Breugem, Alexander

Da Silva, Julien

Decrop, Boudewijn

Martens, Chantal

van Holland, Gijsbert

English

Ghent University Academic Bibliography

Modelling the Eddy Pattern in the harbour of Zeebrugge

The eddy patterns in the harbour of Zeebrugge are studied using TELEMAC-3D and compared to available measurement data. It was found that during flood a clockwise eddy exists, generated by a strong jet near the eastern side of the harbour entrance. This eddy generates a second counterclockwise eddy, which persists in the harbour during the ebb phase, whereas the primary eddy disappears. A sensitivity study was performed to investigate the influence of the turbulence model, the bed roughness and the advection scheme. It appeared that the modelled eddy patterns are quite sensitive to the settings that are used for all these three parameters

Breugem, W.A.

Decrop, B.

Da Silva, J.

van Holland, G.

Martens, C.

Open Marine Archive

TU C 2013, 16-18/10/2013, Karlsruhe - Kopmann, GoII (eds.) - © 2013 Bundesanstalt für Wasserbau ISBN 978-3-939230-07-6
Modelling the eddy pattern in the harbour of 
Zeebrugge
W.A. Breugem, B. Decrop, J. Da Silva, and G. Van 
Holland 
IMDC NV 
Berchem, Belgium 
abr@imdc.be
C. M artens 
afdeling Maritieme Toegang 
Departement Mobiliteit en Openbare werken van de 
Vlaamse overheid 
Antwerpen Belgium
Abstract—The eddy patterns in the harbour of Zeebrugge are 
studied using TELEMAC-3D and compared to available 
measurement data. It was found that during flood a clockwise 
eddy exists, generated by a strong jet near the eastern side of 
the harbour entrance. This eddy generates a second counter­
clockwise eddy, which persists in the harbour during the ebb 
phase, whereas the primary eddy disappears. A sensitivity 
study was performed to investigate the influence of the 
turbulence model, the bed roughness and the advection 
scheme. It appeared that the modelled eddy patterns are quite 
sensitive to the settings that are used for all these three 
parameters.
I. In t r o d u c t io n
The harbour of Zeebrugge is one of the most important 
Belgian seaports. The area surrounding Zeebrugge is 
characterised by strong tidal flows, with a tidal amplitude up 
to 5m during spring tide. In the harbour, complex eddy flow 
patterns are found, varying throughout the tidal cycle. 
Understanding these patterns is important for navigation 
purposes and for increasing our understanding of the siltation 
of the harbour, especially with respect to the redistribution of 
suspended sediment through the harbour.
In order to understand this process, the eddy pattern in 
the harbour is studied using TELEMAC-3D. The results of 
the TELEMAC model are compared with measurements, 
and a sensitivity test is performed with respect to the eddy 
formation by varying the bed roughness, the advection 
scheme and the horizontal turbulence model.
II. P h e n o m e n o l o g y  o f  t h e  e d d y  c u r r e n t s  in  t h e
HARBOUR OF ZEEBRUGGE
In order to study the phenomenology, an existing data set 
of ADCP (Acoustic Doppler Current Profiler) measurements 
was used [1], These measurements were taken on different 
locations in the harbour and the navigation channel on 
various days between November 2009 and March 2010. 
Because the data were taken on different occasions, we put 
together the data from various measurement days, sorting 
them with respect to the time after high water (from now on 
abbreviated as HW) and according to the spring-neap tidal 
cycle. In this paper, we will only study the data from spring 
tide conditions. In the analysis, we focus on what happens in
the period around the occurrence of high water, when the 
