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Home , Wave shoaling, Wind wave

THE INFLUENCE OF DIFFERENT

LEVELS AND WATER HEIGHT IN

DRIVEN CIRCULATION OVER AN

IDEALIZED NINGALOO

Thesis by HELEN REYNOLDS

Centre for Water Reserch

The University of Western Australia

2001 Abstract

Ningaloo Reef is located off the western of Australia, stretching from NorthWest to Gnaraloo (Environment Australia 2000). Coral reefs are complex ecological systems closely connected to their physical environment. Therefore, effective management of a reef system requires an understanding of the physical oceanographic processes controlling the movement of water over and around the reef. This is increasingly important in the Ningaloo region as the tourism industry grows and population , such as waste disposal and boating, increase.

Studies undertaken to date have provided a basic description of the general oceanographic characteristics of the Ningaloo Reef system (D’Adamo & Simpson 2001) They have also included an analytical assessment of possible forcings on water circulation within the backreef . These studies have concluded circulation within lagoons is largely driven by wave pumping of water across the reef (Hearn et al. 1986, Hearn 1999). This project conducted a preliminary investigation of wave driven circulation over an idealized version of Ningaloo Reef. The work considered the effects of different water levels and wave conditions using the 2D vertically integrated numerical model FUNWAVE.

The results of the numerical modelling were used to describe and the magnitude and direction of flow over the reef in an idealized Ningaloo . Preliminary estimates were made of flushing times for the idealized lagoon under , tidal and wave forcing.

Numerical modelling produced results that agreed well with observed and theoretical values of speed and wave setup published in the literature. The relative importance of wave-driven flushing was reconfirmed. However, the project was highly idealized and field data for model verification was not available. This limited the conclusions that could be drawn using the magnitude of modelled setup and currents.

ii Table of Contents

Acknowledgements ______Error! Bookmark not defined. Abstract ______ii 1 Introduction ______1 2 Literature Review ______4 2.1 Regional and Climate of Ningaloo Reef______4 2.1.1 Climate and Meteorology ______4 2.1.2 Large Scale Currents ______5 2.1.3 ______7 2.1.4 ______8 2.1.5 and Salinity ______10 2.2 Reef Geomorphology ______11 2.2.1 General Coral Reef Morphology ______11 2.2.2 Geomorphology of Ningaloo Reef ______13 2.3 Circulation within Coral Reef Lagoons______17 2.3.1 Wind Driven Circulation ______18 2.3.2 Tidally Driven Circulation______19 2.3.3 Wave Driven Circulation______20 2.4 Numerical Modelling of Wave Driven Flow in Coral Reefs______30 3 Methodology ______33 3.1 Numerical Model ______33 3.1.1 Wave Generation and Breaking______33 3.1.2 Bottom Friction ______34 3.2 Model Inputs ______34 3.2.1 ______35 3.2.2 Water Levels ______37 3.2.3 Wave Forcing ______38 3.3 Simulations ______39 3.4 Model Outputs ______39 3.4.1 Surface Elevation ______40 3.4.2 Velocity Vectors ______40 3.4.3 Wave Gauges ______41 4 Results and Analysis______43 4.1 Modelled Results______43 4.2 Comparisons with Experimental Results ______43 4.3 Surface Elevation ______45 4.3.1 Wave Setup ______45 4.3.2 Comparison with Experimental Results______49 4.3.3 Wave Measurements at the Gauges ______50

iii 4.4 Velocity ______53 4.4.1 Velocity Direction______54 4.4.2 Velocity Magnitude______58 4.4.3 Cross-Reef Velocity ______60 4.4.4 Velocity at the Wave Gauges ______63 4.5 Discharge______65 4.5.1 Cross Reef Discharge ______65 4.5.2 Total Discharge ______67 4.6 Flushing Times ______69 4.6.1 Wind Driven Flushing______70 4.6.2 Tidal Flushing ______71 4.6.3 Wave Driven Flushing______71 5 Discussion______73 5.1 Wave Setup ______73 5.2 Wave Induced Currents and Discharge ______75 5.3 Flushing Times ______78 5.4 Influence of Other Factors ______79 5.4.1 Wave Period ______79 5.4.2 Bottom Friction ______80 5.4.3 Irregular Waves______80 6 Conclusions ______81 7 Recommendations ______83 7.1 FUNWAVE and Wave-driven circulation ______83 7.2 Other Forcings ______84 8 Bibliography ______85 9 Appendix A ______89 10 Appendix B ______91 11 Appendix C ______96 12 Appendix D ______100

iv List of Figures

Figure 1.1 Location of Ningaloo Reef on Western Australian Coastline showing location of the (200m isobath) (Taylor & Pearce 1999) ______1

Figure 2.1 Large-Scale Current Regime at Ningaloo (redrawn from Taylor & Pearce 1999) ______6

Figure 2.2 : Timeseries of and Current Speed at Ningaloo Reef. For location of wave rider and current meter, refer to Figure 2.4. (Hearn 1999) ______9

Figure 2.3 Main Geomorphological Features of a Coral Reef ______12

Figure 2.4: Schematic map of a section of Ningaloo Reef (Hearn 1999)______14

Figure 2.5 Division of Ningaloo Reef into sectors based on topographical features (Hearn et al. 1986) __ 16

Figure 2.6 Transect taken in the northern sector of Ningaloo Reef, (Hearn et al. 1986)______17

Figure 2.7 Definition Diagram for Wave Setup (Massel & Gourlay 2000) ______21

Figure 2.8 Setup on a Berm or a Reef ______22

Figure 2.9 Idealized reef defining theoretical model parameters (redrawn from Symonds et al. 1995)____ 23

Figure 2.10 Correlation between Hs and Current Speed, (Hearn 1999) ______28

Figure 2.11 Current speeds indicated by drogue tracking under prevailing southerly-south easterly at Turquoise Bay, (Sanderson 1996) ______29

Figure 3.1 Transect of Turquoise Bay (Sanderson 1996) ______35

Figure 3.2 Idealized Bathymetry of Ningaloo Reef Used in FUNWAVE ______36

Figure 3.3 Location of Wave Gauges relative to bottom contours______42

Figure 4.1 Modelled Wave Setup ______46

Figure 4.2 Change in Maximum Setup with water depth and wave height ______48

Figure 4.3 Non-dimensional Comparison of Setup Results ______48

Figure 4.4 Comparison of Experimental and Modelled Results (after Gourlay 1996a)______50

Figure 4.5 Surface Elevation over Time at Gauges, H=1.34______51

Figure 4.6 Change in Surface Elevation with Time at Gauges, H=1.55m ______52

Figure 4.7 Velocity Field at Lowest Water Level, Wave Height =1.55m______55

Figure 4.8 Velocity Field at Mean Water Level, Wave Height=1.55m ______56

Figure 4.9 Velocity Field at the Highest Water Level, Wave Height=1.55m ______57

v Figure 4.10 Velocity Contours at Mean Water Level ______58

Figure 4.11 Velocity Contours at the Highest Water Level ______59

Figure 4.12 Velocity Profile Along the Reef ______61

Figure 4.13 Velocity Measurements at Gauges, Mean Water Level ______64

Figure 4.14 Discharge per meter through gaps and over reef at a wave height of 1.34m ______66

Figure 4.15 Per Meter Discharge Across Reef and Through Gaps at a wave height of 1.55m ______67

Figure 4.16 Total Discharge Across the Reef Top______68

List of Tables

Table 2.1 Tidal Height at Selected Locations along Ningaloo Reef ( Tables 1996) ______8

Table 2.2 Tidal Constituent and Form Factor, (after Hearn 1999)______8

Table 3.1 Summary of Water Depths______38

Table 3.2 and Wave Period ______38

Table 4.1 Wave Heights at Wave Gauges ______53

Table 4.2 Volume Calculations at Low Water Level ______69

Table 4.3 Volume Calculations at Mean Water Level ______70

Table 4.4 Volume Calculations at High Water Level______70

Table 4.5 Discharge Over the Reef at each Water Level ______72

vi Introduction

1 Introduction

Ningaloo reef lies along the west coast of Australia, stretching from NorthWest Cape down to Gnaraloo Bay. It is the largest system in Australia and the only reef system of its kind located off the western coast of a continent. The Ningaloo Marine Park, which includes most of the main reef line, is under the jurisdiction of both state and federal agencies (Environment Australia, 2000).

Figure 1.1 Location of Ningaloo Reef on Western Australian Coastline showing location of the continental shelf (200m isobath) (Taylor & Pearce 1999)

1 Introduction

Ningaloo reef is significant for both its size and ecological composition. It is becoming an internationally famous tourist destination, based on easy access to the reef from and unique wildlife. For example, whale sharks, the largest fish in the world, are in the region of the marine park between April and June each year. It is believed they are attracted to the reef after the mass spawning of corals in March and April (Taylor & Pearce 1999). The reef also supports a diverse community of more than 500 fish species, over 200 species of coral, and 600 species of mollusc. It is home to dugongs, marine turtles, whales and dolphins (Environment Australia 2000).

The geomorphology of Ningaloo reef is significantly different to many other reef systems. The sedimentary lagoon backing the reef is shallow, with a mean depth of only two meters. It is also located very close to shore, the maximum offshore distance to the reef line is 7km. This proximity to shore is in direct contrast to other major reef systems such as the off Queensland, which is separated from the mainland by an up to 100km wide expanse of lagoon. The only large reef system similar to Ningaloo in its’ proximity to shore is found off the west-coast of Madagascar (Environment Australia 2000).

Coral reefs are productive, biochemically complex systems that exist in an oligotrophic environment. The ecology of any reef system is thus closely connected to the circulation of water, which transports nutrients and disperses animal larvae. Effective management of a reef system requires an understanding of the physical oceanographic processes controlling the movement of water over and around the reef. In addition, the prediction of water movement is vital for risk analysis of contaminant dispersal. This may become increasingly important in the Ningaloo region as the tourism industry grows and population pressures, such as waste-disposal and boating, increase.

Limited studies of the oceanographic conditions within the Ningaloo region have been completed to date (D’Adamo & Simpson 2001). AIMS conducted intensive oceanographic investigations in the lagoons and adjacent area near Vlamingh Head during 1997, including inner and outer lagoon wave measurements. These data are

2 Introduction currently being analyzed and were not available to this project (D’Adamo & Simpson 2001). The studies that have been undertaken so far have provided a basic description of the general oceanographic and geomorphic characteristics of the Ningaloo Reef system. They have also provided an analytical assessment of the possible forcings on water circulation within backreef lagoons. These studies have concluded that circulation within the lagoons is largely driven by wave pumping of water across the reef. However, these analytical assessments were not predictive and there is considerable uncertainty about the effects of natural variability in water level and conditions on wave driven flows.

The aim of this study was to conduct a preliminary investigation of wave driven circulation over an idealized version of a Ningaloo Reef lagoon. In particular, it examined differences in wave setup and wave driven velocities at a range of water levels and wave conditions using a numerical model.

