECCA model should be
develop in order to be able to simulate others major features of the flow in
the Strait, especially to estimate water transports along the whole Strait
and to provide an estimation of the impact of the barrage on these
quantities. The simulations have brought to light an important issue
(increase surface elevation on the Atlantic part) of a closure in the Strait
of Gibraltar. But it also showed that a barrage with an adapted closing can
keep the Mediterranean Sea level constant. Two improvement of this
study can be done in the future: (i) extend the area covered by the model
to cover the whole Mediterranean Sea in order to avoid forcing the
Eastern boundary with surface elevation values. As the Mediterranean isan enclosed sea, it will be able to freely adjust to the forcing of the
Atlantic. From there, one can specify a constant sea level in the
Mediterranean and optimize the corresponding closure of the Strait; (ii)
the global mean sea level increase introduced in the model assumes a
sudden rise of 50 centimetres applied uniformly on the Atlantic. In reality,
this increase takes place in the long term and is highly nonuniformly
distributed over the ocean. A solution could be to make a simulation of
several years with a different sea level increase every year for each
location.
Acknowledgements
I would like to thank my external advisor, Hassan Smaoui (UTC-CETMEF), for his vital guidance during this project. He kindly provided
his numerical model for the purpose of my work. His deep knowledge in
oceanography modelling allowed insightful discussions and constructive
critique of my simulations. I would also like to thank the members of
FlowScience, Frieder Semler, Dr. Matthias Todte and John Wendelbo for
their warm welcome in Rottenburg and for their support. I am also
extremely grateful to Gustav R. Grob (ICEC) for his constant
encouragement and financial support for my trip to Germany.
This project was supervised by Prof. Dr. Anton Schleiss, Mario Franca
and Fraenz Zeimetz from the department of Hydraulic Constructions,
EPFL. I wish to thank them for their willingness to help and advise
throughout the duration of the project.
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Finally, a special thanks to my dear family and friends, for their patience
and for never being short of a few words of encouragement when they
were needed.
REFERENCES
Armi, L., Farmer, D. (1986). Maximal two-layer exchange through a
contraction with barotropic net flow. Journal of Fluid Mechanics 164: 27
51.
Armi, L. (1986). The hydraulics of two flowing layers with different
densities. Journal of Fluid Mechanics 163: 2758.
Armi, L., Farmer, D. (1988). The flow of Mediterranean water through the
Strait of Gibraltar. Prog. Oceanogr. 21: 1105.
Baschek, B., Send, U., Garcia Lafuente, J., Candela, J. (2001). Transport
estimates in the Strait of Gibraltar with a tidal inverse model. Journal of
Geophysical Research: Oceans 106(C12): 3103331044.
Berthet, C. (1996). Flow and three-dimensional coastal transport:
numerical applications. Ph.D. thesis, Universit de Joseph Fourier,
Grenoble, France (in French).
Bills, P., Noye, J. (1987). An investigation of open boundary conditions
for tidal models of shallow seas. In North-Holland Mathematics Studies.
John Noye, ed. Pp. 159194. Numerical Modelling: Applications to
Marine Systems. North-Holland.
Blackadar, A. K. (1962). The vertical distribution of wind and turbulent
exchange in a neutral atmosphere. Journal of Geophysical Research 67(8):
30953102.
Bleck, R. (2002). An oceanic general circulation model framed in hybrid
isopycnic-cartesian coordinates. Ocean Modelling 4(1): 5588.
Bleck, R., Rooth, C., Hu, D., Smith, L. T. (1992). Salinity-driven
thermocline transients in a wind- and thermohaline-forced isopycnic
coordinate model of the north Atlantic. Journal of Physical Oceanography22(12): 14861505.
Blumberg, A. F., Kantha, L. H. (1985). Open boundary condition for
circulation models. Journal of Hydraulic Engineering 111(2): 237255.
Blumberg, A. F., Mellor, G. L. (1987). A description of a three-
dimensional coastal ocean circulation model. In Coastal and Estuarine
Sciences. Norman S. Heaps, ed. Pp. 116. Washington, D. C.: American
Geophysical Union.
Bormans, M., Garrett, C. (1989). The effect of rotation on the surface
inflow through the Strait of Gibraltar. J. Phys. Oceanogr. 19: 15351542.