strongest eddies are formed.
The ADCP data show the following pattern (Fig. 1; note 
that additional arrows have been added to aid interpretation 
of the data):
• 2 h before HW : There is a net flux of water into the
harbour in the form of a jet at the eastern harbour 
dam. The jet increases in length and strength with 
time. This jet generates an eddy in clockwise 
direction, which we will call the primary eddy.
• 1 h before HW : A smaller secondary eddy with a
counter clockwise rotation is also generated by the 
jet.
• Around HW: From this moment, there is no net 
inflow of water in the harbour. Hence the eddy is 
decoupled from the flow at sea and it follows its own 
dynamics. It appears that the primary eddy starts 
decreasing in size and magnitude.
• 1 h after HW: Only the counter clockwise secondary
eddy remains present in the harbour. It moves slowly 
towards the harbour entrance and gradually becomes 
weaker.
3 775
3.765
3.76
2000 2500
37
XXth TELEMAC-MASCARET User Conference Karlsruhe. October 16-18. 2013
Spring tide; Time after HW: -01:00 h
Spring tide; Time after HW: 00:00 h
Spring tide; Time after HW: 01:00 h
Spring tide; Time after HW: 02:00 h
.775
.77
.765
.76
.755 —  
1500 2000 2500 3000 3500
Figure 1. Overview of the eddy development in the harbour o f Zeebrugge 
from ADCP measurements.
Comparable eddy patterns are found in the measurements 
during average tide, whereas the formation of this pattern is 
much less pronounced during neap tide.
One must take care when interpreting the measured data, 
because the presented data was collected during different 
measurement days. There is always some error associated 
with the matching procedure, because the tidal amplitude 
and period are not completely the same for the different 
measurement days. Nevertheless, the discussed pattern 
seems to be representative for the conditions occurring in the 
harbour, since earlier data [2] show similar results for the 
observed eddy patterns.
III. M o d e l  s e t u p
The model was set up in a circular domain centred 
around the harbour of Zeebrugge, starting from Dunkirque 
(France) in the West to Goeree-Overflakkee (the 
Netherlands) in the East (Fig. 2). The Eastern and Western 
Scheldt estuaries are included in the model, although the 
most upstream part of the Western Scheldt was schematized 
using straight prismatic channels. The resolution varied from 
30 m inside the harbour to 5000 m close to the open 
boundary (Fig. 3). Vertically, ten non-equidistant sigma 
layers were used to represent the water column.
Boundary conditions for velocity and water level were 
obtained from the Zuno [3] model, which has a resolution 
comparable to our model at the location of these boundaries. 
These boundary condition were applied as a time series (with 
a time interval of 10 min) at each location on the open 
boundary. Additional discharge boundary conditions were 
applied to schematise fresh water influxes into the model. 
Note that one of the sources of fresh water was located inside 
the harbour.
The model was ran in TELEMAC-3D for a period of 
15 days using a time step of 20 seconds using the 
Smagorinsky scheme for the horizontal eddy viscosity and a 
mixing length model using the mixing length 
parameterization of Nezu and Nakagawa [4] for the vertical 
eddy viscosity.
38
XXth TELEMAC-MASCARET User Conference Karlsruhe. October 16-18. 2013
BOTTOM
■ 7.5
o
-7 .5
-15
-22 5
-30
-37 .5
-45
-52.5■ -60
A comparison of measurement data and model results for 
the water level time series showed typical bias of 0.1 m, and 
a root mean squared error (nns) of 0.15 m. The depth 
averaged velocities have a bias of -0.04 m/s and a nns error 