3 Literature Review and Background Information

2 Literature Review

Although this study is an investigation of modelled circulation in an idealized environment, the bathymetry and forcings aim to reflect the Ningaloo Reef environment as closely as possible. In this context, the regional oceanography and climate of Ningaloo are discussed to provide a description of potential forcings on circulation. The features that make Ningaloo a unique coral reef environment are described in terms of the general geomorphology of coral reefs. A summary of the current state of knowledge on wave driven circulation and in particular, circulation around coral reefs is presented. Finally, numerical modeling of wave driven circulation is discussed.

2.1 Regional Oceanography and Climate of Ningaloo Reef

The regional oceanography and climate of Ningaloo Reef can be described in terms of the climate of the region, large-scale currents, water temperature and salinity, the tidal regime and wave conditions.

2.1.1 Climate and Meteorology

The mid-west of Western Australia, where Ningaloo Reef is located, is a very arid and windy region. Evaporation exceeds precipitation by more than 2 meters per year (D’Adamo & Simpson 2001). Most of the annual rainfall occurs during summer and cyclones associated with the southerly movement of the belt of anti-cyclonic high- systems (D’Adamo & Simpson 2001). During summer, when the belt moves to its most southerly extent, monsoonal wind systems dominate the weather (D’Adamo & Simpson 2001). Summer is also cyclone season; on average, two cyclones cross the Pilbara coast each year, accompanied by intense winds of up to 300kmh-1 and heavy rainfall (D’Adamo & Simpson 2001).

The sporadic nature of rainfall in the Ningaloo region means there is no regular flow of terrestrial run-off into the marine park (Hearn et al. 1986). water flows into the ocean through seasonal creeks, which are generally associated with breaks in the reef (Hearn et al. 1986). An important implication of the lack of regular freshwater flow is

4 Literature Review and Background Information the absence of due to river outflow, which might inhibit a vertically well-mixed . In addition, influxes of low salinity water limit coral growth as coral has a very narrow range of salinity tolerance (Mann 2000). The association of breaks in the reef with seasonal creeks may be attributable to occasional but severe coral stress caused by high influxes of low salinity water.

The wind regime around Ningaloo shows seasonal variations, which like the rainfall , change with the movement of the anti-cyclonic high pressure belt. It also shows a year-round of diurnal variability, with strong afternoon breezes replacing weaker morning offshore trade winds. In summer, wind records at Cape Cuvier (45 km south of Gnaraloo) indicate a mean of 7-9 ms-1, but this falls to about 3 ms-1 in winter due to the more variable wind directions (Taylor & Pearce 1999). Peak wind speeds exceed 14ms-1 throughout the year (Taylor & Pearce 1999). The wind patterns described by Taylor and Pearce (1999) are similar to those described by Hearn et al. (1986) at Carnarvon and Learmonth. This implies that, allowing for topographic effects such as sheltering, wind regimes are probably similar throughout the Ningaloo region.

2.1.2 Large Scale Currents

Large systems can influence the advection of water through a region. It has been suggested (Taylor & Pearce 1999) that there are two large-scale current systems, the Leeuwin and the Ningaloo, operating in the Ningaloo region.

The Leeuwin Current is a southward flowing current of low salinity, warm tropical water. It contributes to maintaining the temperature of the water off the Western Australian coast at suitable for coral growth (Taylor & Pearce 1999). The Leeuwin is driven by an along-shore pressure gradient and flows most strongly in autumn, winter and early spring when pressure head outweighs the prevailing winds (Taylor & Pearce 1999). Satellite imagery indicates the Leeuwin current is narrow and close to the shelf-break in the vicinity of Ningaloo reef. Hearn et al. (1986) reasoned that bottom friction in the shallow reef system probably prevented direct flow of tropical water into the lagoons by

5 Literature Review and Background Information out-balancing the influence of regional pressure head. However, tropical water advected onto the shelf by the current may enter the lagoons via ocean/lagoon exchange processes (Hearn et al. 1986).

Leeuwin Current

Ningaloo Counter Current

Figure 2.1 Large-Scale Current Regime at Ningaloo (redrawn from Taylor & Pearce 1999)

During summer, the prevailing southerly winds are much stronger and the increased the Leeuwin current further offshore. When the Leeuwin current is further offshore, a northward counter-current has been observed (Taylor & Pearce 1999). Taylor and Pearce (1999) proposed the counter current be called the Ningaloo Current. It is a relatively cool counter current driven by strong south-south westerly breezes during summer. It flows equator-ward, with a major perturbation to its flow between Point Cloates and Coral Bay (Taylor & Pearce 1999). This appears to re-direct some of the flow back southwards. This has important ecological significance, as the re- circulation of water means coral spawning in March and April may remain within the

6 Literature Review and Background Information

Ningaloo area itself and not be advected out of the region as previously thought (Taylor & Pearce, 1999)

2.1.3 Tides

Water level variability in the coastal environment is due to the combined effects of astronomical tides, variations and wind direction. Astronomical tides cause cyclic changes in water level and meteorological changes are superimposed on to the tidal record. The magnitude of meteorological effects can be approximated by the inverse pressure effect, where for every 1hPa drop in atmospheric pressure there is a rise of about 1cm (Pond & Pickard 1983). For example, extreme water levels may be induced by the passage of low-pressure cyclones. On-shore wind forcing during Cyclone Vance elevated water levels at Exmouth by nearly 3m (D’Adamo & Simpson 2001).

Ningaloo reef is located just north of the tidal transition area between the southwestern and northwestern Australian zones (D’Adamo & Simpson 2001). Southwestern tides are diurnal micro-tidal while northwestern tides are semi-diurnal macro-tidal. The form factor, which describes whether tides are diurnal or semidiurnal, varies considerably along the coast between Carnarvon and Point Murat (Tide Tables 1996). It is important to point out that although Hearn et al. (1986) stated that tides in the Ningaloo area are mixed, predominately semi-diurnal with a form factor near 0.8 (Hearn et al. 1986), according to Table 2.2, at Point Murat the form factor is 0.4. This implies the tide is more semi-diurnal at the northern end of the reef than at the southern end.

The mean tidal within Ningaloo is about 0.55m, which is very close to the mean sea level over the reef flat (Hearn 1999). The at springs is between one and two meters, increasing towards the northern end of Ningaloo (Table 2.1, Tide Tables 1996, Hearn 1999). Much of the reef is exposed for several hours during the lower of the two low for the four days either side of the spring tides. Cumulatively, this means the reef is exposed for about 10% of each year (Hearn 1999).

7 Literature Review and Background Information

Table 2.1 Tidal Height at Selected Locations along Ningaloo Reef (Tide Tables 1996) Tidal Levels, meters ref. To LAT1 Port Name LAT MHHW MSL MLLW Range Carnarvon 1.03 1.5 1.0 0.6 0.9 Coral Bay 0.84 1.4 0.8 0.2 1.2 Exmouth 1.43 2.3 1.4 0.5 1.8 Point Murat 1.22 2.0 1.2 0.5 1.5 Learmonth 1.55 2.6 1.5 0.5 2.1

Table 2.2 Tidal Constituent Amplitudes and Form Factor, (after Hearn 1999) Amplitude (h) meters Form Factor Tide Type

Location M2 S2 K1 O1 Carnarvon 0.3 0.14 0.2 0.13 0.8 Mixed, mainly semi-diurnal Coral Bay 0.29 0.14 0.19 0.13 0.7 Mixed, mainly semi-diurnal Point Murat 0.49 0.27 0.18 0.13 0.4 Mixed, mainly semi-diurnal Learmonth 0.66 0.36 0.19 0.14 0.3 Mainly semi-diurnal

2.1.4 Waves

The wave climate around Ningaloo and the Northwest Cape has been described by wave- rider data and shipping information (Hearn 1999, WNI Science and Engineering 2000, Sanderson 1996). As expected, the significant wave height appears to show a strong dependence on weather conditions. For example, cyclonic conditions can generate very large sea and swell waves. Extreme cyclone wave conditions typically have significant wave heights of around 10meters, wave periods of 8 to 13 seconds and arrive at the Northwest Cape from the north-northeast (D’Adamo & Simpson 2001).

Extreme conditions are significantly different to the mean wave climate. According to wave-rider data collected off the Northwest Cape (21° 36’ 27’’S, 114° 2’ 5’’E), the swell

1 Explanation of abbreviation in Table 2.1, LAT- Lowest Astronomical Tide, MHHW- Mean Higher High Water, MSL – Mean Sea Level, MLLW – Mean Lower Low Water

8 Literature Review and Background Information direction is predominately from the southwest in both summer and winter (WNI Science and Engineering 2000). Long period swell (T = 12-22s) with a mean significant wave heights (Hs) of 1.5 meters is generated in the Southern Ocean. There is a slight seasonal variation in wave height; the mean Hs in summer is 1.34m, while in winter it increases to 1.55m (WNI Science and Engineering 2000). The southwesterly swell refracts as it passes over the shelf, causing an increase in the western component of swell direction (D’Adamo & Simpson, 2001).

The WNI wave-rider data appears to agree with wave rider data (Figure 2.2) collected off Ningaloo between the 12th of August and the 12th of September 1987 (Hearn 1999). A wave rider buoy was deployed in the ocean outside the main reef in 47 meters of water. This time series recorded significant wave heights that were generally between 1 and 2 meters, with a peak value of 3 meters (Hearn 1999).

Figure 2.2 : Timeseries of Wave Height and Current Speed at Ningaloo Reef. For location of wave rider and current meter, refer to Figure 2.4. (Hearn 1999)

Local winds cause sea waves with periods of between 2 and 8 seconds and heights of 1 to 2 meters to be superimposed on the swell (D’Adamo & Simpson 2001). Even under non- cyclonic conditions sea-wave heights can reach 3.0 to 3.5 meters. Within embayments and lagoons on the reef it appears swell is blocked by the reef and sea-waves predominate (Hearn et al. 1986, D’Adamo & Simpson 2001). According to D’Adamo and Simpson

9 Literature Review and Background Information

(2001), sea-waves would be limited to about heights of about 1 meter under typical sea breeze conditions.

2.1.5 Temperature and Salinity

The combination of strong winds, shallow lagoons and lack of freshwater inflow suggests the water column would be vertically well mixed. A well-mixed water column has been observed both in deeper lagoons and in regions featuring weaker winds (Prager 1991, Kraines et al. 1998). The well-mixed assumption has been confirmed at Ningaloo by observations that appear to show there is no usual vertical temperature or salinity stratification (Hearn et al. 1986).

Although there is no normal vertical density stratification, unpublished observations have been made of horizontal density stratification in the Bills Bay area (D’Adamo & Simpson 2001). The temperature difference between the lagoon and oceanic water masses suggests large-scale intrusion of oceanic waters into lagoons in Ningaloo. This is supported by the fact flushing of a water-body is never instantaneous. Incomplete mixing across the interface between the two water masses would then tend to maintain a horizontal density gradient. Neap tides were suggested as the optimal time for oceanic incursions as the reef crest is covered by water over the entire tidal cycle (Hearn et al. 1986).