Bormans, M., Garrett, C. (1989). The effects of nonrectangular cross
section, friction, and barotropic fluctuations on the exchange through the
Strait of Gibraltar. Journal of Physical Oceanography 19(10): 15431557.
Brandt, P., Alpers, W., Backhaus, J. O. (1996). Study of the generation
and propagation of internal waves in the Strait of Gibraltar using a
numerical model and synthetic aperture radar images of the European
ERS 1 satellite. Journal of Geophysical Research: Oceans 101(C6):
1423714252.
Brandt, P., Rubino, A., Sein, D. V., Dmitry, V., Baschek, B., Izquierdo,
A., Backhaus, J. O. (2004). Sea level variations in the western
Mediterranean studied by a numerical tidal model of the Strait of
Gibraltar. Journal of Physical Oceanography 34(2): 433443.
Brasseur, P., Beckers, J. M., Brankart, J. M., Schoenauen, R. (1996).
Seasonal temperature and salinity fields in the Mediterranean Sea:
Climatological analyses of a historical data set. Deep-Sea Research:Oceanographic Research Papers 43: 159.
Brochier, F., Ramieri, E. (2001). Climate change impacts on the
Mediterranean coastal zones. Fondazione Eni Enrico Mattei.
Bruno, M., Mananes, R., Alonso, J., Izquierdo, A., Tejedor, L., Kagan, B.
(2000). Vertical structure of the semidiurnal tidal currents at Camarinal
sill, the Strait of Gibraltar. Oceanologica Acta - OCEANOL ACTA 23(1):
1524.
Bryden, H. L., Stommel, H. M. (1984). Limiting processes that determine
basic features of the circulation in the Mediterranean Sea. Oceanologica
Acta 7(3): 289296.
Bryden, H. L., Candela, J., Kinder, T. H. (1994). Exchange through the
Strait of Gibraltar. Progress in Oceanography 33(3): 201248.
Buchanan, J. Y. (1877). On the distribution of salt in the ocean, as
indicated by the specific gravity of its waters. Journal of the Royal
Geographical Society of London 47: 72.
Candela, J. (1991). The Gibraltar strait and its role in the dynamics of the
Mediterranean Sea. Dynamics of Atmospheres and Oceans: 267299.
Candela, J., Winant, C., Bryden, H. L. (1989). Meteorologically forced
subinertial flows through the Strait of Gibraltar. Journal of Geophysical
Research: Oceans 94(C9): 1266712679.
Candela, J., Winant, C., Ruiz, A. (1990). Tides in the Strait of Gibraltar.
Journal of Geophysical Research: Oceans 95(C5): 73137335.
Carter, D. B. (1956). The water balance of the Mediterranean and Black
Seas. Drexel Institute of Technology, Laboratory of Climatology.
Castro, M., Garc!a-Rodr!guez, J., Gonzlez-Vida, J., Macias, J., Pares, C.,
Vazquez Cendon, M. (2004). Numerical simulation of two-layer shallow
-
8/10/2019 Synthesis - Numerical modelling of the Strait of Gibraltar.pdf
16/18
16 SYNTHESISREPORT
water flows through channels with irregular geometry. Journal of
Computational Physics 195(1): 202235.
Charlier, R. H., Finkl, C. W. (2009). Ocean Energy: Tide and tidal power.
Springer.
Church, J.A., Clark, P. U., Cazenave, A., Gregory, J. M., Jevrejeva, S.,
Levermann, A., Merrifield, M. A., Milne, G. A., Nerem, R. S., Nunn, P.
D., Payne, A. J., Pfeffer, W. T., Stammer, D., Unnikrishnan, A. S. (2013).
Sea Level Change. In: Climate Change 2013: The Physical Science Basis.
Contribution of Working Group I to the Fifth Assessment Report of the
Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K.
Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex
and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge,
United Kingdom and New York, NY, USA.
Crpon, M. (1961). Influence de la pression atmosphrique sur le niveau
moyen de la Mditerrane Occidentale et sur le flux travers le Dtroit de
Gibraltar.
Cronin, T. M. (2012). Rapid sea-level rise. Quaternary Science Reviews
56: 1130.
Dalziel, S. B. (1990). Rotating two-layer sill flows. In The Physical
Oceanography of Sea Straits. L. J. Pratt, ed. Pp. 343371. NATO ASI
Series, 318. Springer Netherlands.