of less than 0.13 m/s. A comparison of high water and low 
water levels shows typical nns enors of 0.13 m, while a 
comparison of the high and low water levels resulted in a 
typical nns enor of 10 min. These enors compare well with 
those of the Zuno model that was used for the open 
boundaries [3] and they were considered sufficiently 
accurate for our purposes.
Figure 2. Mesh and bathymetry o f the model
BOTTOM
■ -2
-4
-6
-a_ -10
-12
-14
-16
-18■ -20
Figure 3. Detail o f the mesh close to the harbour
The model was calibrated using water level and velocity 
data at sea. This leads to a Manning roughness coefficient of 
0.02 s/m13. Close to the harbour entrance, the friction 
coefficient was increased, in order to represent the effect of 
the friction due to the large concrete elements of the 
breakwater (Fig. 3).
BOTTOM FRICTION
0.032
0.028
0  024  
0.02 
0.016
0.012
0.008
IV. RESULTS
The results of the model are shown in Fig. 5. The model 
reproduces the strong jet found in the measurements, 
although it occurs somewhat later in the tide (Fig. 5a). In the 
model, the jet seems to be even more pronounced than in the 
measurements. However, the jet is located somewhat more to 
the east in the model than in the measurements. The model 
also shows a strong primary eddy. Further, the jet also 
generates a secondary circulation which is weaker than the 
primary eddy (Fig. 5b).
Approximately one hour after high water both the 
primary and secondary eddy are present in the model results 
(Fig. 5c). With the course of time, the primary eddy 
elongates and decreases strongly in strength, while the 
decrease of the secondary eddy is less. As a result of this 
process, the primary eddy disappears completely, just as seen 
in the measurements (Fig. 5d). However, in the model a very 
weak tertiary eddy developed north of the primary eddy, 
with the same direction of rotation as the secondary eddy. 
This eddy could not be observed in the measurements. The 
reason for this is probably that it is to weak and small to be 
observed with the relatively limited spatial resolution 
provided by the ADCP measurements.
Time after HW -00:20
Figure 4. Manning roughness coefficient close to the harbour
39
XXth TELEMAC-MASCARET User Conference Karlsruhe. October 16-18. 2013
Time after HW: 00:40
3./ e -
b.
Time after HW: 01:40
/ f ,
3.76
1500
V . S e n s it iv it y  a n a l y s is
A. Bed roughness
In order to assess the sensitivity towards the bed 
roughness on the formation of the eddy patterns, we 
eliminated the increased bed rouglmess at the harbour 
entrance. Thus the simulation was done using a constant 
Manning rouglmess coefficient of 0.02 s/m13. The modelled 
eddy pattern changes dramatically in comparison with the 
base run (Fig. 6). At first, we see the same jet developing 
(Fig. 6a). However, it lias a slightly different location. This 
gives the primary eddy a slightly stronger circulation and the 
secondary circulation that develops is slightly weaker than in 
the base run (Fig. 6b). Consequently, the primary eddy does 
not disappear with time (Fig. 6c). Thus we end up with two 
eddies in the harbour during the ebb phase, rather than one 
(Fig. 6d), which does not correspond to the measurements.
Time after HW: -00:20
\  \  \
C.
Time after HW: 02:40
d.
1500 2500
V  \  V
\  \  \
I I \
/  t  i
b.
3.77
3.765
3.755
1500 2500 3000
Figure 5. Development o f the modelled eddy pattem (base ran)
40
XXth TELEMAC-MASCARET User Conference Karlsruhe. October 16-18. 2013
Figure 6. Modelled eddy patterns, without increased bottom friction at the 
break waters.
B. Advection scheme
The previous simulations were done using the 
