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QUEEN’S UNIVERSITY BELFAST
FACULTY OF ENGINEERING AND PHYSICAL
SCIENCES
School of Planning, Architecture and
Civil Engineering
Thesis
for the Degree of Master of Science
in Water Resources Management
Title: Assessing Saline Intrusion in the River Lagan
Aisling Corkery
SEPTEMBER 2010
Assessing Saline Intrusion in the River Lagan
By
Aisling Corkery
A Thesis submitted to the Faculty of Engineering and Physical Sciences
School of Planning, Architecture and Civil Engineering
In Partial Fulfilment of the Requirements for the Degree of
MSc. in Water Resources Management
THE QUEEN’S UNIVERSITY BELFAST
2010
i
Declaration
I confirm the following:
(i) the dissertation is not one for which a degree has been or will be conferred by any other
university or institution;
(ii) the dissertation is not one for which a degree has already been conferred by this
university;
(iii) that this work submitted for assessment is my own and expressed in my own words. Any
use made within it of works of other authors in any form (e.g. ideas, figures, text, tables) are
properly acknowledged at their point of use. A list of the references employed is included;
(iv) the composition of the dissertation is my own work.
Signed ………………………………………………………….....
Date …………………………………………………………….
ii
Abstract Hydrodynamic problems linked with half tidal barrages and impounded estuaries can have a
negative influence on water quality, due to stratification caused by saline intrusion and the
formation of an entrapped saline wedge. A three dimensional hydrodynamic model of the
River Lagan between Stranmillis weir and the Lagan weir was developed using MIKE 3
software to simulate the level of saline intrusion in the river. Based on the shoreline data and
bathymetry data acquired a usable mesh was produced, which future models can be based
on.
The time period chosen was based on salinity data recorded on a spring tide over a period of
approximately 2.5 days in July 2002, when the aerators were not in operation. The boundary
conditions created for the harbour were based on existing river flow data and tide heights
calculated from known tidal ranges for the days mentioned above. However, not all tidal
ranges were known and heights of high and low tides were not given, leading to estimation
of a number of tidal ranges.
Modelling the river without the Lagan weir showed that during spring tides the saline
intrusion extends as far as the Ormeau Embankment at high tide and that water beyond this
point is predominantly fresh water. Furthermore the vertical profiles show that at low tides,
no salt water remains in the river upstream of the location of the Lagan weir. It is also
evident that vertical mixing occurs during spring tides, as a saline wedge was not visible.
Various methods were used in an attempt to model the effects of the Lagan weir on saline
intrusion. Using two broad crested weirs of -1.3m and 0.3m OD for the flood and discharge
weir respectively, yielded ambiguous results. The final model was based on weir formula one
and weir levels and widths, received from the River Warden, John Byrne. Damping of the
vertical eddy viscosity was also used to increase stratification and saline intrusion. Using
weir formula one and revised dimensions, saline intrusion was observed as a saline wedge
on the flood tide, reaching a point just downstream of the old McConnell weir at high tide.
Furthermore, a small entrapped saline wedged remained upstream of the Lagan weir and
increased with each successive tide. This may indicate that the model should be run over a
longer period of time to gain results similar to those observed in 2002.
In its current state the model does not correspond to recorded salinity data and thus needs
further calibration.
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Acknowledgements
I wish to express my sincere gratitude to a number of people who have enabled this
research project to be completed.
Firstly, I would like to sincerely thank Dr Bjoern Elsaesser, my supervisor, for his
enthusiasm, patience, support, guidance and encouragement throughout this research
project.
Thanks also to a number of staff in the School of Planning, Architecture and Civil
Engineering. Especially Dr Pauline MacKinnon, for all her help in finding the data I required
and for her patience with my numerous requests for information. Also, to Dr Karen Keaveney
who took the time out to make sure I had the correct OSNI data base layers for my model.
I would also like to thank Lorraine Barry from the School of Geography, Archaeology and
Palaeoecology for her help with any questions I had on ArcGIS.
I would also like to thank River Manager, John Byrne, from the Department for Social
Development, for his time and patience in answering my questions about the Lagan weir.
Thank you to all my friends and my brother Stephen who have provided me with so much
support over the past year.
Special thanks go to my amazing boyfriend Ollie, who has supported me through good and
bad during my MSc. Thank you for always providing a “positive mental attitude” when things
went wrong and fixing my computer when it died. It would have been very difficult without
his love and optimism.
Finally, very special thanks to my Mum and Dad for their never ending love, encouragement
and support.
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Table of Contents 1. Introduction ............................................................................................................ 1
1.1 Introduction ....................................................................................................... 1
1.2 Aims ................................................................................................................. 2
1.3 Objectives ......................................................................................................... 2
2. Literature Review ................................................................................................... 3
2.1 Characteristics of Estuaries .............................................................................. 3
2.2 Tides ................................................................................................................ 3
2.3 Circulation and Salinity Distribution in Estuaries ............................................... 4
2.3.1 Salt Wedge Estuary ................................................................................... 5
2.3.2 Partially Mixed Estuary ............................................................................... 5
2.3.3 Well Mixed Estuary .................................................................................... 6
2.3.4 Salinity Distribution .................................................................................... 7
2.3.5 Stratification – Circulation Diagrams........................................................... 7
2.4 MIKE 3 Governing Equations .......................................................................... 10
2.5 Barrages ......................................................................................................... 11
2.5.1 Tidal Energy Barrages ............................................................................. 11
2.5.2 Flood Protection Barrages ....................................................................... 11
2.5.3 Amenity Barrages .................................................................................... 11
2.5.4 Hydrodynamic and Water Quality Problems and Impounding Barrages ... 12
2.6 The Impounded River Lagan and Associated Water Quality Problems ........... 14
2.6.1 Tidal Limits and River Flow in the River Lagan ......................................... 15
2.7 Practical Salinity Scale ................................................................................... 15
2.8 Review ............................................................................................................ 17
3. Methodology ........................................................................................................ 18
3.1 MIKE 3 Flow Model FM .................................................................................. 18
3.2 Mesh Generation ............................................................................................ 18
3.2.1 Shoreline Data ......................................................................................... 18
3.2.2 Mesh Boundary Conditions ...................................................................... 20
3.2.3 Creating the Mesh .................................................................................... 21
3.2.4 Bathymetry Data and Interpolation ........................................................... 22
3.2.5 Analysing the Mesh .................................................................................. 24
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3.3 Physical Boundary Conditions ........................................................................ 28
3.3.1 Time Series .............................................................................................. 29
3.3.2 Tide Height Time Series ........................................................................... 29
3.3.3 River Flow Time Series ............................................................................ 32
3.4 Running the Flow Model ................................................................................. 33
3.4.1 Hydrodynamic Module ............................................................................. 34
3.4.2 Temperature Salinity Module ................................................................... 39
3.5 Calibrating the Model ...................................................................................... 40
4. Results ................................................................................................................. 42
4.1 Results ........................................................................................................... 42
4.2 Lagan 3D Flow Model with no Weir in Place ................................................... 42
4.2.1 Salinity Horizontal Profiles ....................................................................... 42
4.2.2 Salinity Vertical Profiles ............................................................................ 43
4.2.3 Density Vertical Profiles ........................................................................... 44
4.3 Lagan 3D Flow Model with Two Broad Crested Weirs (Version 1, 2 and 3) .... 45
4.4 Lagan 3D Flow Model with Two Weirs using Weir Formula One ..................... 50
5. Discussion ........................................................................................................... 56
5.1 Lagan 3D Flow Model with no Weir in Place ................................................... 56
5.2 Lagan 3D Flow Model with Two Broad Crested Weirs (Version 1,2 and 3) ..... 57
5.3 Lagan 3D Flow Model with Two Weirs using Weir Formula One ..................... 58
6. Conclusion and Recommendations ...................................................................... 60
6.1 Conclusion ...................................................................................................... 60
6.2 Recommendations for Future Work ................................................................ 61
References .............................................................................................................. 63
Appendix A .............................................................................................................. 67
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List of Figures
Figure 2.1 Positions of the sun, moon and earth during spring and neap tides.....................4
Figure 2.2 Estuary circulation patterns and vertical profiles of salinity versus velocity……...6
Figure 2.3 Hansen and Rattray’s stratification-circulation diagram……………………………..8
Figure 2.4 View of the downstream side of the Lagan weir……………………………………12
Figure 2.5 Entrapped salt wedge and entrainment of saline water into freshwater river
flows…………………………………………………………………………….…………………....13
Figure 2.6 Section view of the fish belly flap gate arrangement of the Lagan weir with
respective operational levels……………………..………………………….…………………….15
Figure 3.1 Shoreline shapefile created in ArcMap is shown in green…....……………………19
Figure 3.2 Boundary conditions as viewed in the Flow Model...............................................20
Figure 3.3 Triangular and quadrangular mesh detail of the first and final mesh, showing the
difference in mesh element size……………………………….………..…………………………22
Figure 3.4 Closer look at bathymetry data before and after interpolation………………….....23
Figure 3.5 Full view of bathymetry data before and after interpolation with the mesh………24
Figure 3.6 Element approaching critical CFL prior to creating a quadrangular mesh at the
Lagan weir location…………..……………………………………………………………………..26
Figure 3.7 Critical CFL numbers at Stranmillis weir………………………………………….....27
Figure 3.8 Critical CFL numbers at the old McConnell weir site…………………………….....27
Figure 3.9 Critical CFL numbers at the Lagan weir................................................................28
Figure 3.10 Mean spring and neap curve used to calculate the tide heights time series.......30
Figure 3.11 Tide height time series with identical sinus period for the warm up and hot start
flow models and the varying sinus periods for the actual flow model....................................31
Figure 3.12 River flow time series.........................................................................................32
Figure 3.13 Position of the weirs based on coordinates........................................................37
Figure 4.1 Salinity horizontal profiles showing saline intrusion at high tide from the bottom
layer (layer 1) to the top layer (layer 5)..................................................................................42
Figure 4.2 Salinity in the River Lagan with no weir in place, for a typical tidal cycle during the
period 24th-26h July…………………………………………………………………………………44
Figure 4.3 Density in the River Lagan with no weir in place for a typical tidal cycle during the
period 24h-26h July…………………………………………………………………………………45
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Figure 4.4 Salinity horizontal profiles for version 1 of the broad crested weir flow model for a
typical tidal cycle showing a minimal amount of saline intrusion beyond the Lagan weir......46
Figure 4.5 Salinity horizontal profiles for version 2 of the broad crested weir flow model for a
typical tidal cycle showing saline intrusion travelling as far as Ormeau Embankment...........46
Figure 4.6 Salinity horizontal profiles for version 3 of the broad crested weir flow model for a
typical tidal cycle showing saline intrusion between Ormeau Bridge and King’s Bridge........46
Figure 4.7 Salinity vertical profiles of broad crested weir simulation version 3 for a typical
tidal cycle...............................................................................................................................48
Figure 4.8 Surface elevations upstream (blue) and downstream (black) of the Lagan weir for
the broad crested weir version 3, indicating the sharp fall in upstream water levels.............48
Figure 4.9 Salinity vertical profiles of broad crested weir simulation version 1 for a typical
tidal cycle...............................................................................................................................49
Figure 4.10 Surface elevations upstream and downstream of the broad crested weir
simulation version 1, showing the upstream elevation remaining at the required
impoundment level.................................................................................................................50
Figure 4.11 Salinity horizontal profiles for a typical tidal cycle using the weir formula one and
revised dimensions, showing saline intrusion downstream of the old McConnell
weir.........................................................................................................................................50
Figure 4.12 Salinity vertical profiles for a typical tidal cycle using the weir formula one and
revised dimensions, showing the formation of a saline wedge on the flood
tide.........................................................................................................................................51
Figure 4.13 Salinity vertical profiles showing the increasing saline wedge upstream of the
Lagan weir at successive low tides........................................................................................52
Figure 4.14 Salinity time series for layer 1, the bottom layer, showing the salinity upstream of
the Lagan weir increase after each tidal cycle.......................................................................53
Figure 4.15 Salinity time series for layer 2, the layer above the bottom layer, showing the
salinity upstream of the Lagan weir increase after each tidal cycle. A slight reduction in
salinity compared to layer one is also visible.........................................................................53
Figure 4.16 Salinity time series for layer 3, the middle layer, showing the salinity upstream of
the Lagan weir increase after each tidal cycle. A slight reduction in salinity compared to layer
two is also visible...................................................................................................................54
Figure 4.17 Salinity time series for layer 4, the layer below the top layer, showing the salinity
upstream of the Lagan weir increase after each tidal cycle. A slight reduction in salinity
compared to layer three is also visible...................................................................................54
Figure 4.18 Salinity time series for layer 5, the top layer, showing the salinity upstream of the
Lagan weir increase after each tidal cycle. A slight reduction in salinity compared to layer
four is also visible...................................................................................................................55
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List of Tables
Table 3.1 Flow Model Time Specifications.............................................................................33
1
Chapter 1: Introduction 1.1 Introduction The hydrodynamic problems linked with half tidal barrages can have a negative influence on
water quality, in the form of stratification caused by saline intrusion. During times of low river
discharge, water upstream of the barrage can become highly stratified forming an entrapped
saline wedge. This can be exacerbated during neap tides when tidal flushing is reduced.