Localized areas of poor flushing are suggested by patches of high salinity/low temperature water in Bills Bay recorded by D’Adamo in 1999 (D’Adamo & Simpson 2001). Evaporative salinity change is a slower process than heat transfer in terms of equivalent density change (D’Adamo & Simpson 2001). This implies these patches of water have been undisturbed for a relatively long time. Given these high salinity/low temperature patches were found within embayments, their existence suggests mean lagoonal circulation fields bypass these areas under particular environmental conditions (D’Adamo & Simpson 2001).

10 Literature Review and Background Information

2.2 Reef Geomorphology

Coral reefs are a unique marine environment, flourishing in apparently nutrient poor waters (Mann 2000). The physical morphology of a coral reef has a significant influence on wave breaking and attenuation (Gourlay 1996a, Gourlay 1996b, Lugo-Fernandez 1998 & others). Thus, it will have a significant influence on wave driven flow and circulation. It is therefore worth describing key reef geomorphological features and their effect on wave breaking and energy attenuation.

2.2.1 General Coral Reef Morphology

Coral reefs are typically described as platform, barrier or fringing reefs. The morphology of each type of reef is shaped by the interaction of ecological and physical factors such as biological growth and the pre-existing substrates (Gourlay 1996a). Platform reefs, also known as , are flat-topped and -like. The reef tends to form a ring around a central lagoon, which may be very deep (Mann 2000). Barrier reefs, such as the Great Barrier Reef, are associated with a landmass. However, the reef line occurs some distance out to sea. For example, the main line of the Great Barrier Reef is generally located about 100km offshore (Gourlay, 1996a). Fringing reefs, such as Ningaloo, are also associated with a landmass, but they are much narrower and closer to shore than barrier reefs (Mann, 2000).

The different zones of a reef are named in Figure 2.3. The reef slope rises rapidly from depths of about 16 to 18 meters. It may have a slope as steep as 1:1 or even be nearly vertical (Massel & Gourlay 2000). The reef crest may also be known as the reef front. The reef front is the zone of the most active growth of corals and coralline algae (Mann 2000). It is exposed to the maximum wave energy, which encourages coral growth through a constant renewal of water (Andrews & Pickard 1990, Mann 2000). The reef flat is located just behind the reef crest, which may be exposed at low tide. If the crest is exposed, the reef flat may be kept moist by water and spray from the waves breaking on the reef front (Mann 2000)

11 Literature Review and Background Information

Figure 2.3 Main Geomorphological Features of a Coral Reef

The seaward reef slope effectively acts as a and dissipates the energy of incident waves. It is estimated that 70 to 95% of the wave energy impinging on a reef is dissipated through frictional processes and wave breaking (Prager 1991, Lugo-Fernandez 1998). Most coral reefs have groove and spur structures on the reef slope and top that dissipate a major fraction of the wave energy through frictional processes (Hearn et al. 1986, Gourlay 1996b). Munk and Sargent (1954) recorded the occurrence of a groove and spur system in their work at Bikini . These grooves can be described as a natural energy dissipating device tuned to the average wave characteristics (Gourlay 1996b) beginning at the depth where wave action becomes significant (Hearn et al. 1986).

Deeper channels are common in coastal lagoons behind reefs; these channels are also known as moats, gutters or drainage channels (Hearn et al. 1986). The currents within these channels are generally substantial enough to be visible to the eye (0.1 to 0.5 ms-1).

12 Literature Review and Background Information

Volume within fringing reef lagoons is usually concentrated in the moat. Outflow channels through the reef line are often fed by the flux through the moat (Andrews & Pickard 1990).

2.2.2 Geomorphology of Ningaloo Reef

Ningaloo Reef is a unique environment; although it is not as long as the Great Barrier Reef, it is much closer to shore. Few large reef systems are so easily accessible from the shoreline. The total length of the reef is approximately 280km (Hearn et al. 1986). The average distance from shore to the reef flat is 2.5 km, although this distance varies from just hundreds of meters up to 7km (D’Adamo & Simpson 2001). In contrast, the Great Barrier Reef is generally around 100km offshore (Hearn et al. 1986).

Groove and spur structures occur on the seaward slope of Ningaloo Reef. The reef line has an outward normal, orientated from northwest to southwest. Grooves appear to be absent from north-facing reef sections, expected as the swell direction is predominately southerly (Hearn et al. 1986). Grooves occur approximately every 10 meters and are normally between 10 and 20 meters long. The water depth at which wave action becomes significant and grooves can be expected to occur is approximately 20 meters under west-coast wind and swell conditions (Hearn et al. 1986).

The fringing reef is broken up into sections, where elongated sections of reef are separated by relatively deep channels. Aerial photography has been used to calculate that under low swell conditions, gaps comprise approximately 15% of the total reef length (Hearn et al. 1986). The size of the gaps in the reef varies along the reef. For example, at Turquoise Bay (Figure 2.11) the main gap in the reef is about 800 meters wide, however there are smaller gaps of about 200 meters width about 3 kilometers south of the main gap (Sanderson 1996). Figure 2.4 shows a schematic map of a section of Ningaloo Reef, including features such as the deeper , wide reef flat and sharp drop from the reef crest to the 20m isobath.

13 Literature Review and Background Information

Figure 2.4: Schematic map of a section of Ningaloo Reef (Hearn 1999)

Although Ningaloo Reef does display common features all the way along its full 280km length, it is not topographically uniform. It can be divided into smaller sections, within which the reef shows fairly homogenous geomorphological features. Hearn et al. (1986) divided the reef into three sectors, based on topographic features (Figure 2.5).

Northern sector:

This sector runs about 120 kilometers from NorthWest Cape to Point Cloates. The lagoon is less than three kilometers wide and the reef runs parallel a straight coast. The shelf break is also parallel to the shore and is located approximately ten kilometers offshore. Lengths of straight barrier reef so close to shore are comparatively rare (Hearn et al. 1986).

Central sector:

The 50-kilometer central sector runs from Point Cloates to Point Maud. In this section the lagoon is about six kilometers wide and has the structure of a long embayment with a major break in the reef at its southern end near Point Maud.

14 Literature Review and Background Information

Southern sector

The most southerly part of Ningaloo reef consists of 90 kilometers of scattered reef between Point Maud and Gnaraloo Bay. The reef at Amherst Point is very scattered and a definite structure is only evident some 35 kilometers south of Point Maud, at Pelican Point. In this sector the lagoon is about 1 kilometer wide (Hearn et al. 1986).

Transects across the reef to determine reef bathymetry have been taken at Turquoise Bay and Sandy Bay (northern sector) have been used to describe the bathymetry as much of the region is unmapped. They show the reef crest is usually at the mean sea level (MSL), the reef flat is less than 2 meters below MSL and the depth of the lagoon as a whole is about 2 meters (Sanderson 1996, Hearn et al. 1986). The gaps in the reef are deeper than the lagoon as a whole. For example, the reef break at the Northern Embayment at Turquoise Bay is about 4 meters below MSL, while the lagoon is between one and three meters deep (Sanderson 1996).

15 Literature Review and Background Information

Figure 2.5 Division of Ningaloo Reef into sectors based on topographical features (Hearn et al. 1986)

16 Literature Review and Background Information

Figure 2.6 Transect taken in the northern sector of Ningaloo Reef, (Hearn et al. 1986)

2.3 Circulation within Coral Reef Lagoons

Circulation within coral reef lagoons could have a variety of different driving forces, including wind, tides, and waves (Andrews & Pickard 1990, Kraines et al. 1998, Prager 1991). The dominant forcing will vary with the reefs’ physical and oceanographic environment. Circulation patterns determine the residence time of the water within a backreef lagoon. This makes the residence time of water within the lagoon a function of lagoon geometry, depth and bathymetric complexity, as well as circulation near gaps in the reef, mixing and the currents flowing over the reef (Andrews & Pickard 1990, Prager 1991).

Residence times are often determined using calculations of flushing. There are a variety of ways to define flushing, but generally flushing time can be defined as the time taken to replace a volume of water at a particular rate of replacement. So, flushing time can be calculated as

V τ = , Equation 2-1 Q where τ is the flushing time, V is the volume and Q is the rate of discharge either into or out of the volume.

17 Literature Review and Background Information

2.3.1 Wind Driven Circulation

Wind driven forcing may be an important component of overall circulation within a coral reef. Wind imparts a surface stress on the ocean surface, adding momentum to the water body and creating a current. The importance of wind forcing varies depends on the typical wind speed, direction and water depth within a particular lagoon. For example, wind speed and direction apparently have a significant effect on current strength in some lagoons (Prager 1991, Yamamoto et al. 1998), but at other locations modeled results including wind forcing are indistinguishable from those that do not include wind forcing (Kraines et al. 1998). The variation in these results is probably due to differences in wind speed and direction as well as topographical differences between locations.

Within Ningaloo, wind stress is predominately from the south with easterly and westerly components at different times of the year. This creates a steady southerly wind pattern with occasional more energetic storm gales from the north (Hearn et al. 1986). The direction of wind-driven circulation is function of both the wind direction and topographical effects. Wind stress within a long, shallow reef lagoon tends to set up a flow in the direction of the wind (Hearn et al. 1986). Given the morphology of Ningaloo reef, wind stress probably creates a gyre that moves water north and out of the lagoon through breaks in the reef (Hearn et al. 1986).

To determine the importance of wind-driven flow in lagoons behind Ningaloo reef, Hearn et al. (1986) made an approximate calculation of the magnitude of the current in the lagoon due to wind stress. They assumed the water depth in the lagoon was shallow enough to allow a balance between wind stress and bottom friction (Hearn et al. 1986). This yielded the relationship

ρ CU2 u = AW Equation 2-2 wind ρ CuD f

18 Literature Review and Background Information

where ρA is the density of air, CW is the surface coefficient, U is the wind speed, ρ is the density of the water and uf is a background water velocity (Hearn et al. 1986). Under -1 typical conditions for Ningaloo, Hearn et al. (1986) calculated a uwind of 0.15 m s , but stated that this was probably an over-estimate as the calculation neglected set-up forces within the lagoon. The conclusion drawn from these calculations was that wind driven circulation was probably only significant close to shore (D’Adamo & Simpson 2001)

Wind-driven flushing was estimated using the calculated value of uwind. This gave an order of magnitude estimate of water velocity of 0.1 ms-1 (Hearn et al. 1986). Disregarding additional flow over or through the reef from the starting point of the particle, it was estimated a particle would exit the reef 28 hours after release for a travel distance of 10 kilometers (Hearn et al. 1986). This yielded a wind driven flushing time in the order of about a day (Hearn et al. 1986).

2.3.2 Tidally Driven Circulation

The tidal cycle causes changes in lagoonal circulation due to fluctuations in water level over the reef and within the lagoon. The difference in water level between the ocean and the lagoon at different stages of a tidal cycle creates a pressure gradient (Prager 1991). This drives water exchange through flow over the reef and through any gaps in the reef.