characteristic method as advection scheme for the advection 
of velocity. In order to test the sensitivity toward the used 
advection scheme, computational runs were performed using 
the two schemes that were especially suited to use in 
combination with the use of tidal flats: the “Leo Postma 
scheme” and the “N-scheme”.
Once again, the resulting eddy patterns change 
dramatically compared to the base ran (Fig. 7) Note that for 
brevity, only two time steps for the N-scheme are shown. 
The Leo Postma scheme gave qualitatively similar results). 
In fact, the eddy pattern that develops is rather similar to the 
simulation without bottom friction at the breakwaters 
(section V.A). We see both a primary eddy and a secondary 
eddy, with the primary eddy being slightly stronger than the 
secondary eddy.
Figure 7. Modelled eddy patterns using the "N-scheme"
C. Turbulence modeling/eddy viscosity
In order to test the sensitivity toward the used horizontal 
turbulence model a model with a constant horizontal eddy 
viscosity of 1.0 nr/s was used. This value is somewhat 
higher than those calculated using the Smagorinsky scheme 
used in the other runs, which were in this area in the order of 
IO'2 nr/s.
The use of a high eddy viscosity coefficient weakens the 
jet at the harbour entrance (Fig. 8a). The secondary eddy 
develops but is weaker than the primary eddy (Fig. 8b). 
Therefore, in this situation only the primary eddy remains in 
the harbour during the start of the ebb phase (Fig. 8c), and it 
is stronger than the secondary eddy. Nevertheless, the 
primary eddy disappears eventually, leading to a flow 
direction that corresponds to the measurements (Fig. 8d).
■
41
XXth TELEMAC-MASCARET User Conference Karlsruhe. October 16-18. 2013
Time after HW: -00:20
Time after HW: 00:40
3.765
b.
Time after HW: 01:40
s* s' s /  s
/  I !  t
y  f  /
I /  /  ,
, k l  ,  ,
.. \
3.76
1500 2500
V. \  V
C.
I  0.6
d.
Figure 8. Model results with a constant eddy viscosity of 1.0 n f/s
Note that simulations with a constant eddy viscosity of 
0.01 nr/s (thus comparable with those calculated using the 
Smagorinsky model) gave similar results for the eddies as 
the base run.
VI. Su m m a r y  a n d  c o n l u s io n s
A TELEMAC-3D model was developed in order to study 
the eddy patterns occurring in the harbour of Zeebrugge. It 
appears that a strong jet is formed some time before high 
water during the moment of strongest inflow. The jet 
generates a clockwise and a counter clockwise eddy, from 
which only the counter clockwise eddy remains visible 
during the ebb phase. A comparison between ADCP 
measurements and the model showed that this behaviour 
could be simulated using TELEMAC. A sensitivity analysis 
showed that the results are very sensitive to the bed friction 
close to the edges of the harbour. The used advection scheme 
and the calculation method for the horizontal eddy viscosity, 
and the variation of these parameters could lead to a different 
number of eddies present in the harbour.
A c k n o w l e d g e m e n t
Project funded under project nmnber '16EF201116.' 
assigned by the Maritime Access Division (aMT) of the 
Department of Mobility and Public Works of the Flemish 
Government.
R e f e r e n c e s
[1] Eurosense and Aquavision, “Stroomatlas Zeebrugge Verwerkingsrap- 
port” 2011 (in dutch)
[2] Ministerie van de Vlaamse Gemeenschap, “Stroomatlas haven van 
Zeebrugge” 1998 (in dutch)
[3] Vanlede, J.; Leyssen.G.; Mostaert, F., (2011) Modellentrein CSM- 
ZUNO, Deelrapport 1: opzet en gevoeligheidsanalyse. WL Rapporten 
WL2011R753_12revl_l (in dutch)
[4] I. Nezu and H. Nakagawa "Turbulence in Open-Channel Flows", 
IAHR Monographs, A.Â. Balkema, 1993, 281 pages
42