Consequently, incoming saline water from higher tides replenishes the saline layer but it may
not fully replace the previously entrapped saline wedge. The saline wedge is cut off from the
atmosphere and relies on the freshwater flowing above to replenish its dissolved oxygen
levels. Due to this the saline layer can quickly become anoxic, as there is high sediment and
biological oxygen demand (Evans 1996, Taylor 2002, Walker 1999).
Reduced dissolved oxygen causes numerous water quality issues, the most considerable of
which is the failure of the estuary to support various fish species and salmonid migration.
Other water quality issues include production of hydrogen sulphate, increases in ammonia
concentrations and the release of metal end products, all of which can be toxic to aquatic
biota, while, hydrogen sulphate also creates unpleasant odours. Furthermore, light
penetration is increased as far as the halocline, which in turn causes the growth of algal
blooms along this interfacial layer. These algal blooms cause a super saturation of dissolved
oxygen at this level during the day but mostly likely reduce overall dissolved oxygen during
night time respiration (Evans 1996, Reilly 1994, Shaw 1995).
All of the above water quality issues are causes for concern for water resources managers in
term of fisheries, aquatic life, ecosystems, industry and recreation. Under the Water
Framework Directive (2000/60/EC) water resources managers will be required to mitigate
against these issues to meet the “good status” objectives by 2015. In order meet water
quality objectives, the barrage and estuary system in question may be investigated using
predictive modelling techniques that can simulate existing conditions and the proposed
mitigating measures. This will enable water resource managers to be better informed on
which combination of remedial measures will perform best and the potential effects these
measures may have on the estuary (H.R. Wallingford Ltd 1999, Maskell 1996, Directive
2000/60/EC).
The Lagan weir is half tidal and was put in place to cover the mudflats at all tide levels, thus
promoting redevelopment along the river embankments and creating waters for recreational
use. The Lagan has been investigated extensively in the past, as water quality issues in this
2
section has caused significant problems and has hindered much needed regeneration along
the embankments. In addition, a vertical two dimensional model was developed for this
section, though this was not further developed in recent years. This project will attempt to
develop a three dimensional hydrodynamic model of the River Lagan between Stranmillis
weir and the Lagan weir.
1.2 Aims This project will attempt to develop a three dimensional hydrodynamic model of the River
Lagan between Stranmillis Weir and the Lagan weir using MIKE 3 software to simulate the
level of saline intrusion in the river, and investigate how far up the river it travels and to what
depths it is present. This three-dimensional model will take account of lateral variations in
the shoreline of the Lagan, where previous two dimensional models used laterally averaged
shorelines. It is hoped that this model may help water resources managers to assess the
level of saline intrusion and determine better ways in which to manage the water quality in
the river, particularly in relation to saline stratification and the pollution issues that it causes.
1.3 Objectives
To research and review previous related work carried out by researchers, in order to gain an
understanding of the principles involved in saline intrusion and how three-dimensional
hydrodynamic models can be used to asses saline intrusion.
To generate an accurate mesh that can be used as the bases for all future models of the
impounded River Lagan. This was carried out by acquiring data such as shoreline
boundaries and bathymetry and using various software such as ArcGIS and Mike Zero Mesh
Generator to generate, refine, interpolate and analyse the mesh.
To generate accurate boundary conditions at the harbour (constriction in the Victoria
Channel) and Stranmillis weir based on tide height and river flow data respectively. This was
done by generating time series based on existing river flow data and calculated tide heights.
These time series were then used for the boundary conditions in all flow models.
Use the three dimensional hydrodynamic model to assess the hydrodynamics of the Lagan
weir itself and the effects it has on saline intrusion. Various scenarios were modelled based
on impoundment levels and measurements described in literature. However, these scenarios
did not yield the required results. A meeting with the River Warden, John Byrne, highlighted
discrepancies in the literature impoundment levels and thus a final model based on up to
date levels was simulated.
3
Chapter 2: Literature Review
2.1 Characteristics of Estuaries
Estuaries undergo a large number of processes which have been studied by many
researchers in the past. Furthermore, these processes vary depending on the type of
estuary, be it high relief estuaries (Fjords), low relief estuaries (v-shaped valleys, coastal
plain estuaries, bar built estuaries and blind estuaries), delta front estuaries or compound
estuaries (Fairbridge, 1980). It has therefore been difficult to give estuaries one specific
definition. However, numerous publications have focused in on the definitions suggested by
(Pritchard, 1963) and (Dionne, 1963). The former states that,
“An estuary is a semi-enclosed coastal body of water which has a free connection to the
open sea and within which seawater is measurably diluted with freshwater derived from land
drainage.”
Pritchard’s definition deals with estuaries that have comparable salinity and density
distributions due to quantifiable mixing processes. It is felt that this definition is somewhat
limited, as it ignores the matter of tidal influence on freshwater river systems (Fairbridge,
1980, Morris A.W. 1985).
As a result of this (Fairbridge, 1980) proposed to use the estuary definition by (Dionne,
1963) which states that,
“An estuary is an inlet of the sea reaching into a river valley as far as the upper limit of tidal
rise, normally being divisible into three sectors: (a) a marine or lower estuary, in free
connection with the open sea; (b) a middle estuary subject to strong salt and freshwater
mixing; and (c) an upper or fluvial estuary, characterised by fresh water but subject to daily
tidal action.”
Both of the above definitions highlight key areas of importance in estuary processes,
although it is not possible to include all estuary characteristics within a single definition.
2.2 Tides
Water movement within estuaries is dominated by both freshwater river flow and the
transient movement of seawater due to incoming (flood current) and outgoing (ebb current)
tidal oscillations. Slack water occurs when there is a change in direction of the tidal currents,
thus there is no inflow or outflow. Tides can be described as cyclical, temporary changes in
ocean surface height at a specific point are caused mainly by the gravitational forces of the
sun and moon and the earth’s motion (Garrison 1995, Speers, 2004). These gravitational
forces can change the height variation of tides depending on the position of the sun and
moon. For example, when full and new moons occur, the sun and moon are linearly aligned,
creating spring tides. Spring tides cause high tides to reach their highest point and likewise,
4
low tides to reach their lowest point. Furthermore, the spring high and low tide extremes
increase when the sun and moon are closest to the earth. As full and new moons occur
every two weeks, so to do spring tides. Similarly, when the moon is in its first and third
quarter, the sun and moon are perpendicular to each other, creating opposing forces and
neap tides. During neap tides the variation between high and low tide is at its smallest. Neap
tides also occur every two weeks, between spring tides. Spring and neap tides represent the
two extremes in tidal ranges and can be seen in figure 2.1 below. All other tidal ranges vary
within these two extremes. Areas that experiences spring and neap tides are semi-diurnal,
that is, high and low tide occurs twice daily. Other tidal patterns which occur include diurnal
(daily high and low tides) and mixed tides (high and low tides occur twice daily but the height
of each high and low tide vary greatly) (Garrison 1995, Pugh, 1987). The majority of the
world’s tides are semi-diurnal, including those in the UK and Ireland (Garrison 1995).
Figure 2.1Positions of the sun, moon and earth during spring and neap tides (Garrison, 1995).
2.3 Circulation and Salinity Distribution in Estuaries
As each estuary is defined by its specific circulation patterns, mixing process and density
stratification, it is better to describe estuaries both in terms of their salinity distribution and
water movement within the estuary. In doing this, estuaries can be divided into three general
categories, namely, the salt wedge estuary, the partially mixed estuary and the well mixed
estuary (Bowden, 1980, Dyer 1973)
5
2.3.1 Salt Wedge Estuary
A salt wedge estuary is highly stratified and occurs when the velocity of river flow dominates
over tidal currents and there is little difference in the width to depth ratio of the channel. As
freshwater is less dense than seawater, the river flows over the surface of the saline wedge,
reducing in velocity as it gets closer to the mouth of the estuary. Without friction, a horizontal
interface exists between the freshwater and saltwater, under these conditions the saline
layer (salt wedge) continues upstream until it reaches the point where the river bed is the
same as the mean sea level. At this point the salt wedge slopes gradually downwards due to
small frictional forces but there is no mixing between the two layers. Furthermore, facing
seawards, the interface also slopes to the right in the northern hemisphere due to the
Coriolis Effect (Bowden 1980, Dyer 1973). In reality, there are also shear velocity forces
present due to the fast moving river flow. This force creates internal waves between the two
layers, which carry the saltwater into the freshwater layer when they break. This process is
called entrainment and is strictly a one way process, that is, no freshwater is carried into the
saline layer. Thus, the salinity and volume of the freshwater layer increases, creating a
higher flow rate towards the mouth of the estuary and a small amount of upstream flow in the
salt wedge. The salt wedge remains at constant salinity throughout the estuary. The most
widely used example of a salt wedge estuary is the Mississippi (Bowden 1980, Dyer 1973).
An intermediate phase between the salt wedge estuary and the partially mixed estuary
occasionally occurs when a mixing zone, with a high salinity gradient, is created between the
freshwater layer and the salt wedge. This mixing zone is called a halocline and is caused by
turbulences carrying freshwater downwards in addition to saltwater upwards. This type of
estuary process can be found in fjords and some coastal plain estuaries (Bowden 1980,
Tully 1958).
2.3.2 Partially Mixed Estuary
Partially mixed estuaries are encountered most often and occur where tidal currents, in the
form of turbulent eddies cause vertical mixing of both salt water to the surface layer and
freshwater to the bottom layer. This creates a salinity profile that is similar in both the top
and bottom layers, with a high salinity gradient in the non moving interface between the
layers, just above mid-depth. In shallow areas of the estuary this high salinity gradient
occurs at the bottom. The salinity profiles are similar throughout the estuary both horizontally
and vertically. However, salinity is increased towards the mouth of the river, while unmixed
freshwater may only be found at the head of the estuary. In addition, the volume of seawater
in the upper layer and the volume of freshwater in the lower layer increase towards the
mouth of the estuary. There is still flow downstream and upstream in the top and bottom
6
layers respectively. The flow volume in each layer is approximately an order of magnitude
greater than the discharge of the river and approximately an order of magnitude less than
the fluctuating tidal currents. However a widely varying range of flow ratios and vertical
salinities can be observed from estuary to estuary, and even within the same estuary,
depending on the various freshwater discharge conditions, for example, high discharge due
to flooding or low discharge during summer flows (Bowden 1980, Dyer 1973).
2.3.3 Well Mixed Estuary
Well mixed estuaries are rare and may occur when tidal currents have a powerful affect on
an estuary in comparison to river discharge. A well mixed estuary may be created when
velocity shear force at the bottom of an estuary, of small cross-sectional area, is great
enough to cause full vertical mixing within the water column. In addition, salt water may get
trapped in shoreline eddies and diffuses back into the water column on the outgoing tide. A
combination of the above phenomena means there is minimal change in salinity between the
top and bottom of the water column. Mixing may also occur in the horizontal direction,
usually with increased salinity towards the mouth of the estuary. In well mixed estuaries the
mean current, which is seaward, varies little with depth and upstream mixing is carried out
by diffusion (Bowden 1980, Dyer 1973).
In wide estuaries lateral variations may be present, for example, the Coriolis effect can
create lateral flow separation whereby, in the northern hemisphere, seaward flow travels at
all depths on the right hand side and upstream flow travels on the left creating horizontal
circulation (Dyer 1973).
Figure 2.2 Estuary circulation patterns and vertical profiles of salinity versus velocity (Morris, 1985).