The back-reef lagoon can be considered analogous to a semi-enclosed water body because it is assumed the lagoon is a bounded region. The simplest calculation of tidal flushing for a semi-enclosed water body uses the tidal prism method (Hearn et al. 1986, Kraines et al. 1998, Prager 1991). It uses only the mean lagoon volume (V), tidal period (T) and volumetric difference between high and low water (∆V) to obtain a residence time, τ.

V τ = T Equation 2-3 tide ∆V

19 Literature Review and Background Information

For a typical Ningaloo lagoon this gives a flushing time of 1 or 2 days (Hearn et al. 1986). However, in shallow water systems such as coral reef lagoons, the incoming tidal prism has a different salinity and temperature to the water within the lagoon. The incoming oceanic water may not mix completely with the water remaining in the lagoon. This could result in the formation of a vertical front that moves in on the flood tide and out on the ebb (Kraines et al. 1998, Prager 1991). According to Hearn et al. (1986) this would increase the tidal flushing time to about five days, depending on the strength of mixing forced by waves, wind and the density difference between the two water masses.

2.3.3 Wave Driven Circulation

Wave-pumping by waves breaking on the reef flat is a third forcing that may have a major impact on circulation around a coral reef. In many environments it has been observed to be the dominant forcing, controlling transport of water in and around a coral reef (Hearn et al. 1986, Kraines et al. 1986, Prager 1991, Pickard & Andrews 1990 & others).

2.3.3.1 Theory

When a wind-wave , its celerity decreases and height increases as the wave feels the effect of the sea floor. Wave steepening can only occur until a critical point, after which the wave breaks. Essentially, a wave breaks when the crest of the wave is travelling faster than the base celerity of the wave. The critical point can be described either in terms of a crest angle of 120° or a ratio of water depth to wave height.

H γ = i Equation 2-4 hb

The ratio, γ, has been found to vary across the (Hearn 1999). In most applications, it is assumed γ equals 0.78 or 0.8 (Horikawa 1978). This value is suitable for the initiation of breaking of monochromatic waves, but it has been shown

20 Literature Review and Background Information the breaking ratio decreases as waves move through the surf zone (Hearn 1999). A range of values of γ, all less than 0.55, have been suggested by several authors. The most relevant to this discussion is the result of Hardy et al. (1991) who found γ reduces to 0.4 over a coral reef.

Figure 2.7 Definition Diagram for Wave Setup (Massel & Gourlay 2000)

The excess momentum flux induced by wave breaking is called . The concept of radiation stress can be briefly explained in terms of a momentum argument. Surface waves induce a momentum, M, in the direction of . When a wave train hits an obstacle the momentum direction is changed and wave occurs at the surface of the obstacle. A force on the obstacle equal to the rate of momentum change is created (Horikawa, 1978). In shallow water, the cross-shore component of radiation stress is

3 S = ρgH 2 Equation 2-5 xx 16

Wave Setup and Setdown

Waves exert a net time averaged force on the fluid mass in which they propagate (van Rijn 1990). This creates a net momentum and net mass flux, which contributes to variations in local mean water depth (van Rijn 1990). The radiation stress gradient

21 Literature Review and Background Information

(excess momentum) is balanced by a hydrostatic pressure gradient due to a mean water level variation (van Rijn 1990), which is expressed for waves shoaling normal to the shore in the equation below.

ƒS ƒη xx + ρg(h +η) = 0 Equation 2-6 ƒx dx So, when waves move into shallow water towards the shore on a plane the decrease in momentum is balanced by an increase in water height over the still water level (Figure 2.8).

Wave setup is preceded by wave setdown at the breakpoint (Figure 2.8). Wave setdown may also be associated with the passage of non-breaking waves. Assuming no energy dissipation (i.e. no breaking) and η<

kH 2 η = − Equation 2-7 8sinh(2kh) where k is the wave number and H is the local wave height (van Rijn 1990).

Ho Set down new SWL

Figure 2.8 Setup on a Berm or a Reef

The above theory describes setup on a plane beach. One of the first analytical descriptions of wave set up over a coral reef was made by Tait (1972) who applied Bowens’ (1968) setup on a plane beach theory to observations made at Bikini Atoll.

Essentially, this showed the magnitude of the set up, ηr, was determined by the depth of

22 Literature Review and Background Information

water at the reef top (hr), the depth at breaking (hb) and the ratio of wave height to breaker depth (γ).

γ 2h  1  η =− b  ()hh− Equation 2-8 r + 8 γ 2 br 16 1 3 

Wave set up was at a maximum when hr = 0 and minimized when hb=hr. That is, setup was lowest when the water depth over the reef was equal to the critical depth and waves did not break on the reef (Gourlay 1996a). Although this theory was developed using observations of setup under relatively large swell conditions, observations of wave set up in a micro-tidal environment also agree reasonably well with Taits’ (1972) equation.

Cross Reef Flow

The magnitude of wave induced currents depends on both the geometry of the reef and magnitude of the forcing (Symonds et al. 1995). A linear, one-dimensional model, which includes wave forcing over an idealized reef has been developed by Symonds et al. (1995). This theoretical model includes both pressure driven flow and bottom friction. Although this model does not account for the three-dimensional nature of a coral reef, it does provide an explanation of the force balance driving flow over a reef.

The theoretical model was based on an idealized one-dimensional reef, shown in Figure 2.9

x=0 surf zone x h hb

β

Figure 2.9 Idealized reef defining theoretical model parameters (redrawn from Symonds et al. 1995)

23 Literature Review and Background Information

Conservation of momentum is expressed as

ƒη 1 ƒS fu g = − xx − Equation 2-9 ƒx ρh ƒx h where g is gravitational acceleration, h is the depth, f is a linear friction coefficient, η is sea surface elevation and u is the cross reef current. Sxx is the cross-shore component of the radiation stress. Equation 2-9 shows the change of momentum across the surf zone is balanced by cross reef flow and a pressure gradient. The offshore pressure gradient is increased by the high values of friction associated with flow over a rough, shallow reef (Symonds et al 1995). Conservation of mass also applies to the flow, so

ƒ(hu) = 0 Equation 2-10 ƒx

A change in water depth over the reef alters the across reef current through two physical effects. First, if the wave set up is considered to be unaltered, an increase in water depth increases the total force because of the resultant pressure gradient relative to bottom friction (Hearn 1999). This tends to increase the current. Second, the increase in water depth over the reef results in a decline in wave breaking, which reduces the wave setup and tends to reduce the current (Hearn 1999).

Symonds et al. (1995) applied this one-dimensional model to observations of wave driven currents at John Brewer Atoll on the Great Barrier Reef. They managed to get good agreement with the observed cross reef currents, however the were non-unique. Different combinations of scaled friction factor and surf zone width could be used to arrive at the same (Symonds et al. 1995).

A further limitation of this one-dimensional model was neglect of the along shore component of radiation stress and the existence of long-shore currents. This was justified in the context of their work by noting they found little correlation between offshore wave height and along reef currents (Symonds et al. 1995). In the context of an atoll, where flow is directed over the top of the reef and is not constrained by a shoreline, the omission of variability in the long-shore direction is probably not a major concern.

24 Literature Review and Background Information

However, neglect of this is a problem for the conversion of the problem two dimensions, where variability is permitted in the y-direction. For example, in shallow water there is also radiation stress in the y-direction, Syy.

1 S = ρgH 2 Equation 2-11 yy 16 The problem becomes even more complicated when the assumption that wave crests normal to the reef is discarded. This means radiation stress has both a cross-shore and a long shore component, which is resolved into Sxy.

1 S = ρgH 2 sin α cosα Equation 2-12 xy 8

On a barred beach, this non-normal component of radiation stress drives long-shore currents and potentially creates rip currents (van Rijn 1990).

For conservation of mass, water entering over the reef must also exit the lagoon. The morphology of the reef will govern how the discharge exits the reef. In a fringing reef discharge is often constrained through relatively narrow outflow gaps. The force driving discharge is the water elevation within the lagoon caused by wave setup. Wave energy is transformed from kinetic energy into potential energy within the lagoon as a higher water level (Hearn et al. 1986). Then, water exits the lagoon through gaps in the reef as potential energy is transformed back into kinetic energy (Hearn et al. 1986).

2.3.3.2 Experiments and Observations

Experimental work and theoretical modelling of waves over coral reefs has been limited due to the complexity of reef hydrodynamics. Steep slopes, the variable roughness of the reef bottom and a complicated bottom slope make it difficult to parameterize work successfully (Massel & Gourlay, 2000). Most of the work that has been done has been limited to studies of wave setup and cross reef flow on two-dimensional reefs (Gourlay

25 Literature Review and Background Information

1996a). This neglects the three dimensional nature of a real coral reef which shows bathymetric variability in both the long-shore and cross-shore directions.

Wave Setup

The earliest published observations of wave setup over a coral reef were at Bikini Atoll in the early 1950’s. Munk and Sargent (1954) observed swell waves caused the water level to be between 0.45 and 0.6 meters higher over the reef-top than in the surrounding ocean. They also observed wave pumping caused an inflow of ocean water into the lagoon (Gourlay 1996a). While measurements of setup over coral reefs in the Pacific have ranged from 0.10m to 0.6m, setup has been measured at only 0.8cm to 1.5cm over a reef in the Caribbean (Lugo-Fernandez 1998). The difference in magnitude can be explained by the micro-tidal regime and low wave energy environment in the Caribbean (Lugo- Fernandez 1998).

The magnitude of meso-scale processes, such as wave currents and wave set up depends on the geometry of the reef and the magnitude of the wave forcing. Despite different reef topographies, the results of most experimental studies, summarized in Gourlay (1996a), tend to agree that wave set up increases both with increasing wave height and period and decreasing water depth over the reef.

Cross Reef Flow

Observations of wave induced flow over reefs have been made at several locations over different types of reefs. Currents over coral reefs have almost universally been described as strong, with speeds of up to 0.8ms-1 over the reef and speeds of more than 1.5ms-1 through outflow channels (Andrews & Pickard 1990).

However, there is severe shortage of long-term observations of wave-driven currents that can be correlated to variables such as wave height and water level. The longest data series collected to date has been described by Symonds et al. (1995). It was a one-month long set of observations taken at John Brewer Reef, an atoll 70 kilometers northwest of Townsville. The data were used to observe variability in cross-reef currents due to tidal

26 Literature Review and Background Information variations in sea level and variations in wave height. Symonds et al. (1995) found cross- reef currents at sub-tidal were highly correlated with offshore rms wave height and that offshore-directed currents were associated with small waves. They theorized a forcing other than wave pumping drove the offshore-directed currents.

John Brewer Reef is a coral atoll, which has a completely different morphology to Ningaloo Reef. A study of wave driven currents in a fringing reef lagoon in Guam by Marsh et al. (1981) is may be more comparable to Ningaloo. This study showed water entered the lagoon via wave pumping over the reef. The water was then entrained into an along-shore current in a drainage channel and flowed out of the lagoon through a large break in the reef. Current speeds through the break in the reef reached speeds of up to 1ms-1 (Marsh et al. 1981).