Davies, A. M., Luyten, P. J., Deleersnijder, E. (1995). Turbulence energy
models in shallow sea oceanography. In Coastal and Estuarine Studies.
Daniel R. Lynch and Alan M. Davies, eds. Pp. 97123. Washington, D.
C.: American Geophysical Union.
Farmer, D., Armi, L. (1986). Maximal two-layer exchange over a sill and
through the combination of a sill and contraction with barotropic flow.
Journal of Fluid Mechanics 164: 53 76.
Garc!a Lafuente, J., Vargas, J., Plaza, F., Sarhan, T., Candela, J.,
Bascheck, B. (2000). Tide at the eastern section of the Strait of Gibraltar.
Journal of Geophysical Research: Oceans 105(C6): 1419714213.
Garc!a Lafuente, J., Delgado, J. Criado, F. (2002). Low-frequencyvariability of the exchanged flows through the Strait of Gibraltar during
CANIGO. Deep Sea Research Part II: Topical Studies in
Oceanography(19): 40514067.
Garca, M. A., Gonzlez, M., Espino, M. I., Snchez-Arcilla Conejo, A.
(2011). Un modelo numrico en elementos finitos para la corriente
inducida por la marea. Aplicaciones al Estrecho de Gibraltar.
Garrett, C., Bormans, M., Thompson, K. (1990). Is the exchange through
the Strait of Gibraltar maximal or submaximal? In The Physical
Oceanography of Sea Straits. L. J. Pratt, ed. Pp. 271294. NATO ASI
Series, 318. Springer Netherlands.
Gonella, M., Teatini, P., Tomasi, L., Gambolati, G. (1998). Flood risk
analysis in the upper adriatic sea due to storm surge, tide, waves, and
natural and anthropic land subsidence. In CENAS. Giuseppe Gambolati,ed. Pp. 313324. Water Science and Technology Library, 28. Springer
Netherlands.
Helfrich, K. (1995). Time-dependent two-layer hydraulic exchange flows.
Journal of Physical Oceanography 25(3): 359373.
Herbaut, C., Crpon, M. (1996). A sensitivity study of the general
circulation of the western Mediterranean Sea. Part I: The response to
density forcing through the straits. Journal of Physical Oceanography -
Journal of Physical Oceanography 26(1): 6584.
Hess, K. W. (1986). Numerical model of circulation in Chesapeake Bay
and the Continental Shelf, vol.6. National oceanic and atmosphericadministration, national environmental satellite, data, and information
service, assessment and information services center.
Hess, K. W. (2000). MECCA2 program documentation. U.S. Dept. of
Commerce, National Oceanic and Atmospheric Administration, National
Ocean Service, Office of Coast Survey, Coast Survey Development
Laboratory.
Higdon, R. L. (2006). Numerical modelling of ocean circulation. Acta
Numerica 15: 385.
Hopkins, T. S. (1978). Physical processes in the Mediterranean basins.
Estuarine Transport Processes: 269310.
Hopkins, T. S. (1999). The thermohaline forcing of the Gibraltar
exchange. Journal of Marine Systems 20: 131.
Horton, B. P., Rahmstorf, S., Engelhart, S. E., Kemp, A. C. (2014). Expert
assessment of sea-level rise by AD 2100 and AD 2300. Quaternary
Science Reviews 84: 16.
Hs, K. J., Ryan, W. B. F., Cita, M. B. (1973). Late miocene desiccation
of the Mediterranean. Nature 242(5395): 240244.
Izquierdo, A., Tejedor, L., Sein, D. V., Backhaus, J. O., Brandt, P.,
Rubino, A., Kagan, B.A. (2001). Control variability and internal bore
evolution in the Strait of Gibraltar: A 2-D two-layer model study.
Estuarine, Coastal and Shelf Science 53(5): 637651.
Jevrejeva, S., Moore, J. C., Grinsted, A. (2012). Sea level projections to
AD2500 with a New generation of climate change scenarios. Global and
Planetary Change 8081: 1420.
-
8/10/2019 Synthesis - Numerical modelling of the Strait of Gibraltar.pdf
17/18
17
Kinder, T., Bryden, H. L. (1987). The 19851986 Gibraltar experiment:
data collection and preliminary results. Eos, Transactions American
Geophysical Union 68(40): 786794.
Kinder, T., Bryden, H. L. (1988). Gibraltar experiment: summary of the
field program and initial results of the Gibraltar experiment.