7
2.3.4 Salinity Distribution
As can be seen from the three estuary types described previously, salinity distribution is
influenced by freshwater flow, tidal currents, density circulation and the turbulent mixing
processes. In this section methods of estimating both the currents and salinity distribution
will be discussed.
Pressure gradient in an estuary is a function density, which in turn depends on salinity,
temperature and pressure (Bowden 1980, Neumann and Pierson 1966). However, within an
estuary, variation in density with pressure and temperature with salinity are minimal. Thus, it
is possible to assume that density is a linear function of salinity and is given by equation 2.1
below.
ρ = ρo(1 + αS) Eqn 2.1
Where ρo is the freshwater density at a specific temperature, S is the salinity in parts per
thousand (‰) and α is a constant equal to approximately 7.8 x 10-4. Therefore, salinity
distribution has an effect on all processes and thus dominates density circulation and
changes mixing processes (Bowden 1980, Hsu 1999).
Mixing processes that salinity has most influence on are the shear stress per unit area, τzx,
caused by mean horizontal flow and the vertical turbulent flux of salt per unit area, caused by
vertical turbulent diffusion.
Shear stress is given by τzx = -ρNz δu/δz Eqn 2.2
Where, Nz is the coefficient of eddy viscosity in vertical shear and u, is the horizontal velocity
component.
Vertical turbulent flux of salt per unit area = -ρKz δS/δz Eqn 2.3
Where, Kz is the coefficient of eddy diffusion in the vertical direction (Bowden 1980, Pritchard
1954, 1956).
The above equations were extended by (Hansen and Rattray 1965) to include longitudinal
eddy diffusion to account for flux of salt upstream.
Longitudinal eddy diffusion of salt upstream = -ρKx δS/δz Eqn 2.4
Where, Kx is the coefficient of eddy diffusion in the horizontal direction (Hansen and Rattray
1965) The above equations can be applied to partially mixed estuaries and allow the various
coefficients to be estimated (Bowden 1980).
2.3.5 Stratification-Circulation Diagrams
Following on from their previous work (Hansen and Rattray 1966) developed subsequent
quantitative ways of classifying estuaries, requiring only salinity and velocity measurements.
The two parameters required to classify estuaries are, a stratification parameter δS/So, which
8
is the change in the surface and bottom salinity δS, divided by the mean cross-sectional
salinity So, and a circulation parameter Us/Uf, which is the ratio between the mean surface
velocity Us and the discharge velocity Uf. The circulation parameter shows the ratio of the
river flow to that of the mean freshwater flow which contains entrained salt water. Based on
these parameters a stratification-circulation diagram was produced with the circulation
parameters along the x-axis and the stratification parameter along the y-axis. The diagram
can be seen in figure 2.3 below and shows the regions related to each general estuary
category (Bowden 1980, Dyer 1973, Hansen and Rattray 1966).
To use the diagram, salinity and current observations, as well as river discharge are required
for specific estuary cross-sections. In turn, these are used to calculate the stratification and
circulation parameters, which can be plotted on the diagram. If information is gathered along
the estuary, each point plotted will represent the estuary category of that stretch of the
estuary. These plots can change depending on river discharge, indicating a change in
estuary category. This method of determining estuary category has the disadvantage of only
using average tidal currents to predict the stratification parameters and therefore, does not
portray a full picture of what is happening in the estuary processes (Bowden 1980, Dyer
1973, Hansen and Rattray 1966).
Figure 2.3 Hansen and Rattray’s stratification-circulation diagram (1966) (Dyer, 1973)
9
In order to be able to use these diagrams more analytically Hansen and Rattray proposed
that two bulk parameters for estuary categories be related to the stratification and circulation
parameters. Namely P and the densimetric Froude Number, Fm, which are defined as:
P = Uf/Ut Eqn 2.5
Fm = Uf/Ud Eqn 2.6
Where Ut is the root mean square tidal current speed and Ud is the densimetric velocity
given by:
Ud = (gDΔρ/ρ)1/2 Eqn 2.7
Where g is acceleration due to gravity, D water depth, Δρ is the density difference between
freshwater at the estuary head and salt water at the mouth and ρ is the mean density. Using
data and analysis from numerous estuaries, lines of constant P and Fm could be plotted on
the Stratification-Circulation Diagram, showing that the circulation parameter is dependent
on Fm, while the stratification parameter is dependent on both parameters. Therefore Us and
the stratification parameter can be approximated from the diagram by calculating P and Fm
(Bowden 1980, Hansen and Rattray 1966).
Following on from Hansen and Rattray’s work (Fischer 1972) established estuary categories
using the “Richardson Number”, large Richardson Numbers signify stratified estuaries, and
is given by
RiE = g (Δρ/ρ) (Qf/bUt3) Eqn 2.8
Where Qf is river discharge and b is estuary width. The Richardson Number correlates with
Hansen and Rattray’s previously established bulk parameters via
RiE = P3/Fm2 Eqn 2.9
Richardson numbers can be plotted as constant lines on the Stratification-Circulation
Diagram and shows that there is a relationship between RiE and the Stratification parameter
(Bowden 1980, Fischer 1972).
10
The previous 2D model of the Lagan estuary was modelled by H R Wallingford using the
model (TIDEFLOW – 2D). In order to predict the effect the Lagan weir had on stratification,
the model used a universal mixing function founded on the Richardson Number (Maskell
1996).
2.4 MIKE 3 Governing Equations
MIKE 3 is a three-dimensional model that can solve the momentum and continuity equations
for the x, y and z directions. Within the 3D model the elements of mass, momentum, salinity
and temperature conservation are needed, as well as equations relating density to salinity.
Thus the three dimensional Reynolds averaged Navier-Stokes equation is required, which
includes turbulence, density and mass conservation
Eqn 2.10
ρ = local density of fluid, ui = velocity in xi-direction, Ωj = Coriolis force, P = fluid pressure, gi
= gravitational vector, νT = turbulent eddy viscosity, δij = Kronecker’s delta, k = turbulent
kinetic energy, t = time.
Transport equations and equations of state are use for salinity, temperature and water
density respectively.
Eqn 2.11
S, T and QH = salinity, temperature and atmospheric heat exchange respectively.
Finite difference techniques are used to reformulate the mass and momentum equations to
calculate discrete changes in space and time. Velocities are defined between the nodes,
while salinity, temperature and pressure are defined in the nodes. This allows spatial
separation of the differential equations, for example the mass equations and momentum
equations are centred every node and corresponding velocity node respectively (DHI Group
2010)
11
2.5 Barrages
A barrage may be defined as a low dam, which uses gates to control the flow and level of a
river or estuary. Barrages have been put in place in many estuaries for numerous purposes,
including tidal energy in areas of large tidal range, for water quality purposes where saline
intrusion extends into areas of abstraction, flood protection, and finally for amenity purposes,
to facilitate leisure activities or where low tide mudflats create an unpleasant environment.
The main purpose of the majority of barrages is to minimise the tidal range along the
impounded section of the estuary (Reilly 1994, Shaw 1995).
2.5.1 Tidal Energy Barrages
Only a few large tidal barrages have been put in place throughout the world, these include
La Rance in France and the Bay of Fundy in Canada. These barrages operate by leaving
sluices open on the flood current and closing them after high tide. As the ebb current flows
out downstream of the barrage, a head develops across the barrage on the upstream side.
When a specific head is reached turbines are signalled to start, which generate electricity.
When evaluated against other forms of electricity generation there are a number of
disadvantages, the most significant of which are that they do not generate electricity
continuously and the period of generation changes from day to day. Other problems include
mechanical issues with generators due to marine growth and high environmental disruption
during the construction period (Burt and Cruickshank 1996, Reilly 1994).
2.5.2 Flood Protection Barrages
Flood protection barrages (barriers) have become necessary in many low land coastal
regions where development has increased along the flood plains. Many of these barrages
have been constructed as movable barriers in order to reduce the possible hydrodynamic
and water quality issues that arise with other types of barrages. Movable barriers are only
put in place when there is a threat of flooding from tidal surges. Examples of this type of
barrage include the Thames and Hull Barriers (Burt and Cruickshank 1996, Reilly 1994).
2.5.3 Amenity Barrages
Many amenity barrages in the UK are focused around regenerating urban areas both
physically and economically by enhancing the visual appearance of their surrounding areas
and improving recreational amenities. This is achieved primarily by creating a constant water
level within the enclosed area ensuring mudflats that occur at low tide are hidden. Examples
of amenity barrages within the UK include the Tawe barrage, the Tees barrage, Cardiff Bay
and the Lagan weir. There are two forms of amenity barrages, namely tidal exclusion
barrages, which are also used to prevent saline intrusion and create a constant freshwater
12
only impoundment upstream of the barrage, and the half-tidal barrage (e.g. Tawe barrage
and Lagan weir), which enables tidal flow to overtop the gates of the barrage at certain
levels, thus partially intruding into the freshwater. However, these partial intrusions can
create water quality issues upstream of the barrage in the form of an oxygen deficient saline
wedge at the base of the barrage (Burt and Cruickshank 1996, Reilly 1994, Shaw 1995,
Speers 2004).
Figure 2.4 View of the downstream side of the Lagan weir (Cochrane & Weir, 1997).
2.5.4 Hydrodynamic and Water Quality Problems Associated with Impounding Barrages
Although most barrages have been constructed to regenerate and enhance the amenity of
an area they have the potential to create serious hydrodynamic and water quality problems.
Flood protection barrages are the least likely to have an influence on estuary water quality
as they only operate during periods of high tidal surges. While tidal exclusion barrages
create a freshwater impoundment upstream of the barrage, which may change the upstream
ecosystem significantly and also make the water upstream more susceptible to pollution
(Shaw 1995, Speers 2004).
Half tidal barrages in particular seem to have the worst affect on water quality. During times
of low river discharge, water upstream of the barrage can become highly stratified forming
an entrapped saline wedge. This problem can be increased during neap tides when tidal
flushing is reduced. Subsequently, incoming saline water from higher tides restores the
saline layer but it may not fully exchange the previously entrapped saline wedge. The saline
wedge is cut off from the atmosphere and relies on the freshwater flowing above to replenish
dissolved oxygen levels. An example of this can be seen in figure 2.5 below. As discussed in
previous sections, without turbulence freshwater is not carried into the saline layer. Due to
13
this, the saline layer can quickly become anoxic, as there is high sediment oxygen demand
from both organically enriched sediments and the microbial degradation processes (Evans
1996, Taylor 2002, Walker 1999).
Figure 2.5 Entrapped salt wedge and entrainment of saline water into freshwater river flows (Laganside, 1997).
Reduced dissolved oxygen causes numerous water quality issues, the most significant of
which is the reduced capacity of the estuary to support various fish species and in some
cases salmonid migration. Other water quality issues caused by anoxic conditions including,
production of hydrogen sulphate, increases in ammonia concentrations and the release of
metal end products, all of which can be toxic to aquatic ecology, while, hydrogen sulphate
also creates unpleasant odours. Another problem created by the stratified layers is
increased light penetration as far as the halocline, which causes the growth of algal blooms
along this interfacial layer. These algal blooms cause a super saturation of dissolved oxygen
at the halocline during the day but mostly likely reduce overall dissolved oxygen during night
time respiration (Evans 1996, Reilly 1994, Shaw 1995).
All of the above water quality issues are causes for concern for water resources managers in
terms of fisheries, aquatic life, ecosystems, industry and recreation. The Water Framework
Directive (2000/60/EC) will require water resources managers to mitigate against these
issues in order to meet the “good status” objectives by 2015. To meet water quality
objectives the barrage and estuary system in question may be investigated using predictive
modelling techniques that can simulate existing conditions and any proposed mitigating
measures. This will enable water resource managers to be better informed on which
remedial measure or combination of remedial measures to use and the potential effects
these measures may have on the estuary. Mitigating measures for half tidal barrages include
14
selective withdrawal of saline water, artificial aeration, dredging and removal of polluting
sediments, removal of floating litter and algal blooms, nutrient loading reduction (H.R.
Wallingford Ltd 1999, Maskell 1996, Directive 2000/60/EC).