Modelling the eddy pattern in the harbour of Zeebrugge

Van Holland, Gijsbert

Hydraulic Engineering Repository

Conference Paper, Published VersionBreugem, Alexander; Decrop, Boudewijn; Da Silva, Julien; Van Holland,Gijsbert; Martens, ChantalModelling the Eddy Pattern in the Harbour of ZeebruggeZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:TELEMAC-MASCARET Core GroupVerfügbar unter/Available at: https://hdl.handle.net/20.500.11970/100425Vorgeschlagene Zitierweise/Suggested citation:Breugem, Alexander; Decrop, Boudewijn; Da Silva, Julien; Van Holland, Gijsbert; Martens,Chantal (2013): Modelling the Eddy Pattern in the Harbour of Zeebrugge. In: Kopmann,Rebekka; Goll, Annalena (Hg.): XXth TELEMAC-MASCARET. User Conference 2013.Karlsruhe: Bundesanstalt für Wasserbau. S. 37-42.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.Modelling the eddy pattern in the harbour of Zeebrugge  W.A. Breugem, B. Decrop, J. Da Silva, and G. Van Holland IMDC NV Berchem, Belgium abr@imdc.be  C. Martens afdeling Maritieme Toegang Departement Mobiliteit en Openbare werken van de Vlaamse overheid Antwerpen Belgium   Abstract—The eddy patterns in the harbour of Zeebrugge are studied using TELEMAC-3D and compared to available measurement data. It was found that during flood a clockwise eddy exists, generated by a strong jet near the eastern side of the harbour entrance. This eddy generates a second counter-clockwise eddy, which persists in the harbour during the ebb phase, whereas the primary eddy disappears. A sensitivity study was performed to investigate the influence of the turbulence model, the bed roughness and the advection scheme. It appeared that the modelled eddy patterns are quite sensitive to the settings that are used for all these three parameters.  I. INTRODUCTION The harbour of Zeebrugge is one of the most important Belgian seaports. The area surrounding Zeebrugge is characterised by strong tidal flows, with a tidal amplitude up to 5m during spring tide. In the harbour, complex eddy flow patterns are found, varying throughout the tidal cycle. Understanding these patterns is important for navigation purposes and for increasing our understanding of the siltation of the harbour, especially with respect to the redistribution of suspended sediment through the harbour.  In order to understand this process, the eddy pattern in the harbour is studied using TELEMAC-3D. The results of the TELEMAC model are compared with measurements, and a sensitivity test is performed with respect to the eddy formation by varying the bed roughness, the advection scheme and the horizontal turbulence model. II. PHENOMENOLOGY OF THE EDDY CURRENTS IN THE HARBOUR OF ZEEBRUGGE In order to study the phenomenology, an existing data set of ADCP (Acoustic Doppler Current Profiler) measurements was used [1]. These measurements were taken on different locations in the harbour and the navigation channel on various days between November 2009 and March 2010. Because the data were taken on different occasions, we put together the data from various measurement days, sorting them with respect to the time after high water (from now on abbreviated as HW) and according to the spring-neap tidal cycle. In this paper, we will only study the data from spring tide conditions. In the analysis, we focus on what happens in the period around the occurrence of high water, when the strongest eddies are formed. The ADCP data show the following pattern (Fig. 1; note that additional arrows have been added to aid interpretation of the data): • 2 h before HW: There is a net flux of water into the harbour in the form of a jet at the eastern harbour dam. The jet increases in length and strength with time. This jet generates an eddy in clockwise direction, which we will call the primary eddy. • 1 h before HW: A smaller secondary eddy with a counter clockwise rotation is also generated by the jet. • Around HW: From this moment, there is no net inflow of water in the harbour. Hence the eddy is decoupled from the flow at sea and it follows its own dynamics. It appears that the primary eddy starts decreasing in size and magnitude.  • 1 h after HW: Only the counter clockwise secondary eddy remains present in the harbour. It moves slowly towards the harbour entrance and gradually becomes weaker.  TUC 2013, 16-18/10/2013, Karlsruhe - Kopmann, Goll (eds.) - © 2013 Bundesanstalt für Wasserbau ISBN 978-3-939230-07-637XXth TELEMAC-MASCARET User Conference Karlsruhe, October 16–18, 2013      Figure 1.  