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.

iii

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

vi

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

vii

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

viii

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.

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Figure 4.13 Salinity vertical profiles showing the increasing saline wedge upstream of the Lagan weir at

successive low tides.

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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.

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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.

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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.

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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

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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.

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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

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