In the case of the Lagan weir sluices and withdrawal pipes are located at the bottom of the
weir. Each of the four supporting piers house two 900mm diameter pipes, each with control
sluices. The pipes have been put in place to flush out the anoxic saline layer on the outgoing
tide and the sluices allow a fresh inflow of salt water on the flood current. (Cochrane & Weir
1997, Speers 2004)
2.6 The Impounded River Lagan and Associated Water Quality Problems
The River Lagan was first impounded by the McConnell Weir in 1937, which was replaced
by the Lagan weir in 1994. As mentioned previously the Lagan weir is half tidal and was put
in place to cover the mudflats at all tide levels, thus promoting redevelopment along the river
embankments and creating waters for recreational use. The weir was constructed with five
hydraulic fish belly gates that are lowered to riverbed level for a number of hours either side
of high tide, allowing free flow of saltwater into the estuary and then raised on the outgoing
tide to maintain the water level. A diagram of the gates is depicted in figure 2.6 below.
Furthermore, anoxic saline water held behind the weir is selectively removed on the outgoing
tide via low-level pipes located in the supporting piers (Cochrane and Weir 1997, Speers
2004). These pipes were thought to be somewhat successful at mitigating the dissolved
oxygen issues adjacent to the weir. However, inadequate mixing of water upstream of the
weir could cause stratification and the formation of a saline layer at the bottom, during low
river flow periods. Within the River Lagan there is a high sediment oxygen demand, which
will gradually deplete the saline layer of oxygen, as dissolved oxygen cannot penetrate
through the halocline. Because of this, it was felt that atmospheric aeration could not meet
the dissolved oxygen demands and thus artificial aeration was provided in an attempt to
alleviate the problem (Cochrane 1993, Speers 2004).
15
Figure 2.6 Section view of the fish belly flap gate arrangement of Lagan weir with respective operational levels
(Cochrane & Weir, 1997)
2.6.1 Tidal Limits and River Flow in the River Lagan
The tides in Belfast Lough and the Lagan estuary are semi-diurnal, while the average tidal
range at spring tides is 3.1m and 1.9m at neap tides. Mean high water at spring and neap
tides is 3.5m and 2.9m respectively, while mean low water at spring and neap tides is 0.4m
and 1.1m respectively. Spring tidal currents run at a rate of .33knots and neap tidal current
at .25knots (Belfast Harbour 2010). The tidal section of the River Lagan extends upstream
approximately 9km as far as Stranmillis weir. The distance of the tidal impoundment from
Stranmillis weir to the Lagan weir is approximately 4.6km. River flow for the Lagan varies
from 70m3/s to 0.5m3/s at high and low flows respectively and mean flow rate is
approximately 3.5m3/s from April to September (Cochrane 1993, Speers 2004, Wilson
1985).
2.7 Practical Salinity Scale
In September 1980 The Practical Salinity Scale was devised and adopted by the
Unesco/ICES/SCOR/IAPSO Joint Panel on Oceanographic Tables and Standards and
endorsed by numerous other international bodies by 1981. In the Unesco 1978 publication
the Practical Salinity Scale is define as:
“The practical salinity, symbol S, of a sample of seawater, is defined in terms of the ratio K15
of the electrical conductivity of the seawater sample at the temperature of 15oC and the
pressure of one standard atmosphere, to that of a potassium chloride (KCl) solution, in which
the mass fraction of KCl is 32.4356 x 10-3, at the same temperature and pressure. The K15
16
value exactly equal to 1 corresponds, by definition, to a practical salinity exactly equal to 35.
The practical salinity is defined in terms of the ratio K15 by the following equation
S = 0.0080 – 0.1692K151/2 + 25.3851K15 + 14.0941K15
3/2 – 7.0261K152 + 2.7081K15
5/2 “
Eqn 2.12 (Unesco 1978)
The equation has validity for practical salinities, S, of 2 to 42. It should be noted that the
practical salinity scale has no units and any mistake where the practical salinity is
symbolised by parts per thousand (‰) is an error and should have the symbol, S.
The practical salinity scale can be calculated for any temperature or pressure using the
following methods and equations.
At temperature t and pressure of 1 std. atm., Rt is the ratio of the conductivity of seawater to
the conductivity of seawater of practical salinity 35, then R15 has the same value as K15 and
equation 2.12 may be used to calculate the practical salinity. As all measurements of
practical salinity are taken with reference to standard seawater conductivity (S = 35), it is the
quantity Rt that is available for calculating salinity. If the ratio is taken from in situ
measurement rather than the laboratory, then the quantity R is the ratio of in situ conductivity
to the standard conductivity at S = 35, t = 15oC and pressure, p = 0, then R is in three parts
R= RprtRt Eqn 2.13
Where R = ratio of in situ conductivity to the conductivity of the same sample and same
temperature but at pressure P = 0.
Rt = ratio of reference seawater conductivity with S = 35 at temperature t, to the reference
seawater at t = 15oC
Therefore, if Rp and rt are known Rt can be calculated from the in situ data via:
Rt = R/Rprt Eqn 2.14
It was discovered that Rp, rt and Rt can be expressed as functions of the numerical values of
the in situ parameter r, T and p, when t is in oC and p in bars (105Pa) in the following manner
Rp = 1 + p(e1 + e2p + e3p2)/(1 + d1t + d2t
2 + (d3 + d4t)R) Eqn 2.15
Where e1 = 2.0700 x 10-2, e2 = -6.370 x 10-8, e3 = 3.989 x 10-12, d1 = 3.426 x 10-2,
d2 = 4.464 x 10-4, d3 = 4.215 x 10-1, d4 = -3.107 x 10-3
17
And
Rt = co +c1t +c2t2 + c3t
3 + c4t4 Eqn 2.16
Where co = 0.676 6097, c1 = 2.00564 x 10-2, c2 = 1.104.259 x 10-4, c3 = -6.9698 x 10-7,
c4 = 1.0031 x 10-9
A correction ∆S can be added to the practical salinity calculation by replacement of Rt for K15
in equation 2.12, thus taking into account of the fairly small difference between Rt and R15.
As a result the practical salinity can be calculated via
S = ao +a1rt1/2 + a2Rt + a2Rt3/2 + a4Rt2 + a5Rt5/2 + ∆S Eqn 2.17
Where ∆S = (t-15)/(1 + k(t – 15)) (b0 + b1Rt1/2 + b2Rt + b3Rt3/2 + b4Rt2 + b5Rt5/2)
With constants ai defined in equation 2.12 and b0 = 0.0005, b1 = 0.0056, b2 = -0.0066,
b3 = -0.0375, b4 = 0.0636, b5 = -0.0144, k = 0.0162.
Equation 2.15 to 2.17 are valid for temperatures (12 to 35oC), pressures (0 to 1000 bars)
and S = (2 to 42), equation 2.17 can be used for laboratory salinometers, while in situ
measurements must begin by calculating Rp, rt and Rt before using equation 2.17 to
calculate practical salinity (Unesco 1978).
2.8 Review
It can be seen from the literature review that half-tidal barrages such as the one on the River
Lagan have been causing numerous water quality issues and hydrodynamic problems due
to saline intrusion and salt wedge entrapment. While a two-dimensional model of the river
lagan and the Lagan weir has been carried out in the past, with some success at predicting
saline intrusion levels, it is felt that a three dimensional model is required to take account of
the lateral boundary variations and assess the saline intrusion more accurately. If the model
is successful it may provide a useful tool for water resource managers, enabling them to
operate the Lagan weir more efficiently and assess the water quality issues caused by saline
intrusion.
18
Chapter 3: Methodology
3.1 MIKE 3 Flow Model FM
The assessment of saline intrusion in the River Lagan will be carried out using the MIKE 3
Flow Model FM, which is a Hydrodynamic Model created by the DHI Group. MIKE 3 can
simulate unsteady flow taking account of density variations, bathymetry and external forces
such as meteorology, tidal elevation, currents and other hydrographic conditions. It can be
used to solve numerous three dimensional (3D) problems such as, coastal and
oceanographic circulation, lake and reservoir hydrodynamics, flow variations and changes in
water level, and coastal and inland flooding. For this project it will be used to predict the
density stratification and saline intrusion caused by the Lagan weir. The 3D model is
founded on the three dimensional incompressible Reynolds averaged Navier-Stokes
equations using Boussinesq and hydrostatic assumptions. Therefore, the model is inclusive
of continuity, momentum, density, temperature, salinity equations and is closed by a
turbulence closer scheme. The finite cell method is used to carry out spatial separation of
the equations. The spatial domain, in this case the River Lagan from Stranmillis weir to the
end of the narrow section of the Victoria Channel, is discretised by subdividing it into
elements that do not intersect. A structured and unstructured mesh is used in the vertical
and horizontal planes of the 3D model respectively, the elements of the mesh forming bricks
or prisms with quadrilateral or triangular faces respectively on the horizontal plane. Data
required to generate the mesh include shoreline vectors and bathymetry (DHI Group, 2010).
3.2 Mesh Generation
To be sure of getting reliable results, it is important to ensure that the MIKE Zero mesh
generator has sufficient data to create an accurate mesh. In order set up the mesh, the area
in question needs to be defined, bathymetric values need to be obtained and boundary
conditions established.
3.2.1 Shoreline Data
As stated previously the area required to create the mesh is the River Lagan from Stranmillis
weir to the end of the narrow section of the Victoria Channel. Shoreline boundaries for this
area were obtained from the OSNI large scale database layers. These layers were imported
into the geographical information system, ArcGIS, and used to create a shoreline shapefile.
The properties for the shoreline shapefile were set in ArcCatalog, setting the shapefile as a
polygon and the coordinate system for the shoreline as Irish National Grid (GCS_TM65). It
was also important to ensure the coordinates contained z-values, so 3D data could be
obtained at a later date. Once the properties were set, the shapefile was transferred into
19
ArcMap, where the editor tool was used to trace the shoreline from the OSNI large scale
database layers. In order for the shoreline shapefile to be recognised by the MIKE Zero
Mesh Generator, it was required to convert the shapefile into a .xyz ASCII text file, thus
digitising the coordinates of the shapefile. This was done in ArcMap by using the Feature
Class Z to ASCII tool in the 3D Analyst toolbox, which converts 3D polygons to xyz ASCII
text files.
Once the shoreline was digitised, the data was imported into the Mesh Generator
workspace, ensuring that Irish National Grid was chosen for the geographical projection.
When the Mesh Generator workspace was created, the geographical projection was also
specified as Irish National Grid. The shoreline shapefile as produced in ArcMap can be seen
in figure 3.1 below.
Figure 3.1 Shoreline shapefile created in Arc Map is shown in green.
20
3.2.2 Mesh Boundary Conditions
The next step in forming the mesh was assigning boundary conditions to the shoreline data.
Logically land boundaries are those between land and water, and open boundaries are
those that have river discharge or tidal variations. In this case the open boundaries will be
Stranmillis weir and the Victoria Channel, and the land boundaries will be the shorelines.
The shoreline data appears in the mesh generator as series of interconnected vertices,
which need to be edited to generate the boundary conditions and mesh. To assign the
boundary conditions, arcs were created at the open boundaries by changing the vertices
either side of the open boundaries to nodes and assigning arc properties to each of the four
arcs created. The two land arcs, i.e. the eastern and western shoreline boundary were given
an arc attribute of 1, which is the model attribute for land. The two open boundaries at
Stranmillis weir (upstream boundary) and the Victoria Channel (downstream boundary) were
given the arc and end node attributes of 2 and 3 respectively. This allows the model to
identify the various boundary types in the mesh. Figure 3.2 below shows the boundary
conditions as seen once they are input into the flow model.
Figure 3.2 Boundary conditions as viewed in the Flow Model
21
3.2.3 Creating the Mesh
When the shoreline data is initially imported into the mesh generator the vertices along the
shoreline are very detailed. It was necessary to physically check the river shoreline to check
for sections that may contain pontoons or piles, as the river flows underneath these and thus
they can be removed from the shoreline in the mesh generator. A mesh generated from the
initial shoreline data contained numerous generated triangles that were very small,
particularly in areas where vertices were close together. While in the centre of the river
channel many of the generated triangles were too large. Triangles that are too small result in
a long simulation time when running the model. While triangles that are too large may yield
inaccurate results. Therefore the vertices along the shoreline needed to be redistributed and
maximum triangle areas needed to be set. Looking at the Lagan from Stranmillis weir to the
Lagan Weir it is apparent that some sections of the river are more uniform than others.
Because of this the river was divided into numerous sections by creating polygons for each
of the separate sections. In section of the river, where the shoreline and river area appeared
uniform, it was possible to apply a quadrangular mesh by specifying maximum stream
lengths and transversal lengths, and redistributing the vertices to fit these specifications.