At the small scale, the direction of flow over and around a reef is complicated by the irregular surface created by coral growth. The roughness of a coral reef varies over the reef profile, according to both the morphology and ecology of the reef (Gourlay 1996b). Coral growth also affects the porosity of the reef. The coral framework may contain significant cavities that permit flow within the reef matrix as well as over the top of the reef (Gourlay 1996b). Very little work has addressed this aspect of flow within a coral reef (Andrews & Pickard 1990, Gourlay 1996a).

2.3.3.3 Wave Driven Circulation in Ningaloo Reef

Hearn et al. (1986) made a series of observations at Ningaloo reef that led them to conclude wave generated flow was an extremely important component of lagoonal circulation. These observations included examination of aerial photos, current meters and are supported by drogue tracking by Sanderson (1996).

Aerial photos showed lines in the that run across the reef towards shore. These grooves were probably created by and scour caused by transport of biological material originating on the reef crest (Hearn et al. 1986). They are likely to be specific to

27 Literature Review and Background Information wave-pumped currents because high current speeds are required to transport particles the size of coral rubble (Hearn et al. 1986). These lines are roughly normal to the direction of the reef and terminate in a deeper channel that runs along-shore. A northward along-shore motion in the deep channels is suggested by the way the lines swing north as they approach the shore. This probably reflects the predominately southerly swell and wind waves (Hearn et al. 1986). Near breaks in the reef, the lines make a 180-degree turn and exit back out the reef (Hearn et al. 1986). The seabed grooves provide a long-term average picture of wave induced currents and cover almost the entire bottom of the lagoon (Hearn et al. 1986).

A further observation suggesting a strong linkage between wave overtopping and circulation within the lagoon was a correlation between offshore significant wave height and current speeds within the along-shore channel (Hearn et al. 1986). However, this data does not isolate how flow over the reef changes with wave height. Other forcings, particularly wind, may also affect current speed in the near shore deep channel.

Figure 2.10 Correlation between Hs and Current Speed, (Hearn 1999)

28 Literature Review and Background Information

Observations by Sanderson (1996) of surface currents at Turquoise Bay reinforced the conclusions drawn by Hearn et al. (1986) from the aerial photographs. Drogue tracking of surface currents under southeasterly to southerly wind conditions showed current vectors directed shoreward behind the reef and then turning northward to run along-shore. The most rapid movement of water occurs through the gap in the reef (Sanderson 1996). The strength of the exit current has been observed to increase as the surf-state becomes heavier (Hearn et al. 1986) but this has not been measured directly.

<5cm/s 5-10 cm/s 15-20 cm/s 20-25 cm/s >25 cm/s

Figure 2.11 Current speeds indicated by drogue tracking under prevailing southerly- south easterly winds at Turquoise Bay, (Sanderson 1996)

29 Literature Review and Background Information

2.4 Numerical Modelling of Wave Driven Flow in Coral Reefs

Numerical modelling can be a useful tool to represent physical processes that occur in the natural environment, and for making predictions about those processes. However, like any problem there are a variety of ways to approach a solution in modelling. For example, there have been two different approaches to numerical modelling of wave driven flow. One approach incorporates radiation stress as a forcing in the conservation of momentum equations, yielding an overview of meso-scale circulation in the lagoon. The other focuses on the propagation of waves in shallow water, giving better resolution of the dynamics forcing circulation.

Modelling of wave induced flow in coral reef lagoons, using a vertically integrated two- dimensional model has been carried out in three locations (Prager 1991, Kraines et al. 1998, Wolanski et al. 1993). These models have incorporated a numerical algorithm for radiation stress based on the work of Longuett-Higgins and Stewart (1964) into the conservation of momentum equation. This accounts for momentum transfer due to breaking waves, localized in reef containing model grids (Kraines et al. 1998, Prager 1991, Wolanski et al. 1993). They also accounted for bottom friction in shallow water using a quadratic friction law (Kraines et al. 1998, Prager 1991, Wolanski et al. 1993) that relates friction to water depth over the reef (Hearn 1999)

Using this approach, changing water levels associated with the tidal cycle have been found to affect wave driven flow across coral reefs. According to radiation stress theory, when the water depth has increased past the breaking depth, waves will pass over the reef without breaking. Thus, there will be no mass transport and no wave pumping (Prager, 1991, Kraines et al. 1998, Hearn, 1999). One study found the magnitude of across reef flow depended more on the water depth over the reef than on whether the tide was ebbing or flooding (Kraines et al 1998). However, the Prager (1991) study concluded that flow over the reef was strongest in the early to mid-flood tide and weakest at the ebb. The difference between these conclusions demonstrates the variability of the natural

30 Literature Review and Background Information environment. For example, the differences could be attributed to different tidal ranges, different water depths over the reef or swell conditions in Japan and the Caribbean.

While previous 2D vertically integrated modelling approaches have incorporated the effect of changing wave heights on wave driven circulation, they have also made a range of simplifying assumptions about the nature of the wave field approaching the reef. The effect of wave direction and non-monochromatic wave fields is a component of coral reef circulation that has not been addressed in any of the published studies to date. The only reference to a relationship between wave direction and current direction was made in the Prager (1991) paper. According to Prager (1991), wave induced back-reef currents tend to flow roughly parallel to the reef trend, independent of the direction of wave approach. In all cases, the simplifying assumption has been made that all wave shoal normal to the shore and radiation stress is considered only normal to the reef flat (Kraines et al 1998, Wolanski et al. 1993, Prager 1991).

These models appear to describe the general circulation features in a coral reef lagoon. However, they do not resolve smaller scale circulation features that occur on the reef. The key features required to model over a coral reef include the ability to deal with a relatively large model domain, resolution of wave breaking processes and the ability to model non-linear interactions between waves and currents. Models based on the Boussinesq equations can predict the propagation and shoaling of shallow water nonlinear waves in the nearshore region (Naval Postgraduate School 2000). Models of this type can be used to accurately predict the wave height decay and shape changes of waves propagating across the surf zone (Chen et al. 1999).

Only one study so far has attempted to use a Boussinesq model to describe wave set down and setup on a coral reef (Skotner & Apelt 1999). This study compared experimental measurements and the results of numerical modelling using a weakly non- linear model. Skotner and Apelt (1999) concluded their model accurately computed the set down and setup of regular waves of small incident wave height, but there was a tendency to underestimate wave setup as the incident wave height increased. Their

31 Literature Review and Background Information model was not fully non-linear; but they predicted that using a fully non-linear Boussinesq model would improve the agreement between modelled and experimental results (Skotner & Apelt 1999).

FUNWAVE2D is a fully non-linear Boussinesq wave model, available in the public domain. It was developed by Kirby et al. (1998) at the Center for Applied Coastal Research at the University of Delaware. It has been used in nearshore circulation studies, such as wave shoaling, rips, and wave run-up on planar (Kirby et al. 1998, Chen et al. 1999). It allows prediction of mean flows, including long-shore and rip-currents and the interaction of waves and currents (Chen et al. 1999). This is particularly important for a coral reef as strong currents exiting outflow gaps may block incoming waves.

The use of FUNWAVE to model large nearshore regions has been made possible by recent advances in computer technology (Chen et al. 1999), however model runtime can still be very long. In addition, FUNWAVE was not developed for use on the extremely steep slopes characteristic of coral reefs. However, Chen et al. (1999) stated adjustments to shore permeability and localized filtering may be used to avoid numerical instability. This means it is probably suitable for investigation of the fundamental characteristics of wave setup and wave driven flow across a coral reef.

32 Methodology

3 Methodology

The methodology details FUNWAVE2D, the numerical model used to describe circulation around the idealized reef. It also describes the inputs to the model and forms of data generated by the model.

3.1 Numerical Model

FUNWAVE2D is a publicly available fully non-linear Boussinesq wave model, developed by Kirby et al. (1998). The model simulates the nearshore propagation of nonlinear surface gravity waves and predicts the underlying unsteady flow generated by wave breaking (Kirby et al. 1998). FUNWAVE provides simulation of a range of dynamic information including velocity vectors and surface elevation. It has been used in nearshore circulation studies, such as wave shoaling and wave run-up on planar beaches (Kirby et al. 1998). It has also been used to model rip currents off a barred beach (Chen et al. 1999). The barred beach profile used to model rip currents is analogous to the profile of the idealized reef used in this study.

3.1.1 Wave Generation and Breaking

FUNWAVE calls input files for the initial wave field and either a time-series of wave amplitude or a source function for wave input. Waves are generated using an internal source mechanism, where water mass is added or subtracted along a source line within the computational domain (Kirby et al. 1998). The index line used in all runs was x=31. FUNWAVE uses a spatially distributed source function f(x,y,t) where f(x,y,t)=g(x)s(y,t). g(x) is a Gaussian shape function and s(y,t)=Dsin(λy-ωt) describes the wave form, where

D is the magnitude of the source function and λ is the component of the wave number in the y-direction (i.e. λ=ksinθ) (Kirby et al. 1998). Calculation of the source function requires information about the , direction and power of the wave field (Kirby et al. 1998). The wave field may be monochromatic or directional.

33 Methodology

Sponge layers are placed at the ends of the domain to damp the energy of outgoing waves with different frequencies and directions (Kirby et al. 1998). The usual values (Kirby et al. 1998) were used for the coefficients of the three different types of sponge layers.

* The start and finish of wave breaking is determined by the parameter ηt (Kirby et al.

1998). For bar/trough beaches this parameter is defined as

h 0.15 gh t ? 5 g η = t − t Equation 3-1 t* + 0 − ≤ − < h 0.35 gh (0.15 gh 0.35 gh) 0 t t 0 5 h g 5 g where h is the water depth, g is gravitational acceleration, t0 is the time when wave breaking occurs, and t-t0 is the age of the breaking event (Kirby et al. 1998).

3.1.2 Bottom Friction

Bottom friction is modelled in FUNWAVE using the quadratic law (Chen et al. 1999),

f R = uα uα Equation 3-2 f h + η

The friction coefficient was chosen as f=4.0 x 10-3. The choice of f was taken at the upper end of the range of typical values suggested by Kirby et al. (1998). This is still likely to be an underestimate of the actual friction coefficient over a coral reef (Gourlay 1996a).

3.2 Model Inputs

FUNWAVE calls input files for the water depths within the model domain and the wave field. The contents of the input files are described in the following sections. Details of the data files used, including relevant parameter values, are provided in Appendix A.

34 Methodology

3.2.1 Bathymetry

Ningaloo Reef is not well mapped, and a bathymetric map suitable for digitization was not available. Instead, an idealized bathymetry was generated based on the general characteristics of the Ningaloo lagoons described by Sanderson (1996), Hearn et al. (1986) and Hearn (1999). The bathymetry was generated by adapting MATLAB code developed by Johnson (2001). The reef bathymetry included the usual geomorphic features described in Section 2.2, such as a steep reef face, a slightly elevated reef rim and a broad reef flat (Figure 3.1). It does not include a deeper channel within the lagoon. This feature was omitted as flow was not constrained in the along-shore direction due to the open boundary condition of the model. Other small-scale bathymetric irregularities, such as the spur and groove system, could not be resolved within the spatial scales used in the model domain.