Lacombe, H., Richez, C. (1982). The regime of the Strait of Gibraltar.
Elsevier Oceanography Series: 1373.
Lamb, H. (1994). Hydrodynamics 6th Edition. Fluid dynamics and solid
mechanics. Cambridge University Press.
Loget, N., Van Den Driessche, J. (2006). On the origin of the Strait of
Gibraltar. Sedimentary Geology 188189. The messinian salinity crisis
revisited next messinian Colloquium: 341356.
Longo, A., Manzo, M., Pierini, S. (1992). A model for the generation of
nonlinear internal tides in the Strait of Gibraltar. Oceanologica Acta
15(3): 233243.
Maidment, D. (1993). Handbook of hydrology. First edition. New York:
McGraw-Hill Professional.
Meehl, G. A., Stocker, T. F., Collins, W. D., Friedlingstein, P., Gaye, A.
T., Gregory, J. M., Kitoh, A., Knutti, R., Murphy, J. M., Noda, A., Raper,
S. C. B., Watterson, I. G., Weaver, A. J., Zhao, Z. C. (2007). Global
Climate Projections. In: Climate Change 2007: The Physical Science
Basis. Contribution of Working Group I to the Fourth Assessment Reportof the Intergo ernmental Panel on Climate Change [Solomon, S., D. Qin,
M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L.
Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom
and New York, NY, USA.
Mela, P. (1998). Pomponius Melas description of the world. University
of Michigan Press.
Mellor, G., Yamada, T. (1982). Development of a turbulence closure
model for geophysical fluid problems. Reviews of Geophysics 20(4):
851875.
Morozov, E. G., Trulsen, K., Velarde, M., Vlasenko, V. (2002). Internal
tides in the Strait of Gibraltar. Journal of Physical Oceanography 32(11).
Munk, W., (1948). Notes on a theory of the thermocline. Sears
Foundation for Marine Research.
Nicholls, R. J., Hoozemans, F. M. J. (1996). The Mediterranean:
vulnerability to coastal implications of climate change. Ocean & Coastal
Management 31(23). Sustainable Development at the Regional Level:
The Mediterranean: 105132.
Nicholls, R. J. (2002). Analysis of global impacts of sea-level rise: A case
study of flooding. Physics and Chemistry of the Earth, Parts A/B/C
27(3234): 14551466.
Nielsen, J. N. (1912). Hydrography of the Mediterranean and adjacentwaters.
Orlanski, I. (1976). A Simple boundary condition for unbounded
hyperbolic flows. Journal of Computational Physics 21(3): 251269.
Padman, L., Erofeeva, S. (2005). Tide Model Driver (TMD) manual.
Earth & Space Research.
Parrilla, G., Neuer, S. (2002). Topical studies in oceanography: Canary
Islands Azores Gibraltar Observations (CANIGO). Deep-Sea Research
Part II - Topical Studies in Oceanography - DEEP-SEA RES PT II-TOP
ST OCE 49(17): 34093413.
Edward, P. L., Atiemo-Obeng, V., Kresta, S. (2004). Handbook of
industrial mixing: science and practice. John Wiley & Sons.
Reid, J. L. (1979). On the contribution of the Mediterranean Sea outflow
to the Norwegian-Greenland Sea. Deep-Sea Res. 26: 11991223.
Richez, C. (1994). Airborne synthetic aperture radar tracking of internal
waves in the Strait of Gibraltar. Progress in Oceanography 33(2): 93159.
Sannino, G., Bargagli, A., Artale, V. (2002). Numerical modeling of the
mean exchange through the Strait of Gibraltar. Journal of Geophysical
Research: Oceans 107(C8): 91.
Sannino, G., Bargagli, A., Artale, V. (2004). Numerical modeling of the
semidiurnal tidal exchange through the Strait of Gibraltar. Journal of
Geophysical Research C: Oceans 109: C05011 123 C05011 2323.
Sannino, G., Carillo, A., Artale, V. (2007). Three-layer view of transports
and hydraulics in the Strait of Gibraltar: A three-dimensional model study.
Journal of Geophysical Research: Oceans 112(C3): C03010.
Schot, S. H. (1992). Eighty years of Sommerfelds radiation condition.
Historia Mathematica 19(4): 385401.