When redistributing the vertices for a quadrangular mesh, it was important to ensure that
each shoreline within a polygon had the same number of segments between vertices, in
order for the quadrangles to align correctly. A triangular mesh was applied to sections of the
river that were non-uniform and had more detailed shorelines by specifying a local maximum
area for each of the polygons to be triangulated and redistributing the vertices to correspond
to the local maximum area. In revisions of the original mesh, sections of less importance, for
example the river downstream of the Lagan weir were given a higher local maximum area
than section upstream of the Lagan weir, where river and tidal flow is more important.
When all the properties were set for each polygon it was possible to generate the mesh
ensuring the smallest allowable angle for triangulation was 32o. The initial mesh was revised
a number of times to allow the model to run more efficiently. Mesh revisions will be
discussed in a further section. Figure 3.3 below shows both triangular and quadrangular
meshed areas from the first and final mesh generated, drawing attention to the difference in
mesh detail between them.
22
Figure 3.3 Triangular and quadrangular mesh detail of the first and final mesh, showing the difference in mesh
element size.
3.2.4 Bathymetry Data and Interpolation
A hydrographic survey of the Lagan impoundment from Stranmillis weir to the Lagan
Lookout, adjacent to the Lagan weir, was carried out by Six West Ltd on behalf of Atkins Ltd
and the Department of Social Development. The survey used both echo soundings and GPS
horizontal and vertical positioning to achieve accurate bathymetry data to ordnance datum
and the Irish National Grid.
The bathymetry data was obtained as a 2004 DWG file and had to be digitised into a .xyz
ASCII text file to be recognised by the MIKE Zero mesh generator. This was done using the
converter DXF2XYZ2.0, which converted the bathymetry data viewed as levels in the DWG
file to a .xyz ASCII text file, showing the levels with their relevant Irish National Grid
coordinates and a z coordinate representing the depth. Initially the converter had problems
with the DWG file as it was not compatible with the programme. It was discovered that the
programme was only compatible with the 2000 version of DWG files. So the 2004 DWG file
23
had to be saved as a 2000 version for the converter to work. The text file generated by the
converter then had to be copied into excel to remove a column of text that was not required,
as the mesh generator only accepts xyz coordinates in three columns delimited by a comma.
The excel file was then saved as a .csv file, so it could be opened in notepad and viewed
with the correct column delimiters.
Once the bathymetry was converted to a .xyz ASCII text file, it could be imported into the
mesh generator, specifying the projection as Irish National Grid. The river downstream of the
Lagan weir was not included in the bathymetry data, so depths for that section of the river
were taken from the Belfast Harbour Chart Datum for the Victoria Channel. The chart datum
for the Victoria Channel was -5m, while the chart datum for the Abercorn Basin varied from -
3m to -2m between the southern and northern sides of the basin respectively. Depth
measurements in chart datum were converted to ordnance datum by adding 2.01m to the
chart datum, giving depths of -2.99m, -0.99m and +0.01m for the Victoria Channel, the
southern side of the Abercorn Basin and the northern side of the Abercorn Basin
respectively. These values were entered into mesh generator workspace by adding them
individually as scatter data points and then saving them as a scatter data xyz ASCII text file.
When both the bathymetry data and the scatter data points were entered into the mesh
generator they could be interpolated into the mesh using natural neighbour interpolation.
Natural neighbour interpolation estimates geometries using natural neighbourhood regions
created around each of bathymetry and scatter data points by generating triangulated
irregular networks from the points. It is particularly good at interpolating spatial data sets
(DHI Group, 2009). Figure 3.4 and 3.5 below shows bathymetry data before and after
interpolation.
Figure 3.4 Closer look at bathymetry data before and after interpolation.
24
Figure 3.5 Full view of Bathymetry data before and after interpolation with the mesh.
3.2.5 Analysing the Mesh
After interpolating the bathymetry into the mesh, the mesh was analysed for mesh elements
that may cause a restricting time step when the model simulation runs. To analyse the mesh
the critical (Courant Friedrich Levy) CFL number was initially set at 0.8. The CFL number
determines the stability of the model and models are normally stable if the CFL number is
less than one. However, instabilities can still occur as the CFL number is only an estimate
calculation. For this reason the limiting CFL number is usually set to 0.8 but values can
range from 0 to 1 (DHI Group, 2009).
For shallow water equations with xy coordinates the CFL number can be defined as
CFLHD = (√gh +|u|)∆t/∆x +(√gh + |v|)∆t/∆y Eqn 3.1
Where, h is the total water depth, u and v are velocity components in the x and y directions,
g is acceleration due to gravity, ∆x and ∆y are a characteristic length scale for an element in
the x and y direction and ∆t is the time step interval.
25
For the transport equation in xy coordinates the CFL number is defined as:
CFLAD = +|u|∆t/∆x + |v|)∆t/∆y Eqn 3.2
The CFL number is calculated for each individual mesh element allowing critical elements to
be highlighted and edited using the mesh editor (DHI Group, 2009).
When running the model simulation the CFL number can also be saved as an output to
check for areas that may be unstable. A test simulation over a short time period of
approximately 6 hours was generated to check the simulation run time and thus the mesh
efficiency. However, when this simulation was run it took almost 18 hours, i.e. three times
the actual time period. Therefore, it was required to review the mesh. The mesh for the test
simulation had a maximum area of 50m2 for elements within each triangular mesh polygon.
While the quadrangular mesh polygons had a maximum stream length of 20m and a
maximum transversal length of 5m. However, vertices every 10m along the land boundary
meant that the actual stream length for each element was 10m. It was felt that both
triangular and quadrangular meshes were too detailed based on the length of time taken for
the simulation to run and thus, changes to the mesh were required.
The revised mesh had a maximum area of 200m2 for elements within the triangular mesh
downstream of the Lagan weir. While elements in the triangular mesh upstream of the Lagan
weir had a maximum area of 150m2. Quadrangular mesh polygons were revised to have a
maximum stream length of 40m and a maximum transversal length of 15m. However, when
vertices were set at 40m along the land boundary the shoreline was distorted too much.
Therefore, the vertices were set at approximately 30m, ensuring the number of segments in
each polygon were the same for both land boundaries. The area around the Lagan weir, as
seen in figure 3.6 had a particularly high CFL number, almost reaching the critical number.
This was due to a combination of a constriction in the river channel and the greater water
depth at this point. To try and correct this, the mesh in this location was split into five equal
quadrangles spanning the river and running along the length of the constriction. This
replicated the weir within the mesh allowing river and tidal flow through the constriction more
effectively. The test simulation was re-run using this mesh and the simulation time was
reduced to approximately 3 hours. The revised mesh was then used for the for the no weir
scenario simulation, which had an approximately 12 hour warm up simulation, a 2.5day hot
start simulation and 2.5day actual simulation. Using the revised mesh the simulation time
took approximately 18 hours for each 2.5 day time period.
26
Figure 3.6 Element approaching critical CFL prior to creating a quadrangular mesh at the Lagan weir location.
Again, it was felt that this was too long and the CFL output for the flow model was analysed
to find areas within the model that were approaching the critical CFL number. It was
observed that areas around Stranmillis weir, the old McConnell weir and downstream of the
Lagan weir were approaching the critical CFL number. On closer examination, shorelines
near Stranmillis weir and the old McConnell weir contained mesh vertices that were only 5m
apart. These were increased to a 10m distance and a narrow channel on the eastern
shoreline at Stranmillis weir was edited to remove areas containing small triangular
elements. Upstream of the Lagan weir the vertices on the western shoreline were edited to
fix areas containing small triangular elements. Using this mesh the simulation time took just
over 12 hours for each 2.55 day time period, which was deemed to be more acceptable.
Figure 3.7, 3.8 and 3.9 below show the areas approaching the critical CFL number at
Stranmillis weir, the Old McConnell weir and the Lagan weir respectively.
27
Figure 3.7 Critical CFL numbers at Stranmillis weir.
Figure 3.8 Critical CFL numbers at the old McConnell weir site.
28
Figure 3.9 Critical CFL numbers at the Lagan weir.
3.3 Physical Boundary Conditions
The upstream boundary lies at Stranmillis weir, here boundary conditions in terms of
freshwater dilution are assumed to be solely fresh water, as this is the head of the estuary
and thus given a value of zero on the salinity scale. Variation in river flows and water levels
were measured upstream of this point at Newforge by the Rivers Agency and this data was
required for the model simulation. The downstream boundary lies in Belfast harbour, at the
constriction in the Victoria Channel. Beyond this, boundary conditions in terms of freshwater
dilution are assumed to be fully mixed and were given a value of 32 on the practical salinity
scale. Flow at the downstream boundary is tidal and the tidal data, which was also required
for the model simulation, was calculated from Belfast Harbour tide prediction charts. In order,
for the flow data and tidal data to be in the correct format for MIKE 3 Flow Model FM a time
series had to be created for each data set. Both time series were based on data from the
24th - 26th July 2002, as this represented a time period when the tidal flow was at mean
spring tide and the aerators were not operational. This means that salinity data recorded on
these dates by PhD student David Speers, was most representative of natural spring tide
conditions in the estuary and was not affected by artificial aeration, thus giving the best data
for model calibration. Tide height and river flow time series were created as follows.
29
3.3.1 Time Series
To run an accurate simulation in MIKE 3 Flow Model FM, it is required to have an initial
warm up simulation and a hot start simulation prior to simulation of the required time period.
The warm up and hot start simulations are used to stabilize the model, so that the model is
in a “quasi” steady state condition prior to the actual simulation period. Furthermore, the last
time step of the warm up simulation is required to be the same as the first time step of the
hot start, and likewise the last time step of the hot start is required to be the same as the first
time step of the actual simulation period. The actual simulation time period is approximately
2.5 days from 24th to 26th July, as this is the time period when the salinity data was gathered.
The hot start simulation period, is usually run for the same amount of time as the actual
simulation period and thus goes from the 21st to 24th July. The warm up simulation is run for
a small amount of time prior to the hot start. In this case, the warm up simulation ran for one
tidal cycle on the 21st July. Therefore the total time series for both river flow and tidal data
ran from 02:13 on 21st July to 19:43 on 26th July.
3.3.2 Tide Height Time Series
Tidal data for the time period described above was not available but can be calculated from
the Belfast harbour tide mean spring and neap curves, if the heights of high and low tides
and thus the tidal ranges for each day were known. Tides heights are calculated with
respect to chart datum. The equation used to calculate the tide height at each time step is as
follows:
(Factor x Range) + Height of Low Tide = Tide Height Eqn 3.3
On the mean spring and neap curve the factor 1, represents high tide and the factor 0,
represents low tide. Factors between low and high tide can be extrapolated from the curve
for the required time intervals by drawing a line up from the time interval until it hits the curve
and then drawing a perpendicular line across to read the factor required. The mean spring
and neap curve is shown in figure 3.10 below.
30
Figure 3.10 Mean spring and neap curve used to calculate the tide heights time series (Belfast Harbour 2010).
The information gathered by David Speers when collecting salinity data also included the
times of high tide for each monitoring day and the ranges of tides during the time of testing.
However, the actual heights of high and low tides on each day were not given, making it
difficult to calculate the exact tidal conditions for the time period required. Furthermore, night
time tidal ranges were omitted.
Initially the first tide height time series created was used to check the run time of the flow
model simulation and thus the efficiency of the mesh. A tidal period of approximately 6 hours
from low tide to high tide was used. The range chosen was the mean spring range of 3.1m,
the mean low water spring (MLSW) of 0.4m was used for low tide and the mean high water
spring (MHSW) of 3.5m was used for high tide. The high tide chosen was 12:43 on 25th July
and thus the tide heights prior to this time were calculated in Excel from the mean spring and
neap curve every half hour, as explained above, until low tide was reached. This gave tide
heights with respect to chart datum and thus these heights were converted to ordnance
datum by subtracting 2.01m from the calculated heights. The time series created in Excel
was then saved as an ASCII file in the format required by the Flow Model. The ASCII file
could then be imported into the Time Series Editor selecting the time description as
equidistant calendar axis. The properties of the time series were defined as water level in
meters and the graphical representation as instantaneous. While the heights were calculated
every half hour the time step was required to be every 15 minutes, therefore missing heights
were calculated using the time series interpolation tool.