Figure 3.1 Transect of Turquoise Bay (Sanderson 1996)

35 Methodology

Figure 3.2 Idealized Bathymetry of Ningaloo Reef Used in FUNWAVE

In the idealized bathymetry (Figure 3.2), the reef ran parallel to the shoreline with a north-south orientation, approximately 1.8km offshore. The reef crest was 100 meters wide and was backed by a reef flat 350 meters wide. The reef line was broken by two gaps. A wide range of gap widths has been observed along the Ningaloo reef line (Sanderson 1996, Hearn et al. 1986). To investigate the differences in circulation caused by differences in gap width and depth, the gaps were asymmetric. Gap 1 was 600 meters wide and 4 meters deep. Gap 2 was wider (800 m) and deeper (6m) than Gap 1. The stretch of unbroken reef between the two gaps was 2000m. The backreef lagoon is generally shallow at Ningaloo (Sanderson 1996, Hearn et al. 1986). Depths typically range between 1 and 2 meters (Figure 3.1). The lagoon depth in the idealized bathymetry was set at -2 meters datum level. The beach had a slope of 1:15 and a width of 200 meters. The water depths at the datum level over each part of the bathymetry are summarized in the first column of Table 3.1.

36 Methodology

The model-grid was a Cartesian domain divided into 301 10-meter wide grids in the cross-shore direction and 201 20-meter long grids in the along-shore direction. This gave a total model domain of 4km by 3km. The grids were non-square as a compromise between the size of the lagoon and resolution of wave processes. Greater resolution in the cross-shore direction than the along shore direction was required to accurately capture the processes occurring on the face of the waves as they break. Offshore width from the reef crest to the boundary was originally 1000m, however a preliminary model run suggested greater width was required to prevent outflow being pushed back into the reef gaps. The offshore width was increased to 1500 meters; this appeared to allow sufficient space for wave generation in the ocean.

3.2.2 Water Levels

The water levels used in the model were based on a combination of depth observations (Hearn et al. 1986, Sanderson 1996) and tidal information from points along the Mid- west coast (Tide Tables 1996).

Observations of water depth (Hearn et al. 1986, Sanderson 1996) were used to establish datum water levels within the lagoon. The reported mean sea level (MSL) over Ningaloo reef is 0.53m (Hearn, 1986). For convenience, this was rounded up to 0.55m. The level of the lowest water, 15cm below the reef crest, was established by the observation that the reef was exposed at low water for four days either side of spring tide (Hearn 1999).

The magnitude of the water level range was established using tidal records. Tide tables indicate the range of MLLW to MHHW varies along the coast from approximately 0.9 meters at Carnarvon to 2 meters at Point Murat (Table 2.1). However, Hearn et al (1986) found the predicted tides at Carnarvon correlated better in phase and amplitude to the tides in their study area than the tides at Point Murat (Hearn et al. 1986). For this reason, the final choice of a 1.15m range in MLLW to MHHW was based on the tidal range at Coral Bay, at the south end of the reef rather than Exmouth, at the northern end of the reef. Water levels used in the model runs are summarized in Table 3.1.

37 Methodology

Table 3.1 Summary of Water Depths

Location AHD MLLW Mid 1 MSL Mid 2 MHHW Depth from 0 AHD 0 0.05 0.25 0.55 0.85 1.15 Off reef -16 16.05 16.25 16.55 16.85 17.15 Reef crest 0.2 -0.15 0.05 0.35 0.65 0.95 Reef flat 0 0.05 0.25 0.55 0.85 1.15 Lagoon -2 2.05 2.25 2.55 2.85 3.15 Gap 1 -4 4.05 4.25 4.55 4.85 5.15 Gap 2 -6 6.05 6.25 6.55 6.85 7.15

3.2.3 Wave Forcing

The model was run using a seasonally divided monochromatic wave regime. WNI Science and Engineering (2001) provided percentage occurrence data from their wave rider off the Northwest Cape, which was used to determine the wave regime at Ningaloo. The data was recorded at 21° 36’ 27’’S, 114° 2’ 5’’E between June 1999 and July 2000.

The water depth at the recording location was 200m MSL (WNI Science and Engineering 2001).

The percentage occurrence matrices were divided into seasonal sea and swell. Summer was defined as October to March, while winter was defined as April to September. Swell waves are considered more significant in wave-pumping than sea waves, consequently the wave field used in the model was based on swell conditions. The significant wave height and peak period for seasonally divided swell are summarized in Table 3.2.

Table 3.2 Significant Wave Height and Wave Period Summer Winter

Max Min Mean Max Min Mean Wave Period (T) s 23.08 9 12.95 21.68 9 14 Significant Height (Hs) m 4.087 0.348 1.335 4.098 0.32 1.55

38 Methodology

According to the WNI data, swell arrives at the Northwest Cape from the southwest more than 90% of the time in both summer and winter. This was incorporated into the model by setting the wave direction at 45 degrees to the reef line.

3.3 Simulations

The number of model runs was severely limited by the very long run-time required by each simulation. Producing an “hour” of model time required a run-time in the order of days. Minimum coverage was provided by runs simulating circulation patterns at five discrete tidal water levels with two different wave regimes for a total of 10 runs.

The size of the time step dt was chosen using

dt < 0.5dx Equation 3-3 ghmax

where dx was the grid size in meters in the cross-shore direction and hmax was maximum water depth (Kirby et al. 1998). This gave a value of 0.43s, which was rounded up to 0.5s to reduce run time slightly for no obvious loss of stability.

One of the runs, at hr=0.05m, Ho=1.55m, crashed due to numerical instability. The instability could have been fixed by decreasing the size the time-step or increasing the porosity of the reef to reduce reflection (Johnson pers. comm. 2001). Increasing the porosity of the reef, while not unreasonable in terms of reef morphology, may have reduced the comparability of the runs. However, reducing the time-step was not an option due to the extended run-time required by small time-steps. Consequently, the hr=0.05m and Ho=1.55m run was omitted from the results.

3.4 Model Outputs

FUNWAVE outputs a range of dynamic information, including velocity and surface elevation. The data is output for each grid point and averaged over a defined number of

39 Methodology wave periods to condense the size of output files. The length of the time average depends on the number of waves over which the average is taken and the period of those waves. For all runs, a five-wave average was taken. During the summer runs, the wave period was 13 seconds, so averaged results were output every 65 seconds. The wave period in winter was one second longer, so results were output every 70 seconds. However, a time- series of velocity and surface elevation at each time-step was recorded at five points within the model grid using “wave gauges”.

It took some time for the simulation to ramp up and approach a fully developed, relatively steady velocity pattern. The exact length of time varied between simulations but was generally between 45 and 50 mean time-steps. Comparisons between the outputs for different water levels were made on the 50th mean time-step. This ensured comparability between steady-state model simulations.

3.4.1 Surface Elevation

The initial surface elevation was defined as the mean water level at every point it the model domain. The time averaged output of η was used to determine the mean water elevation within the model domain. This was then plotted to show wave setup and setdown over the reef.

3.4.2 Velocity Vectors

The initial velocity of all points within the domain was zero. The depth integrated velocity vectors for the entire model domain could be visualized as an animation cycling through the time averaged results or as single frames taken at each mean time-step. Velocity vectors could also be extracted and displayed as transects in the along-shore or cross-shore direction. The velocity along the reef line was isolated and displayed to highlight how velocity changes with depth along the reef line.

The u components of the velocity vectors were used to calculate the mass flux of water across the reef. The values were used to interpolate a velocity profile along the front of

40 Methodology the reef. The mass flux was calculated through grids 10 meters wide and with a height equal to the water depth.

3.4.3 Wave Gauges

In FUNWAVE, “wave gauges” record u, v and η at a point without time averaging the variables. This allows visualization of the variation in time within the mean time-step, in this case five waves. Wave gauges were positioned at five points along the reef line. There were five gauges positioned along the reef crest on the same along-shore line. Two of the gauges were positioned 200 meters apart within the shallower gap. There were another two gauges positioned within the deeper gap, also 200 meters apart. The last gauge was positioned over the reef flat. Gauge position relative to the reef flat and gaps is indicated in Figure 3.3.

The velocity data were used to construct plots showing the magnitude and direction of the velocity at the each gauge for each combination of water level and wave height. Comparisons between the simulations were made using the last six waves before the model run finished.

41 Methodology

Location of Gauges Along the Reef 0 3 1 2 4 5

s 1 r e t 2 e m 3 , h t p 4 e D 5

6

7 0 500 1000 1500 2000 2500 3000 3500 4000 Distance Along the Reef, meters

Figure 3.3 Location of Wave Gauges relative to bottom contours

The water elevation η recorded at the gauges was used to determine the wave height at each location. Wave height was determined using

H=max(η)-min(η) Equation 3-4

42 Results and Analysis

4 Results and Analysis

The results of the nine successful model simulations were data sets of surface elevation and velocity. These results were used to calculate discharge at different water levels. Preliminary estimates of wind, tidal and wave driven flushing times were calculated for the idealized lagoon.

4.1 Modelled Results

The results of the numerical modeling were used to describe the dynamics of circulation over the idealized Ningaloo reef. The results obtained can be summarized as follows. Surface elevation data were used to describe wave breaking and wave set-up over the reef. Surface elevation data taken at the wave gauges were used to identify changes in waveform and height. Velocity data were used to describe the magnitude and direction of flow within the lagoon. The still water level and velocity data were used to calculate discharge at different water levels. Where appropriate, modelled set-up was compared with experimental results from Gourlay (1996a). Finally, estimates were made of the flushing time of the idealized lagoon under wind, tidal and wave forcing.

4.2 Comparisons with Experimental Results

One of the difficulties in working with a numerical model is determining if the results give a good approximation of the environmental processes being represented. In the study of coral reef circulation it is difficult to compare results to the real world directly, as there is a scarcity of current meter or setup measurements taken over real reefs. This is especially true for currents through outflow gaps. In addition, several authors (Gourlay 1996b, Pickard & Andrews 1990) have pointed out that reef profiles are very variable and it cannot be expected that results in one location will give a good description of the conditions at other locations. In particular, Gourlay’s (1996b) comparison of several sets of experimental data showed clearly that reef profile will have a considerable effect on wave setup.

43 Results and Analysis

Despite these problems, comparisons of wave setup values have been attempted with Gourlay’s (1996a) experimental results. There are enough similarities between the experimental and modelled scenarios to potentially allow a comparison. Gourlays’ (1996a) experimental set-up was a “relatively smooth, impermeable horizontal reef top, with a steep, rough reef face subjected to steady, regular waves.” The modelled scenario could also be described as a relatively smooth, impermeable horizontal reef top. However, there was a step down of 20 centimeters from the reef crest to the reef flat in the modelled bathymetry. This was probably less important than the similarity between the model and experiment of the reef face slope. Gourlay (1996b) identified one of the main controls on set up being the reef face slope, because it controls attenuation of wave energy as the waves approach the reef. The modelled reef face had a slope of 1:1.2, while the experimental reef had a slope of 1:1. The modelled reef face was not as rough as the experimental reef face. Both reefs were subjected to steady, regular waves, although the direction of wave approach differed. In the experiment waves approached normal to the reef, while in the numerical model the waves had a 45° angle of approach.