Schott, G. (1915). Die Gewsser des Mittelmeeres: vorzugsweise nach
den Arbeiten des dnischen Forschungsdampfers Thor, 1908-1910. E.S.
Mittler.
Sharqawy, M. H., Lienhard, J., Zubair, S. M. (2010). Thermophysical
properties of seawater: A review of existing correlations and data.
Desalination and Water Treatment 16(1-3): 354380.
-
8/10/2019 Synthesis - Numerical modelling of the Strait of Gibraltar.pdf
18/18
18 SYNTHESISREPORT
Smagorinsky, J. (1963). General circulation experiments with primitive
equations, I, The basic experiment. Monthly Weather Review 91(3): 99
164.
Smaoui, H. (1996). Three-Dimensional numerical modeling ofhydrodynamics and sediment transport in the eastern part of the English
Channel and the southern part of the North Sea. Ph.D. Thesis, University
of Lille, France (in French).
Smaoui, H., Ouahsine, A. (2006). 2D numerical simulation of the tidal
flow in the Strait of Gibraltar. Report of the Convention CNRS/CNRST,
Contract SP105/06.
Smith, W. H. F., Sandwell, D. (1997). Global Sea Floor Topography from
Satellite Altimetry and Ship Depth Soundings. Science 277(5334): 1956
1962.
Snoussi, M., Ouchani, T., Niazi, S. (2008). Vulnerability assessment of
the impact of sea-level rise and flooding on the Moroccan coast: The case
of the Mediterranean eastern zone. Estuarine, Coastal and Shelf Science
77(2). Land Ocean Interactions in the Coastal Zone, LOICZ: Lessons
from Banda Aceh, Atlantis, and Canute: 206213.
Stommel, H., Farmer, H. (1953). Control of salinity in an estuary by a
transition. J. Mar. Res. 12: 1320.
Sverdrup, H. U., Johnson, M. W., Fleming, R. H. (1942). The Oceans:
their physics, chemistry, and general biology. Asia Publishing House.
Tejedor, L., Izquierdo, A., Kagan, B., Sein, D. (1999). Simulation of the
semidiurnal tides in the Strait of Gibraltar. Journal of Geophysical
Research: Oceans 104(C6): 1354113557.
Tester, J. W. (2005). Sustainable Energy: choosing among options. MIT
Press.
Tixeront, J. (1969). Le bilan hydrologique de La Mer Noire et de La Mer
Mditerrane. International Association of Scientific Hydrology. Bulletin
14(4): 6169.
Torsvik, T. (2013). Introduction to computational fluid dynamics and
ocean modelling. In Preventive Methods for Coastal Protection. Tarmo
Soomere and Ewald Quak, eds. Pp. 65100. Springer International
Publishing.
Tsimplis, M. (2000). Vertical structure of tidal currents over the
Camarinal sill at the Strait of Gibraltar. Journal of Geophysical Research:
Oceans 105(C8): 1970919728.
Tsimplis, M., Proctor, R., Flather, R. (1995). A two-dimensional tidal
model for the Mediterranean Sea. Journal of Geophysical Research:
Oceans 100(C8): 1622316239.
Tsimplis, M., Bryden, H. (2000). Estimation of the transports through the
Strait of Gibraltar. Deep Sea Research Part I: Oceanographic Research
Papers 47(12): 22192242.
Vargas, J. (2004). Fluctuaciones subinerciales y estado hidrulico del
intercambio a travs del estrecho de Gibraltar. Universidad de Sevilla.
Vargas, Y. M. (2010). Cambio climtico en el Mediterrneo espaol. Inst.
Espaol de Oceanografa.
Wang, D. P. (1989). Model of mean and tidal flows in the Strait of
Gibraltar. Deep Sea Research Part A. Oceanographic Research Papers
36(10): 15351548.
Wang, D. P. (1993). The Strait of Gibraltar model: internal tide, diurnalinequality and fortnightly modulation. Deep Sea Research Part I:
Oceanographic Research Papers 40(6): 11871203.
Xia, J., Falconer, R. A., Lin, B. (2010). Impact of different operating
modes for a Severn barrage on the tidal power and flood inundation in the
Severn estuary, UK. Applied Energy 87(7): 23742391.
Xia, J., Falconer, R. A., Lin, B., Tan, G. (2012). Estimation of annual
energy output from a tidal barrage using two different methods. Applied
Energy 93: 327336.