31
The tide height time series generated for the required time period, 02:13 on 21st July to
19:43 on 26th July, was created initially by calculating the average of the tidal ranges
documented by David Speers, the average being 2.6m, and using this to generate identical
sine curves for each tidal cycle over the required time period. High tide and low tide were
estimated by decreasing the high tide height from 3.5m (MHSW) and increasing the low tide
height from 0.4m (MLSW) until the range of 2.6m was reached. This gave a high tide and
low tide of 3.2m and 0.6m respectively. Again tide heights between these values were
calculated using the mean spring and neap curves and converted to ordnance datum. This
time series was then revised to incorporate varying tide heights over the period where tidal
ranges tidal ranges were documented, i.e. from 05:13 on 24th July to 19:43 on 26th July.
During this period tidal ranges were not documented between the evening high tide and the
following morning low tide, thus the average range was used between evening high and
morning low tide. The full tide height time series for the period 02:13 on 21st July to 19:43 on
26th July can be seen in figure 3.11.
Figure 3.11 Tide height time series with identical sinus period for the warm up and hot start flow models and the
varying sinus periods for the actual flow model
32
3.3.3 River Flow Time Series
Rivers Agency data from July 2002 recorded river flows at the Newforge gauging station
every 15 minutes and this was used as to generate the time series required by MIKE 3 Flow
Model FM. Using the time period 02:13 on 21st July to 19:43 on 26th July, a time series was
created in Excel and saved as an ASCII file in the format required by the Flow Model. The
ASCII file could then be imported into the Time Series Editor selecting the time description
as equidistant calendar axis. The properties of the time series were defined as discharge in
m3/s and the graphical representation as instantaneous. The time series produced can be
seen in figure 3.12.
Figure 3.12 River flow time series.
33
3.4 Running the Flow Model
Throughout the project a number of flow models were run as follows:
Test simulation – to check simulation run time and mesh efficiency
No Weir
Weir (Broad Crest Formula) version 1
Weir (Broad Crest Formula) version 2
Weir (Broad Crest Formula) version 3
Weir (Weir Formula 1)
This section will discuss in general terms how the models were set up dealing with
parameters that were required for all models. Differences in parameters within the various
flow models will also be discussed
The model domain was set up by importing the generated mesh file into the flow model and
selecting the number of layers required to divide up the vertical mesh. The vertical mesh
chosen was the sigma mesh, which was then divided into 5 equidistant layers and the
boundary names were defined as Stranmillis weir and Harbour for code 2 and 3 respectively.
These were the codes set originally for the open boundaries within the mesh. The time
specifications for each of the flow models are shown in Table 3.1.
Table 3.1 Flow Model Time Specifications
Flow Model Simulation Period No. Time Steps Start Date Time
Test Simulation 900sec (15mins) 26 25/07/2002 06:13
No Weir Warm up 900sec (15mins) 50 21/07/2002 02:13
No Weir Hot Start 900sec (15mins) 250 21/07/2002 14:43
No Weir Actual 900sec (15mins) 250 24/07/2002 05:13
Weir Warm Up v1 900sec (15mins) 50 21/07/2002 02:13
Weir Hot Start v1 900sec (15mins) 250 21/07/2002 14:43
Weir Actual v1 900sec (15mins) 250 24/07/2002 05:13
Weir Warm Up v2 900sec (15mins) 50 21/07/2002 02:13
Weir Hot Start v2 900sec (15mins) 250 21/07/2002 14:43
Weir Actual v2 900sec (15mins) 250 24/07/2002 05:13
Weir Warm Up v3 900sec (15mins) 50 21/07/2002 02:13
Weir Hot Start v3 900sec (15mins) 250 21/07/2002 14:43
Weir Actual v3 900sec (15mins) 250 24/07/2002 05:13
Weir Warm Up (F1) 900sec (15mins) 50 21/07/2002 02:13
Weir Hot Start (F1) 900sec (15mins) 250 21/07/2002 14:43
Weir Actual (F1) 900sec (15mins) 250 24/07/2002 05:13
.
34
3.4.1 Hydrodynamic Module
Within the hydrodynamic module numerous parameters need to be chosen in order for it to
calculate the resulting flow and salinity distributions. These parameters will be discussed in
the following section.
Solution Technique
This specifies the time and accuracy of the numerical calculations. For all flow models the
lower order, fast algorithm option was chosen for both time integration and space
discretization within the shallow water equation. This means that calculations will be faster
but less accurate than the higher order option. The minimum and maximum internal time
steps were set as 0.01sec and 30sec respectively for both the shallow water and transport
(advection-dispersion) equations. The CFL number was set to 0.8 as discussed previously
(DHI Group, 2009).
Flood and Dry
As the model is tidal, flooding and drying will occur and therefore a wetting depth, a drying
depth and a flooding depth were required. The model monitors each element within the
mesh and recalculates the simulation depending on their state of flooding or drying. An
element is wet if the water depth is greater than hwet (wetting depth). In this case both
momentum and mass fluxes are calculated. A flooded element is one where water is re-
entering the element (e.g. as the tide is flowing in or as river flow rises). An element is
flooded if it meets the following two requirements, the water depth on one side of an element
face must be less than the drying depth, hdry, and the water depth on the other side must be
greater than the flooded depth, hflood. Furthermore, the sum of the still water depth on the dry
side and the surface elevation on the flooded side must be greater than zero. An element is
dry when the water depth is less than hdry and there are no flooded boundaries along the
element faces. In this case the element is omitted from the model calculations. When an
element is partially dry the water depth is greater than hdry but less than hwet, or when the
water depth is less than hdry and one of the boundaries along an element face is flooded.
When this occurs only the mass flux is calculated and the momentum flux is zero (DHI
Group, 2009).
Recommended values for drying depth, hdry, flooding depth, hflood and wetting depth, hwet are
0.005m, 0.05m and 0.1m respectively i.e. hdry<hflood<hwet. These values were used for all flow
model simulations.
35
Density
Density is a function of both salinity and temperature but as salinity is much more dominant
in density determination, all flow models were based on density being a function of salinity
only. However, a reference temperature and salinity were required to be specified, as this
improves the accuracy of the density calculation by subtracting the reference values from the
temperature salinity fields before the density is calculated. The density is calculated from
UNESCOs standard equation of state for sea water, which is valid for temperatures of -2.1oC
to 40.0oC and salinities between 0 and 45 on the practical salinity scale. If density is only a
function of salinity then it is calculated based on the actual salinity and the reference
temperature. The reference temperature was 16oC, as this was the average water
temperature in the impoundment for July. While the reference salinity was 32, as this is the
assumed salinity of Belfast Harbour. These values were used in all flow model simulations.
Horizontal Eddy Viscosity
The horizontal eddy viscosity chosen was the Smagorinsky Formulation as this uses an
effective eddy viscosity associated with a characteristic length scale to convey sub-grid
transport (DHI Group, 2009).
The sub-grid scale eddy viscosity is given by
A = Cs2l2√2SijSij Eqn 3.4
Where Cs is a constant, l is a characteristic length and Sij is the deformation rate given by
Sij = ½(∂ui/∂xj +∂uj/∂xi) (i, j = 1, 2) Eqn 3.5
The constant Smagorinsky coefficient of was given the default value of 0.28. Minimum and
maximum eddy viscosity parameters were specified as the default values of 1.8x10-6 m2/s
and 100,000,000m2/s respectively.
Vertical Eddy Viscosity
The Log Law Formulation was chosen for vertical eddy viscosity as this uses a parabolic
eddy coefficient which is scaled with local depth as well as bed and surface stresses (DHI
Group, 2009). The Log Law Formulation is calculated by
vt = Uτh + (c1 (z + d)/h +c2 ((z + d)/h )2) Eqn 3.6
Where Uτ = max(Uτs, Uτb) , c1 and c2 are two constants, d is the still water depth and h is
the total water depth. Uτs and Uτb are the friction velocities associated with the surface and
36
bottom stresses, c1 = 0.41 and c2 = -0.41 gives the standard parabolic profile (DHI Group,
2009).
Minimum and maximum eddy viscosity parameters were specified as the default values of
1.8x10-6 m2/s and 0.4m2/s respectively. In version 3 of the broad crested weir model and the
weir formula one model damping was selected, to take account of vertical stratification.
Damping takes account of vertical stratification by using Richardson number damping of the
eddy viscosity coefficient (DHI Group, 2009). The Munk-Anderson Formulation is calculated
by
vt = vt*(1 + aRi)-b Eqn 3.7
Where vt* is the undamped eddy viscosity and Ri is the local gradient Richardson number
Ri = -g/ρo∂ρ/∂z((∂u/∂z)2 +(∂v/∂z)2)-1 Eqn 3.8
a = 10 and b = 0.5 are empirical constants.
Bed Resistance
The Bed Resistance was specified by the roughness height with constant domain set at the
default value of 0.05m, as a small value for roughness height relates to low friction (DHI
Group, 2009).
Coriolis Forcing
The coriolis forcing was chosen as constant in domain as it is not expected to vary along the
river. The constant coriolis forcing was calculated based on a reference latitude of 55o, the
latitude for Belfast.
Wind forcing, ice coverage, tidal potential, precipitation, evaporation, wave radiation and
sources were not included in the calculations for all model simulations.
Structures
In order to simulate how the Lagan weir might work, a simplified version of the weir was
initially implemented by using two broad crested weirs. Weir 1 was set at a level of -1.3m to
allow the incoming tide to travel up the river, as it was thought this was the level of the Lagan
weir when the flap gates are lowered. Weir 2 was set at a level of +0.3m for the ebb tide, as
it was thought this was the level of minimum impoundment for the ebb tide and thus the level
the flap gates were raised to during salinity data collection by David Speers. Both weirs were
input at the location of the Lagan weir by specifying xy coordinates of 334375, 374530 and
37
334505, 374530 for each of the weirs. The width of both weirs was specified as 122m, the
width of the river in this location, as measured from the shoreline shapefile in ArcMap. The
position of the weirs based on the coordinates can be seen if figure 3.13.
Figure 3.13 Position of the weirs based on coordinates
Valves were used to regulate the flow over both weirs so that flow could travel upstream only
on the incoming tide and downstream only on the on the ebb tide. When a valve allows only
positive flow, negative flow cannot occur and vice versa. For the simulation, weir version 1,
weir one was assigned a negative valve and weir two was assigned a positive valve.
However, initially it was thought that this valve allocation was incorrect, as once the
simulation was run, the horizontal profile showed the incoming tide reaching the weir but was
prevented from going much further upstream. Therefore, for the simulations, weir version 2
and 3, weir one was assigned a positive valve and weir two was assigned a negative valve,
thus allowing the incoming tide flow upstream and the outgoing tide flow downstream. On
closer examination of the vertical profiles for each weir it was discovered that the initial valve
allocation for version 1 was correct but it was felt that a combination of broad crested weir
and possible issues with heights and width of the weirs meant the model was not accurate.
For the broad crested weir formula recommended headloss factors for both positive and
negative flow across the weirs were used, as there was not expected to be a large amount of
headloss over the weirs. These values were 0.5 for inflow, 1.0 for outflow and 1.0 for free
overflow. When upstream and downstream areas are set to large numbers the total headloss
38
coefficient equals the inflow coefficient plus the outflow coefficient. The Free overflow head
loss factor is a critical flow correction factors (DHI Group, 2009).
Rapid flow response due to small changes in upstream and downstream water levels can
result when the water level gradient across the weir is small and the gradient of the
discharge across the weir is large. The Alpha zero value is used to control this by defining
the water level difference beneath which the discharge gradient is contained. The
recommended alpha zero value of 0.01m was used, as the weirs did not show oscillatory
behaviour (DHI Group, 2009).
As the scenarios using the broad crested weir formula appeared inaccurate, a fourth model
was run using weir formula one. A reassessment of how to analyse the weir was also
required. The first issue highlighted was that the weir did not extend for the full length of the
river, as it was separated by four piers. The width of each weir in the fourth model was input
as 97.5m the total length of the five gates excluding the piers. The second issue came about
from a conflict of information within the literature reviewed regarding the heights of weirs
during flood and ebb tides. Following a meeting with the river warden, John Byrne, heights
for the impounding weir were set at 0.35m OD (7.35m in relation to the invert level) and
heights for the flood weir were set at -2.06m OD (4.94m in relation to the invert level).
Furthermore, the invert level was set at -7m, the datum at the location of the weir structure
(Pers. Comm., Byrne, 2010).