Dimensional analysis was required to compare the modelled and experimental results. The dimensionless parameters used follow from the argument of Gourlay (1996a). He stated that for a given reef geometry, including roughness, the maximum setup, ηmax, and the unit discharge q, are functions of wave height H, period T, water depth on the reef hr, and gravitational acceleration g, i.e.

(ηmax, q) = f(H, T, hr, g) Equation 4-1

He showed a suitable set of parameters for describing non-dimensional wave setup were

η  η max = hr √ f , √ Equation 4-2 Ho Ho T gHo ↵

44 Results and Analysis

4.3 Surface Elevation

Surface elevation data were used to determine wave setup and wave set down. Values of maximum wave setup were compared with Gourlay’s (1996a) experimental values.

4.3.1 Wave Setup

Wave setup was calculated by taking the mean of the surface elevation across the reef flat and the gaps. Bottom contours were used to define the boundaries between the gaps and the reef flat.

Wave set down began before the usual surf-zone wave breaking condition of hb/H = 0.78 was reached. This condition occurred in the same grid square, grid 90, for both the wave heights of 1.34m and 1.55m. The location of grid 90 is indicated by a straight-line through 900m offshore on Figure 4.1. The end of the reef flat was also indicated by a straight-line on Figure 4.1. These lines highlight the rapid changes in mean surface elevation across the reef flat and the more gradual changes through gaps in the reef.

The low water surface profile was distinct from the other surface profiles at both wave heights. Setup peaked much closer to the front of the reef than at the other water levels and it was then constant across the reef into the lagoon. There was no change in surface profile that might indicate a change in bottom contours at the leeward edge of the reef. At both wave heights the final set-up within the lagoon was lowest at the low water level.

There appeared to be some wave set down in the gaps in the reef. The size of the set down varied little with changes in water depth or gap width. The surface elevation did increase from the front of the gap to the back, and once the gap met the lagoon, the water level increased to converge with the final setup in the lagoon.

45 Results and Analysis

, n o Mean Surface Elevation from Offshore to Shore Over the Reef Flat, H =1.34m i o t 0.1 a v e 0 l E -0.1 s r e e -0.2 c t a e h /H =0.78 Lagoon starts f -0.3 r o m r (A) u -0.4 S, n 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 o i Me an Surface Ele vation from Offshore to Shore Through Ga p 1, H =1.34m t 0.1 o a v 0 e h =0.95 l r E -0.1 h =0.65 s r re h =0.35 e -0.2 r c t h =0.05 a r e f -0.3 h =-0.15 m r r (B) u , -0.4 S n 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 o i Mean Surface Elevation from Offshore to Shore Through Gap 2, H =1.34m t 0.1 o a v 0 e l E -0.1 e -0.2 c a f -0.3 r (C) u -0.4 S 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 Distance from Offshore, meters

, n o Mean Surface Elevation from Offshore to Shore Over the Reef Flat, H =1.55m i o t 0.1 a v 0 e l E -0.1 s er e -0.2 h /H=0.78 c r Lagoon starts at fe -0.3 rm (A) u -0.4 S, n 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 o Mean Surfa ce Elevation from Offshore to Shore Through Ga p 1, H =1.55m i o t 0.1 a v 0 e l h =0.95 sE -0.1 r r h =0.65 e -0.2 r tc h =0.35 a r e -0.3 h =-0.15 mf r r (B) ,u -0.4 nS 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 o Mean Surface Elevation from Offshore to Shore Through Gap 2, H =1.55m i o t 0.1 a v 0 e l E -0.1 e -0.2 c a f -0.3 r (C) u -0.4 S 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 Distance from Offshore, meters

Figure 4.1 Modelled Wave Setup

46 Results and Analysis

The magnitude of the wave set down was greater for larger wave heights, but there did not appear to be a corresponding increase in setup. The size of the final mean setup within the lagoon did not appear to vary greatly with water depth either. The final setup experienced in the lagoon was a few centimeters different despite a water depth range of one meter.

Generally, set-down on the reef increased as the water level decreased. The greatest set- down occurred at the second lowest water level. The point of maximum set-down also moved shoreward as water depth decreased. However, the point of maximum set-up converged at the leeward edge of the reef.

The maximum surface elevation at each water level over the reef flat was plotted against the still water depth at the reef crest in Figure 4.2. This clearly shows a trend for the

Ho=1.34m run where set up decreases as water depth increases. For the Ho=1.55m run, the 0.35m and 0.65m runs were on the same line as the smaller wave heights. However, the setup at the highest water level was more than a centimeter greater when the run was repeated with the larger wave-height. The setup on the reef flat when the water level was below the reef crest was low, and not on the line of the other results.

47 Results and Analysis

e Change in Maximum Mean Water Surface Elevation with SWL Depth at Reef Crest l E 0.055

e c H =1.55 a o 0.05 H 1.34 f o= r u S 0.045 r e t a 0.04 W

n a 0.035 e M

m u 0.03 m i x a 0.025 M

0.02 -0.2 -0.05 0.1 0.25 0.4 0.55 0.7 0.85 1 1.15 Still Water Depth on Reef Crest, meters

Figure 4.2 Change in Maximum Setup with water depth and wave height

Non-dimensional Comparison of Set-up Results 0.0012

0.001 Modelled Data 0.0008 Linear 0.0006 (Modelled y = -0.0006x + 0.0011 Data) 2

/(Tsqrt(gHo)) R = 0.7535 η η η η 0.0004

0.0002

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 hr/Ho

Figure 4.3 Non-dimensional Comparison of Setup Results

48 Results and Analysis

As the model runs were not controlled for wave period, set up results were non- dimensionalized for set up, offshore wave height, period and water depth at the reef crest (Figure 4.3). This was done using the non-dimensional parameters

h  η r √ max √ η √ and , where max was the maximum set-up on the reef top, hr was the H ↵ √ o T gH o ↵ still water level depth at the reef crest and Ho was the offshore wave height,. As suggested by Gourlay (1996a) and described in Section 4.2. The set up values when the water level was below the reef top were omitted. The remaining data fit a linear relationship with an R2 value of 0.75. This was only slightly different to the R2 value of 0.77 calculated for the plot of water depth versus setup (Figure 4.2).

4.3.2 Comparison with Experimental Results

Gourlay’s (1996a) experimental results for set-up were compared with modelled results using the same parameters as in the previous section. The two series of experimental data compared against represented a “fringing” reef and a “platform” reef. In the fringing reef flow was constrained to remain within the lagoon and it could only flow out of the lagoon during the backwash phase of wave breaking. In the platform reef scenario, flow moved across the reef and exited the lagoon at the back of wave tank. However, flow was still constrained laterally.

Including the modelled results initially suggested values of wave setup had been seriously underestimated (Figure 4.4). However, it should be noted that data for various “natural” reef profiles were consistently below that for an idealized horizontal reef (Gourlay 1996b). Probably more importantly, lateral variability was not permitted in either experimental scenario. In contrast, lateral flow was permitted and clearly occurred in the modeled scenario.

49 Results and Analysis

Comparison of Experimental and Modelled Results

0.035

0.03

0.025 Platform 0.02 Modelled 0.015 Fringing /Tsqrt(gHo) η η η η 0.01

0.005

0 0 0.5 1 1.5 2 2.5 3 hr/Ho

Figure 4.4 Comparison of Experimental and Modelled Results (after Gourlay 1996a)

4.3.3 Wave Measurements at the Gauges

The wave gauges recorded a time-series of water elevation at each time-step. This was used to describe the waveform as it passed each location.

A time-series of measurements was produced for a 75second period as this amount of time exceeded the number of time-steps over which the mean results were produced. That is, mean results were produced over 5 wave periods, which was equivalent to 65seconds in summer and 70seconds in winter. The pattern was steady and cyclic so for visual clarity a 25second portion of the time-series was used in Figure 4.5. Incident wave height was determined at the five wave gauges by subtracting the minimum surface elevation from the maximum surface elevation. These values are summarized in Table 2.1.

50 Results and Analysis

e M Change in Water Elevation with Time at Gauges 1 , n 0 o i -1 t -2 Gauge 1 a v 0 5 10 15 20 25 e l 1 E 0 e -1 c a -2 Gauge 2 f r 0 5 10 15 20 25 u S 1 0 -1 -2 Gauge 3 0 5 10 15 20 25 n o i 1 t a 0 v e -1 l -2 Gauge 4 E 0 5 10 15 20 25 e c 1 data1 a f 0 data2 r data3 u -1 data4 S -2 Gauge 5 data5 0 5 10 15 20 25 Time, Seconds

0.95m 0.65m 0.35m 0.05m -0.15m

Figure 4.5 Surface Elevation over Time at Gauges, H=1.34

51 Results and Analysis

e M Change in Surface Elevation with Time at Gauges 1 , n 0 o i -1 Gauge 1 t -2 a v 0 5 10 15 20 25 e l 1 E 0 e -1 c Gauge 2 a -2 f r 0 5 10 15 20 25 u S 1 0 -1 -2 Gauge 3 0 5 10 15 20 25

n o i 1 t a 0 v e -1 l -2 Gauge 4 E 0 5 10 15 20 25 e c 1 a f 0 r u -1 S -2 Gauge 5 0 5 10 15 20 25 Time, Seconds

0.95m 0.65m 0.35m -0.15m

Figure 4.6 Change in Surface Elevation with Time at Gauges, H=1.55m

52 Results and Analysis

Table 4.1 Wave Heights at Wave Gauges SWL @ Crest -0.15 0.05 0.35 0.65 0.95

Ho 1.34 1.55 1.34 1.55 1.34 1.55 1.34 1.55 1.34 1.55

Gauge 1 0.22 0.32 1.26 - 1.31 1.42 1.29 1.39 1.25 1.34 Gauge 2 0.22 0.29 1.20 - 1.25 1.30 1.30 1.35 1.29 1.41 Gauge 3 0.19 0.29 2.50 - 1.99 2.47 1.65 1.89 1.37 1.56 Gauge 4 0.27 0.37 1.18 - 1.22 1.27 1.08 1.21 1.08 1.26 Gauge 5 0.26 0.36 1.12 - 1.37 1.17 1.32 1.25 1.08 1.11

The waveform recorded at the gauges in Gap 1 was steady at each water level. The wave was peaked, with a broader and slightly asymmetric trough. There was very little difference between the recordings at Gauges 1 and 2, which were located 200 meters apart in the narrower gap.

Gauge 3, on the reef flat, recorded different waveforms at each water level. The amplitude of the wave was greatest at the second lowest water level. However, the wave amplitude decreased as the water depth increased. In general, the wave crests were broader and the wave troughs narrower than recorded at the gauges situated in the gaps.