Overview of the eddy development in the harbour of Zeebrugge from ADCP measurements. Comparable eddy patterns are found in the measurements during average tide, whereas the formation of this pattern is much less pronounced during neap tide. One must take care when interpreting the measured data, because the presented data was collected during different measurement days. There is always some error associated with the matching procedure, because the tidal amplitude and period are not completely the same for the different measurement days. Nevertheless, the discussed pattern seems to be representative for the conditions occurring in the harbour, since earlier data [2] show similar results for the observed eddy patterns. III. MODEL SETUP The model was set up in a circular domain centred around the harbour of Zeebrugge, starting from Dunkirque (France) in the West to Goeree-Overflakkee (the Netherlands) in the East (Fig. 2). The Eastern and Western Scheldt estuaries are included in the model, although the most upstream part of the Western Scheldt was schematized using straight prismatic channels. The resolution varied from 30 m inside the harbour to 5000 m close to the open boundary (Fig. 3). Vertically, ten non-equidistant sigma layers were used to represent the water column. Boundary conditions for velocity and water level were obtained from the Zuno [3] model, which has a resolution comparable to our model at the location of these boundaries. These boundary condition were applied as a time series (with a time interval of 10 min) at each location on the open boundary. Additional discharge boundary conditions were applied to schematise fresh water influxes into the model. Note that one of the sources of fresh water was located inside the harbour. The model was run in TELEMAC-3D for a period of 15 days using a time step of 20 seconds using the Smagorinsky scheme for the horizontal eddy viscosity and a mixing length model using the mixing length parameterization of Nezu and Nakagawa [4] for the vertical eddy viscosity. 38XXth TELEMAC-MASCARET User Conference Karlsruhe, October 16–18, 2013    Figure 2.  Mesh and bathymetry of the model  Figure 3.  Detail of the mesh close to the harbour The model was calibrated using water level and velocity data at sea. This leads to a Manning roughness coefficient of 0.02 s/m1/3. Close to the harbour entrance, the friction coefficient was increased, in order to represent the effect of the friction due to the large concrete elements of the breakwater (Fig. 3).  Figure 4.  Manning roughness coefficient close to the harbour A comparison of measurement data and model results for the water level time series showed typical bias of 0.1 m, and a root mean squared error (rms) of 0.15 m. The depth averaged velocities have a bias of -0.04 m/s and a rms error of less than 0.13 m/s. A comparison of high water and low water levels shows typical rms errors of 0.13 m, while a comparison of the high and low water levels resulted in a typical rms error of 10 min. These errors compare well with those of the Zuno model that was used for the open boundaries [3] and they were considered sufficiently accurate for our purposes. IV. RESULTS The results of the model are shown in Fig. 5. The model reproduces the strong jet found in the measurements, although it occurs somewhat later in the tide (Fig. 5a). In the model, the jet seems to be even more pronounced than in the measurements. However, the jet is located somewhat more to the east in the model than in the measurements. The model also shows a strong primary eddy. Further, the jet also generates a secondary circulation which is weaker than the primary eddy (Fig. 5b).  Approximately one hour after high water both the primary and secondary eddy are present in the model results (Fig. 5c). With the course of time, the primary eddy elongates and decreases strongly in strength, while the decrease of the secondary eddy is less. As a result of this process, the primary eddy disappears completely, just as seen in the measurements (Fig. 5d). However, in the model a very weak tertiary eddy developed north of the primary eddy, with the same direction of rotation as the secondary eddy. This eddy could not be observed in the measurements. The reason for this is probably that it is to weak and small to be observed with the relatively limited spatial resolution provided by the ADCP measurements.  . a.  39XXth TELEMAC-MASCARET User Conference Karlsruhe, October 16–18, 2013   b. c.  d. Figure 5.  