Weir formula one is based on the Villemonte formula:
Q = WC(Hus – Hw)k[ 1 – (Hds – Hw)/(Hus – Hw)]0.385 Eqn 3.9
Where Q is the discharge through the structure, W is the width, C is the weir coefficient, K is
the weir exponential coefficient, Hus and Hds are the upstream and downstream water levels
respectively and the invert level the lowest datum point at the upstream or downstream
section of the weir.
Initial Conditions
In the test simulation and all warm up flow models the initial values for hydrodynamic
variables were set as constant, using surface elevation equal to 0m, u-velocity equal to
0m/s, v-velocity equal to 0m/s and ws-velocity equal to 0m/s. These values were not yet
known and would be calculated in the output files based on the tide height and river flow
data specified for each flow model.
39
For all hot start flow models the water depth (2D area) and volume output files from the
warm up flow model were used. Ensuring that total water depth was selected as the
parameter from the water depth file and u, v and ws velocities were specified from the
volume file.
For all actual flow models the water depth (2D area) and volume output files from the hot
start flow model were used. Ensuring that total water depth was selected as the parameter
from the water depth file and u, v and ws velocities were specified from the volume file.
Boundary Conditions
For all flow models the land boundary was specified as Land (zero normal velocity), meaning
full slip boundary conditions were in place, i.e. the normal velocity component is zero. This is
applied when the land attribute in the mesh is set to one, as was the case in this instance.
For all flow models the harbour boundary was set to a specified water level that varied in
time with a linear time interpolation and was constant along the boundary. This required tide
height times series to be specified for each flow model. The tide height times series used for
each flow model were discussed in the time series section above. For the test flow model
and all warm up flow models a sinus variation soft start was also specified to prevent shock
waves occurring in the model. The reference value for the soft start was set at the ordnance
datum of 0m. This would allow the model to gradually reach the required starting tide height
over a short period of approximately one hour (3600 sec).
The Stranmillis weir boundary was set to a constant specified discharge of 5.185m3/s for the
test simulation and 11.5m3/s for all warm up simulations. Again a soft start was specified.
For all hot start and actual flow models the specified discharge was varying in time, with a
linear time interpolation and was constant in along the boundary. The river flow time series
was used for all hot start and actual flow models and the vertical profile was set to uniform.
3.4.2 Temperature/Salinity Module
Equation
As stated previously, density is calculated from UNESCOs standard equation of state for sea
water, which is valid for temperatures of -2.1oC to 40.0oC and salinities between 0 and 45 on
the practical salinity scale. These values were used in all flow models as the minimum and
maximum temperatures and salinities.
40
Solution Techniques
Again, this specifies the time and accuracy of the numerical calculations. For all flow models
the lower order, fast algorithm option was chosen for both time integration and space
discretization within the shallow water equation. This means that calculations will be faster
but less accurate than the higher order option (DHI Group, 2009).
Horizontal and Vertical Dispersion
As the dispersion coefficients were not known, both horizontal and vertical dispersion were
scaled from the eddy viscosity formulation for all flow models, using the recommended
scaling factor of 1.
Initial Conditions
The spatial distribution of salinity at the beginning of the test simulations and warm up
simulations was specified at a constant value of 32 on the practical salinity scale. While the
spatial distribution of salinity at the beginning of the all hot start flow model simulations were
specified as varying in domain and salinity was based on the volume output from the
previous warm up simulation, ensuring the salinity was specified from the volume file.
Likewise the spatial distribution of salinity at the beginning of the actual flow model
simulations were specified as varying in domain, and salinity was based on the volume
output from the previous hot start flow model, ensuring salinity was specified from the output
file.
Boundary Conditions
For all flow models the boundary conditions at the harbour were set at a constant value of 32
on the practical salinity scale, as this is the assumed salinity for Belfast Harbour. Boundary
conditions at Stranmillis weir were set at a constant value of zero on the practical salinity
scale, as this is a freshwater boundary.
Heat Exchange and Sources were not included.
3.5 Calibrating the Model
To ensure that the model is simulating the saline intrusion correctly, the model needs to be
calibrated against known salinity data. Salinity test were carried out upstream of Governors
Bridge as part of PhD research done by David Speers. Tests were carried out using two
probes (one for conductivity and one for dissolved oxygen) and were converted to the
practical salinity scale using the conductivity of the water as discussed in the literature
review. The water was tested every 0.25m until the bottom was reached. From the results,
41
which can be seen in Appendix A, it was possible to see distinct differences in salinity
throughout the different layers and stratification was evident in this location.
A flow model that simulated the effects the Lagan weir has on saline intrusion accurately
was not produced. In order to do this, more research into the mixing process and dispersion
of salt water within the impoundment needs to be carried out. It will be possible to calibrate
the salinity data from the research with salinity data from the monitoring point location in the
flow model once a more accurate estimation of the dispersion coefficient is acquired, as the
dispersion coefficient is the main calibration factor within the flow model.
42
Chapter 4: Results 4.1 Results This chapter presents the results for each of the flow models discussed in Chapter 3. Plots
of salinity horizontal profiles, salinity vertical profiles and in some cases density vertical
profiles are displayed each flow model for typical tidal cycles during the period from 24th-26th
July. Surface elevations upstream and downstream of the Lagan weir and salinity time series
upstream of the Lagan weir are also used to demonstrate how certain assumption were
made.
4.2 Lagan 3D Flow Model with No Weir in Place The first hydrodynamic model simulates flows in the River Lagan up to Stranmillis weir
without the Lagan weir in place. This was done to ensure the interpolated mesh and
boundary condition time series were working effectively for future simulations with the Lagan
weir. From this simulation it was also possible to get an idea of the tidal effects on the river
and saline intrusion without the weir in place. The sections below describe the horizontal
profiles for salinity and vertical profiles for salinity and density for the period from 24th – 26th
July.
4.2.1 Salinity Horizontal Profiles
It can be seen from figure 4.1 below that saline intrusion extends as far as the Ormeau
Embankment at high tide and that there is little difference in salinity between the bottom and
top layers. Within the model there are five horizontal layers in total, which can be viewed
from left to right, the bottom most layer being on the left and the top most layer on the right.
Figure 4.1 Salinity horizontal profiles showing saline intrusion at high tide from the bottom layer (layer 1) to the
top layer (layer 5).
43
4.2.2 Salinity Vertical Profiles
Figure 4.2 below shows the vertical profiles of a typical tidal cycle for the period from the 24th
– 26th July. The profiles show the progress of saline intrusion upstream towards Stranmillis
weir as high tide approaches and its regress as the tide falls back to low tide. Evidence of a
saline wedge can be seen on the ebb tides. While the flood tide profiles shows the intrusion
advancing in vertical columns, with similar salinities in each column. It can also be seen that
little or no salt water is evident in the river beyond the location of the Lagan weir at low tide
or beyond Ormeau Embankment at high tide.
44
Figure 4.2 Salinity in the River Lagan with no weir in place, for a typical tidal cycle during the period 24th
-26h July.
4.2.3 Density Vertical Profiles
Density vertical profiles corresponding to the salinity vertical profiles above can be seen in
figure 4.3 below. Again it can be seen that the saline wedge only forms on the ebbing tide
and that little or no salt water is present upstream of Ormeau Embankment and the Lagan
weir location at high tide and low tide respectively.
45
Figure 4.3 Density in the River Lagan with no weir in place for a typical tidal cycle during the period 24h-26h July.
4.3 Lagan 3D Flow Model with Two Broad Crested Weirs (Version 1, 2 and 3)
The salinity horizontal profiles for version 1, 2 and 3 of the broad crested weir scenarios can
be seen in figures 4.4 to 4.6. From the horizontal profiles it was assumed that the valve
setting for the weirs in version 1 were incorrect as saline intrusion was minimal. Thus the
valves were reversed for version 2 and 3. Damping of the vertical eddie viscosity was also
used in version 3 in an attempt to simulate vertical stratification and increase saline intrusion.
It can be seen from figure 4.6 that damping increased saline intrusion by some 350m.
46
Figure 4.4 Salinity horizontal profiles for version 1 of the broad crested weir flow model for a typical tidal cycle
showing a minimal amount of saline intrusion beyond the Lagan weir
Figure 4.5 Salinity horizontal profiles for version 2 of the broad crested weir flow model for a typical tidal cycle
showing saline intrusion as far as Ormeau Embankment
Figure 4.6 Salinity horizontal profiles for version 3 of the broad crested weir flow model for a typical tidal cycle
showing saline intrusion between Ormeau Bridge and King’s Bridge
47
However, on analysis of the salinity vertical profile of version 3 it was clear that the valve
allocation was incorrect. It can be seen in figure 4.7 that at low tide the water level upstream
of weir drops to approximately -1.2m OD. While the flood tide only over tops the weir once
the water level reaches 0.3m OD and low water levels remain upstream of the weir until
overtopping occurs. Thus, the initial assumption that flow is positive in the downstream
direction and negative in the upstream direction for version 1 were correct. This can be seen
in the salinity vertical profiles for version 1 in figure 4.9. Surface elevations upstream and
downstream of the Lagan weir for version 1 and 3 as seen in figure 4.8 and 4.10 confirm
this.
48
Figure 4.7 Salinity vertical profiles of broad crested weir simulation version 3 for a typical tidal cycle.
Figure 4.8 Surface elevations upstream (blue) and downstream (black) of the Lagan weir for the broad crested
weir version 3, indication the sharp fall in upstream water levels.
49
Figure 4.9 Salinity vertical profiles of broad crested weir simulation version 1 for a typical tidal cycle.
50
Figure 4.10 Surface elevations upstream and downstream of the broad crested weir simulation version 1,
showing the upstream elevation remaining at the required impoundment level.
4.4 Lagan 3D Flow Model with Two Weirs using Weir Formula One
A fourth revision of the weir was modelled using weir formula one and the revised
dimensions discussed in Chapter 3. This yielded a slightly more favourable model which
demonstrated saline intrusion just downstream of the old McConnell weir at high tides as
seen in figure 4.11. The upstream advection of the salt water on the flood tide shows signs
of a saline wedge formation as seen in figure 4.12. Furthermore, an increasing saline wedge
is evident upstream of the weir at each successive low tide, this can be seen in figure 4.13.
Figures 4.14 to 4.18 show the salinity time series for each layer of the mesh from the bottom
(Layer 1) to the top (Layer 5). From these time series it is easier to see the small increases
in salinity with time upstream of the Lagan weir.
Figure 4.11 Salinity horizontal profiles for a typical tidal cycle for the weir formula one simulation, showing saline
intrusion downstream of the old McConnell weir.
51
Figure 4.12 Salinity vertical profiles for a typical tidal cycle using the weir formula one and revised dimensions,
showing the formation of a saline wedge on the flood tide.
52
Figure 4.13 Salinity vertical profiles showing the increasing saline wedge upstream of the Lagan weir at
successive low tides.
53
Figure 4.14 Salinity time series for layer 1, the bottom layer, showing the salinity upstream of the Lagan weir
increase after each tidal cycle.
Figure 4.15 Salinity time series for layer 2, the layer above the bottom layer, showing the salinity upstream of the
Lagan weir increase after each tidal cycle. A slight reduction in salinity compared to layer one is also visible.
54
Figure 4.16 Salinity time series for layer 3, the middle layer, showing the salinity upstream of the Lagan weir
increase after each tidal cycle. A slight reduction in salinity compared to layer two is also visible.
Figure 4.17 Salinity time series for layer 4, the layer below the top layer, showing the salinity upstream of the
Lagan weir increase after each tidal cycle. A slight reduction in salinity compared to layer three is also visible.
55
Figure 4.18 Salinity time series for layer 5, the top layer, showing the salinity upstream of the Lagan weir increase
after each tidal cycle. A slight reduction in salinity compared to layer four is also visible.
56
Chapter 5: Discussion 5.1 Lagan 3D Flow Model with No Weir in Place The initial hydrodynamic model simulated flows in the River Lagan up to Stranmillis weir
without the Lagan weir in place for the spring tide period of 24th-26th July. This was done to
ensure the interpolated mesh and boundary condition time series were working effectively
for future simulations with the weir. From this simulation it was also possible to get an idea of
the tidal effects on the river and saline intrusion without the Lagan weir in place. It can be
seen from the horizontal and vertical profiles produced by the model simulation that during
spring tides the saline intrusion extends as far as the Ormeau Embankment at high tide and
that water beyond this point is predominantly fresh water. Furthermore the vertical profiles
show that at low tides no salt water remains in the river upstream of the location of the
Lagan weir.
In addition, horizontal profiles show little difference in salinity between the layers within the
model from the bottom to the top, while the horizontal densities vary slightly. When this is
compared to the salinity and density vertical profiles for flood tides and high tides, it can be
seen that the saline intrusion appears as vertical columns, decreasing in salinity in the
upstream direction. This may be indicative of vertical mixing due to the tidal energy of the
incoming spring tide creating turbulent conditions due to mean flow velocity gradients and
horizontal density differences. Perhaps if the model had used a neap tide for the harbour
boundary condition, a saline wedge would have been observed, as the tidal energy of neap
tides is much smaller than that of spring tides.
Furthermore, river flow prior to the period 24th-26th July was higher than average summer
levels, while flow for period 24th-26th July was at a medium discharge, as can be seen in
figure 3.12. This may limit the extent of saline intrusion within the model and encourage
further vertical mixing when combined with the spring tide conditions mentioned above.
Another factor affecting the tidal conditions and thus the observed results may be the lack of
bathymetry data in the harbour downstream of the Lagan weir. As the bathymetry was not
known, depths from the Belfast Harbour Chart Datum were used, giving depths of -2.99m, -
0.99m and +0.01m for the Victoria Channel, the southern side of the Abercorn Basin and the
northern side of the Abercorn Basin respectively, when converted to ordnance datum. This
meant that the Victoria Channel was of uniform depth throughout the model. While in reality
both tidal and fluvial flow cause bed irregularities due to sediment transport, which in turn
57
encourages eddy formation. Eddy formation affects both tidal flow and turbulence by
creating bed resistance and thus may have influenced the turbulent vertical mixing
conditions of the incoming spring tide in all flow models (McDowell, 1997). In the Abercorn
Basin a swirling effect was observed when viewing the horizontal profiles and it tended to
remain a high in salinity. This effect may have been accentuated by the uniform depth in the
Victoria Channel, as well as a lack of bathymetry data for the basin itself, further contributing
to inaccurate results in all flow models.
Evidence of a saline wedge and a small vertical density difference can be seen on the ebb
tides.
5.2 Lagan 3D Flow Model with Two Broad Crested Weirs (version 1, 2 and 3)
In order to simulate the Lagan weir in a simple manner, two broad crested weirs were
modelled in the location of the Lagan weir. Each weir was given a width of 122m, which is
the full width of the river at that location. The height of the flood weir in place for the flood
tide was set at -1.3m, while the height of the discharge weir in place for the ebb tide was set
at 0.3m. Initially the flood tide was assumed to flow in a negative direction and the ebb tide
was assumed to flow in a positive direction, and thus the flood weir and discharge weir were
given negative and positive valve settings respectively. When the salinity horizontal profiles
for this weir set up were analysed, it was assumed that this valve set up was incorrect, as
the tide appeared to be prevented from going upstream by the 0.3m weir. Therefore, the
valve set up was reversed and the model was rerun.
The salinity horizontal profiles for version 2 of the model showed saline intrusion as far as
Ormeau Embankment, similar to that of the no weir scenario and thus it was initially thought
that the weir was working in this version of the model.
Following on from this a third version (version 3) of the simulation was carried out using the
version 2 valve set up. This simulation was run using damping of the vertical eddy viscosity,
which can be used when vertical stratification is expected in the river. As salinity data for the
simulation period showed the presence of vertical stratification, it was felt that using damping
of the vertical eddy viscosity may increase the amount of saline intrusion upstream towards
Stranmillis weir, thus bringing the intrusion more in line with the salinity data results. When
version 3 was modelled the salinity horizontal profile showed saline intrusion reaching a
point between Ormeau Bridge and Kings Bridge. Thus, damping of the vertical eddy
viscosity increased the level of saline intrusion upstream by a distance of approximately
58
350m. However, as the tide ebbed back to low tide the salinity of the impoundment was
observed to reduce back to fresh water levels.
While it was obvious from the salinity horizontal profiles that salinity levels modelled in the
impoundment would not correspond to the recorded salinity data, it was at this point that
further analysis of the salinity vertical profiles revealed that both version 2 and 3 of the broad
crested weir combination were incorrect. Based on the surface elevations upstream and
downstream of the weir viewed in the vertical profiles throughout the simulation it was
obvious that the valve setting for each weir were in the wrong direction and thus the direction
set in version 1 was actually correct. A plot of the upstream and downstream surface
elevations for the time period further confirmed this.
Following on from this, an analysis of the salinity vertical profiles for version 1 of the broad
crested weir model confirmed that the valve setting for the weirs were correct. However the
salinity vertical profiles revealed that saline intrusion only went as far as Albert Bridge at high
tide and no saline wedge remained behind the weir at low tide. In addition, the saline
intrusion again appeared as vertical columns, decreasing in salinity in the upstream
direction. Which like the scenario with no weir, may be indicative of vertical mixing due to the
tidal energy of the incoming spring tide.
5.3 Lagan 3D Flow Model with Two Weirs using Weir Formula One
It was felt version 1 of the flow model with the two broad crested weirs did not model the
Lagan weir accurately enough and thus a reassessment of how to analyse the weir was
required. The first issue highlighted was that the weir did not extend for the full length of the
river, as it was separated by four piers. In fact each of the five gates is 19.5m wide, leading
to a total width of 97.5m, 24.5m narrower than previously modelled. The second issue came
about from a conflict of information within the literature reviewed regarding the heights of
weirs during flood and ebb tides and the timing of the raising and lowering of the weir gates.
In order to solve this issue a meeting with the river warden, John Byrne, confirmed that the
gates were lowered to -2.06m OD approximately 2.5 hours prior to high tide when the water
level downstream of the weir equals the water level upstream of the weir. While the gates
were raised to +0.35m OD approximately 2.5 hours after high tide, again when the water
level upstream of the weir equals the water level downstream of the weir (Pers. Comm.,
Byrne, 2010).
A fourth model was run using the above information and weir formula one instead of the
broad crest weir formula. Damping of the vertical eddy viscosity was also used. In this case
59
the salinity vertical profiles show the saline intrusion advancing as a saline wedge on the
flood tide and reaching a point just downstream of the old McConnell weir at high tide. More
significantly, on the ebb tide an entrapped saline wedge, albeit of low salinity, remains
upstream of the Lagan weir and this entrapped saline wedge increases with each ebb tide.
This can be seen in both the vertical profiles and also in the salinity times series created
within each layer for a point just upstream of the Lagan weir within the saline wedge. This is
a possible indication that if the model had been run for a much longer period of time, the
entrapped salt wedge may have increased in salinity and also in length upstream. Indeed the
recorded salinity data is taken from July 2002, some eight years after the construction of the
Lagan weir, allowing a significant amount of time for stratification to occur in the
impoundment. Perhaps then, it was unrealistic to think that a model run over a short period
of time could model a phenomenon that could take numerous years to develop. For
example, while the model shows salinities fractionally above zero upstream of Governor’s
Bridge, salinity data recorded at this location for the simulation period displays salinities of
approximately 20-27ppt in the lower regions of the channel below -1.25m. While the layers
above -1.25m have salinities of typically 3-15ppt. Recorded salinity data can be seen in
Appendix A.
As discussed in section 5.1 above, mixing processes within the model may also be affected
by a combination of the tidal energy from incoming spring tides, high river flows and a lack of
bathymetry data downstream of the Lagan weir. This in turn may have an impact on the
results of this flow model.
60
Chapter 6: Conclusion and Recommendations
6.1 Conclusion The aim of the project was to attempt to develop a three dimensional hydrodynamic model of
the River Lagan between Stranmillis weir and the Lagan weir using MIKE 3 software to
simulate the level of saline intrusion in the river both horizontally and vertically. Lateral
variations in the shoreline of the Lagan and bathymetry data were to be taken into account to
provide an accurate mesh on which to base the 3D hydrodynamic model, where previous
two dimensional models used laterally averaged shorelines.
Based on the shoreline data and bathymetry data acquired a usable mesh was produced,
which future models can be based on. In the time frame given the mesh produced was as
accurate as possible. It may be possible to increase the efficiency of the mesh further by
increasing the element size. However, for this project it was felt that this may reduce the
accuracy of the shoreline and thus the model. Because of this the run time for the model was
possibly a little long. A lack of bathymetry data downstream of the Lagan weir and the use of
depths from Belfast Harbour Chart Datum, converted to ordnance datum for this area may
also have contributed to inaccuracies in the mesh and flow model.
The time period chosen was based on salinity data recorded on a spring tide over a period of
approximately 2.5 days in July 2002, when the aerators were not in operation, as it was
hoped to be able to calibrate the model against this data. The majority the salinity data was
recorded during times when the aerators were in operation and thus was not useful for
model calibration. Therefore, the boundary conditions created for the harbour were based on
existing river flow data and tide heights calculated from known tidal ranges for the days
mentioned above. However, not all tidal ranges were known and heights of high and low
tides were not given, leading to estimation of a number of tidal ranges. This may have lead
to minor inaccuracies within the model.
Modelling the river without the Lagan weir showed that during spring tides the saline
intrusion extends as far as the Ormeau Embankment at high tide and that water beyond this
point is predominantly fresh water. Furthermore the vertical profiles show that at low tides no
salt water remains in the river upstream of the location of the Lagan weir. It is also evident
that vertical mixing occurs during spring tides, as a saline wedge was not visible.
61
Various methods were used in an attempt to model the effects of the Lagan weir on saline
intrusion. Using two broad crested weirs of -1.3m OD for the flood weir and 0.3m for the
discharge weir yielded ambiguous results. It was discovered that this may have been due to
inaccuracies in weir heights and widths. The final model of the river with the Lagan weir in
place was based on weir formula one and weir levels and widths, received from the River
Warden, John Byrne. Damping of the vertical eddy viscosity was also used to increase
stratification and saline intrusion. When the Lagan weir was model using weir formula one
and revised dimensions, saline intrusion was observed as a saline wedge on the flood tide,
reaching a point just downstream of the old McConnell weir at high tide. Furthermore, a
small entrapped saline wedged remained upstream of the Lagan weir and increased with
each successive tide. This may indicate that the model needs to be run over a much longer
period of time to gain results similar to those observed in 2002.
In its current state the model does not correspond to recorded salinity data and thus needs
further calibration.
6.2 Recommendations for Future Work
It was felt that the amount salinity data recorded during a time when the aerators were not
operational was not sufficient for model calibration. As this effected the period over which the
simulation was run, as well as the boundary conditions. If salinity was recorded at all tidal
phases from spring tide to neap tide a model could be run for all scenarios. It goes without
saying that accurate tide times, heights and tidal ranges would need to be recorded over this
period in order to calculate accurate tide height boundary conditions. Furthermore, river flow
conditions for the full tidal phase would need to be obtained for the boundary at Stranmillis
weir. Salinity would also need to be recorded at varying depths and at different monitoring
points along the impoundment.
The full effects of Lagan weir on saline intrusion may not have been observed due to
inaccurate dispersion coefficients and thus inaccurate vertical mixing. Calibration of the
model requires an in depth study into the mixing process within the River Lagan and
identification of the dispersion coefficient corresponding to these processes. This in turn will
lead to better calibration of the model. In addition, the use accurate bathymetry data both
upstream and downstream of the Lagan weir will further aid the study of mixing process and
thus model calibration.
The Lagan weir was modelled in this project in its simplest form using two weirs of different
height to represent the flood weir and the discharge weir. In reality the Lagan weir is a series
62
of five fish belly gates. It may be more appropriate to model the Lagan weir using gates and
a time series to control these gates. For example, in MIKE 3, when gates are fully open a
factor of one is used and when gates are fully closed a factor of zero is used. Therefore, the
minimum impoundment factor needs to be calculated, as its level lies between a factor zero
and one. A time series would need to be created to indicate the lowering of the gates
approximately 2.5 hours prior to high tide and the raising of the gates to minimum
impoundment level approximately 2.5 hours after high tide. A gated weir model could also
facilitate simulations in which one or a number of the weirs are not operational and are either
fully raised or fully lowered. This could have significant benefits for river managers wanting
to simulate river conditions in the event of a weir malfunction or during weir maintenance
periods.
63
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Appendix A Salinity Data Recorded by David Speers for PhD Research
68