Development of the modelled eddy pattern (base run) V. SENSITIVITY ANALYSIS A. Bed roughness In order to assess the sensitivity towards the bed roughness on the formation of the eddy patterns, we eliminated the increased bed roughness at the harbour entrance. Thus the simulation was done using a constant Manning roughness coefficient of 0.02 s/m1/3. The modelled eddy pattern changes dramatically in comparison with the base run (Fig. 6). At first, we see the same jet developing (Fig. 6a). However, it has a slightly different location. This gives the primary eddy a slightly stronger circulation and the secondary circulation that develops is slightly weaker than in the base run (Fig. 6b). Consequently, the primary eddy does not disappear with time (Fig. 6c). Thus we end up with two eddies in the harbour during the ebb phase, rather than one (Fig. 6d), which does not correspond to the measurements.   a.  b. 40XXth TELEMAC-MASCARET User Conference Karlsruhe, October 16–18, 2013    c.  d. Figure 6.  Modelled eddy patterns, without increased bottom friction at the break waters. B. Advection scheme The previous simulations were done using the characteristic method as advection scheme for the advection of velocity. In order to test the sensitivity toward the used advection scheme, computational runs were performed using the two schemes that were especially suited to use in combination with the use of tidal flats: the “Leo Postma scheme” and the “N-scheme”. Once again, the resulting eddy patterns change dramatically compared to the base run (Fig. 7) Note that for brevity, only two time steps for the N-scheme are shown. The Leo Postma scheme gave qualitatively similar results). In fact, the eddy pattern that develops is rather similar to the simulation without bottom friction at the breakwaters (section V.A). We see both a primary eddy and a secondary eddy, with the primary eddy being slightly stronger than the secondary eddy.  a.  b. Figure 7.  Modelled eddy patterns using the "N-scheme" C. Turbulence modeling/eddy viscosity In order to test the sensitivity toward the used horizontal turbulence model a model with a constant horizontal eddy viscosity of 1.0 m2/s was used. This value is somewhat higher than those calculated using the Smagorinsky scheme used in the other runs, which were in this area in the order of 10-2 m2/s.  The use of a high eddy viscosity coefficient weakens the jet at the harbour entrance (Fig. 8a). The secondary eddy develops but is weaker than the primary eddy (Fig. 8b). Therefore, in this situation only the primary eddy remains in the harbour during the start of the ebb phase (Fig. 8c), and it is stronger than the secondary eddy. Nevertheless, the primary eddy disappears eventually, leading to a flow direction that corresponds to the measurements (Fig. 8d). 41XXth TELEMAC-MASCARET User Conference Karlsruhe, October 16–18, 2013    a. b.c.  d. Figure 8.  Model results with a constant eddy viscosity of 1.0 m2/s  Note that simulations with a constant eddy viscosity of 0.01 m2/s (thus comparable with those calculated using the Smagorinsky model) gave similar results for the eddies as the base run.  VI. SUMMARY AND CONLUSIONS A TELEMAC-3D model was developed in order to study the eddy patterns occurring in the harbour of Zeebrugge. It appears that a strong jet is formed some time before high water during the moment of strongest inflow. The jet generates a clockwise and a counter clockwise eddy, from which only the counter clockwise eddy remains visible during the ebb phase. A comparison between ADCP measurements and the model showed that this behaviour could be simulated using TELEMAC. A sensitivity analysis showed that the results are very sensitive to the bed friction close to the edges of the harbour. The used advection scheme and the calculation method for the horizontal eddy viscosity, and the variation of these parameters could lead to a different number of eddies present in the harbour. ACKNOWLEDGEMENT   Project funded under project number '16EF201116.' assigned by the Maritime Access Division (aMT) of the Department of Mobility and Public Works of the Flemish Government. REFERENCES [1] Eurosense and Aquavision, “Stroomatlas Zeebrugge Verwerkingsrap-port” 2011 (in dutch) [2] Ministerie van de Vlaamse Gemeenschap, “Stroomatlas haven van Zeebrugge” 1998 (in dutch) [3] Vanlede, J.; Leyssen,G.; Mostaert, F., (2011) Modellentrein CSM-ZUNO, Deelrapport 1: opzet en gevoeligheidsanalyse. WL Rapporten WL2011R753_12rev1_1 (in dutch) [4] I. Nezu and H. Nakagawa "Turbulence in Open-Channel Flows", IAHR Monographs, A.A. Balkema, 1993, 281 pages 42

Modelling the Eddy Pattern in the Harbour of Zeebrugge

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Modelling the Eddy Pattern in the harbour of Zeebrugge

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