The waveform recorded by the gauges in the broader gap (Gap 2) was the same general shape as that recorded by the gauges in the first gap. However, there were differences between the water elevations recorded at the two gauges within the gap. The amplitude of the wave decreased as the water depth increased at the fifth Gauge. At the fourth gauge however, the wave amplitude was roughly constant.

4.4 Velocity

The velocity field produced by wave breaking during each model run was visualized in a variety of ways to fully describe the spatial variability of velocity within the model domain.

53 Results and Analysis

4.4.1 Velocity Direction

The velocity vector field was used to visualize changes in the direction and magnitude of currents over and around the reef. Selected graphs are presented in the results section, the complete set is provided in Appendix B.

The velocity field varied along the reef, showing along-shore and cross-shore variability that may be attributed to the presence of the gaps in the reef. Generally, water was directed into the reef across the reef top and flowed back out the gaps. This pattern was obvious during all the model runs, except for the two simulations where the water level was below the reef crest.

At the lowest water level, flow was directed parallel to the reef front (Figure 4.7). Flow was also parallel to the reef line in the narrower gap. However, in the wider gap, flow was slightly more outward directed, which appeared to be drawn from within the backreef lagoon. There was very little difference in either direction or magnitude in the low water model simulations at the different wave heights.

54 Results and Analysis

Mean Velocity Field at t= 58min, h = -0.15m, H =1.55m r o 3000

222

2500

2000

2 2 1500 2 2

0 0 0 0 2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

Figure 4.7 Velocity Field at Lowest Water Level, Wave Height =1.55m

When the water level was above the reef crest, the velocity field was far more complex. It showed evidence of eddying, deflection, re-circulation and asymmetry. Changes in water level and wave height affected the occurrence and location of these features.

Flow into the lagoon occurred across the reef. There were strong inward directed vectors at the south side of both gaps. This feature occurred at all water levels, however the vectors were most intense at higher water levels. As the water level decreased, inward directed vectors also started to occur at the north side of the outflow gaps. This feature

started to develop at the north side of the wider gap when hr was 0.65m and the wave

55 Results and Analysis height was 1.55m. However, when the water level was decreased to 0.35m at the reef crest (Figure 4.8), there was strong unidirectional inward flow at both the northern and southern edges of both gaps.

Mean Velocity Field at t= 58min, h =0.35m, H =1.55m r o 3000 22 2

2500

2000

1500 2 2 2

2

2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

Figure 4.8 Velocity Field at Mean Water Level, Wave Height=1.55m

Re-circulation of water from the outflow currents back into the lagoon was evident at higher water levels. This feature appeared to be most intense at the northern edge of both gaps. Water exiting the lagoon from the gap seemed to be moving back into the lagoon across the reef almost immediately when the water level was greater than 0.65m (Figure 4.9)

56 Results and Analysis

The two gaps tend to pull water towards themselves from the south. At most water levels, the broader gap appeared to draw inflow from about 1500m south along the reef line. The narrower gap pulled water from about 400m north and from the south to the model domain boundary. As the water level decreased the direction of flow became more parallel to the reef.

Mean Velocity Field at t=58min, h r=0.95m, H o=1.55m 3000 222

2500

2000

W

1500 2 2 2

2

2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

Figure 4.9 Velocity Field at the Highest Water Level, Wave Height=1.55m

Eddying features in the outflow current were more pronounced at higher water levels and larger wave heights. At the two highest water levels the outflow currents seemed to terminate in an eddy (Figure 4.9). In contrast, at lower water levels the currents maintained their direction and only lost magnitude as they progressed into deeper water (Figure 4.8).

57 Results and Analysis

4.4.2 Velocity Magnitude

Velocity contour plots were used to identify areas of maximum inflow and outflow. It was easier to identify these areas using filled contour plots of the u component of velocity than in the directional vector field plots. Selected plots are presented here, the complete set is presented in Appendix C. Despite the lack of bottom contour information in these plots, it is usually obvious from the velocity profiles where the gaps and reef crest are located. However, it is less clear where the reef flat starts to fall away into the backreef lagoon.

s r Magnitude of Velocity Field, H =1.34m, h =0.35s e o r t 4000 1 e m 3500

, 3000 0.5 e c 2500 n 0 a 2000 t 1500 s i 1000 -0.5 D 500 -1 500 1000 1500 2000 2500 3000 Distance, meters (A) s r Magnitude of Velocity Field, H =1.55m, h =0.35s e o r t 4000 1 e m 3500

, 3000 0.5 e c 2500 n 0 a 2000 t 1500 s i 1000 -0.5 D 500 -1 500 1000 1500 2000 2500 3000 Distance, meters (B)

Figure 4.10 Velocity Contours at Mean Water Level

58 Results and Analysis

The fastest velocities were localized at the front of the reef and the edges of the gaps. That is, the most rapid inward directed velocities were associated with rapid changes in bottom contours. Also, current velocity tended to increase as the wave height increased. This was particularly noticeable in Figure 4.11 where the water depth was 0.95m. A large patch of high velocity appeared on the reef flat at Ho=1.55m that was not present when Ho=1.34m. An increase in velocity with increased wave height was also obvious in Figure 4.10, which shows velocity at mean water level.

s Magnitude of Velocity Field, H =1.34m, h =0.95s r o r e 4000 1 t e m 3000 0.5 , e c n 2000 0 a t s i 1000 -0.5 D

-1 500 1000 1500 2000 2500 3000 Distance, meters (A) s Magnitude of Velocity Field, H =1.55m, h =0.95s r o r e 1 t 4000 e m 3000 0.5 , e c n 2000 0 a t s i 1000 -0.5 D

-1 500 1000 1500 2000 2500 3000 Distance, meters (B)

Figure 4.11 Velocity Contours at the Highest Water Level

59 Results and Analysis

The location of the strongest outflow currents was highlighted in dark blue in Fig. 4.10 and 4.11. Outflow currents were strongest at higher water levels, and the peak currents tended to be elongated and narrow within the gaps. At the highest water level, there were patches of high velocities at the leeward edge of the broader gap. These patches increased in size at the higher wave height (Figure 4.11). There was also a patch of outward directed velocities at the rear of the reef in the mean water level winter simulation (Figure 4.8). This feature was not present in any of the other contour plots.

4.4.3 Cross-Reef Velocity

The results of the velocity contour plots suggested the best place to directly compare wave driven velocities at different water levels and wave heights was at the front of the reef. Direct comparison of the velocity at the reef crest and through the gaps was carried out by taking the mean of the u-component of velocity across 5 grids (50meters) along the line of the reef crest. This was then plotted along the transect of the reef line for each water level. The different wave heights were presented on separate graphs (Figure 4.12A,B)

60 Results and Analysis

Velocity profile along the reef crest, H =1.34m 1 o h =0.95 r 0.8 hr=0.65 h =0.35 s 0.6 r / h =0.05 m r h =-0.15 0.4 r , y t 0.2 i c 0 o l e -0.2 V -0.4

-0.6

-0.8

-1 0 500 1000 1500 2000 2500 3000 3500 4000 Distance along the reef, meters (A)

Velocity profile along the reef crest, H =1.55m 1 o h =0.95 r 0.8 hr=0.65 h =0.35 r s 0.6 h =-0.15 / r m 0.4 , y t 0.2 i c 0 o l e -0.2 V -0.4

-0.6

-0.8

-1 0 500 1000 1500 2000 2500 3000 3500 4000 Distance along the reef, meters (B)

Figure 4.12 Velocity Profile Along the Reef

61 Results and Analysis

The velocity profile along the front of the reef line indicated the location of the gaps and reef flat at all water levels. Velocity directed into the reef was positive and negative out through the gaps. Figure 4.12 clearly showed the difference in wave induced velocities at different water levels.

As seen in the contour plots, the velocity across the reef crest tended to increase with water depth. The velocity over the reef at low water was much less than the velocity experienced at the front of the reef at the other water levels. However, the maximum wave driven velocity did not occur at the highest water level when the wave height was

1.34m. The wave driven velocity was actually greater at the second highest (hr=0.65m) water level. In contrast, the greatest wave driven velocity occurred at the highest water level when the wave height increased to 1.55m. This suggested the increase in wave height was enough to continue to make the waves break at the front of the reef and drive water across the reef.

The velocity profile through the gaps also showed variability with water level. In general, the greater the velocity across the reef, the greater the velocity through the gaps. The velocity of the current through the narrower gap was greater than the velocity of currents through the wider gap. They were also more strongly localized down the northern edge of the gap. In contrast, the wider gap often showed a two or three peaked- velocity profile. The high water, second highest and mean water level all showed a three peaked pattern with inflow on the northern edge of the gap, strong outflow in the center of the gap and weaker outflow at the northern edge of the gap. The magnitude of the velocity was similar at mean and high water, however the peak was shifted slightly north at the mean water level. At low water, the velocity out of the gaps was much lower than at higher water levels.

62 Results and Analysis

4.4.4 Velocity at the Wave Gauges

A time-series of velocity was recorded at each of the five gauges along the reef. This showed the oscillation in current direction in time during each wave cycle. The time- series showed the and backwash phase of wave movement. At the lowest water level, the velocity profile was positive throughout the time-series. However, it still showed an oscillation in magnitude. In general, at each water level, the velocity was stronger when the wave height was 1.55m than when it was 1.34m.

Gauge 3 was located on the reef flat. The time-series of velocity shows the swash and backwash phases as the wave moves past the gauge. When compared to the swash and backwash at the other gauges, the strongest backwash clearly occurred at Gauge 3.

The gauges also showed that waves tend to arrive at Gauges 1 and 2 before they arrive at Gauges 3,4 and 5. This can be seen in Figure 4.13, where the peak current speed occurred at t=8s (16*0.5s) at Gauges 1 and 2, but only reached Gauge 3 at t=12s. This effect was more pronounced at particular water levels (refer to Appendix C).

63 Results and Analysis

Velocity at the Wave Gauges, hr=0.35m, Ho=1.34m 2 Gauge 1 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 2 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 3 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 4 1 1 -s ms 0 m -1 , 0 10 20 30 40 50 2 1y -t Gauge 5 i 1 c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

Figure 4.13 Velocity Measurements at Gauges, Mean Water Level

64 Results and Analysis

4.5 Discharge

The total discharge was calculated using velocity data generated by FUNWAVE at the 50th mean time-step for all simulations. The u-components of the vectors were interpolated from a 20meter wide grid to a 10meter grid. The discharge through each grid was calculated using the simple formula Q=V*A for each grid, where A=10 * hr.

4.5.1 Cross Reef Discharge

The discharge across the reef was expressed on a per-meter basis. The discharge across the reef crest into the lagoon was summed over each section of reef between the limits defined by bottom contours. The total cross-reef flow was divided by the total length of the reef sections to get a per meter value. Discharge through each gap was calculated separately. The total discharge through Gap 1 was divided by 600 meters, while the total discharge through Gap 2 was divided by 800m to yield discharge per-meter (m3s-1m-1).

The discharge at each water level was plotted against the still water level at the reef crest with each wave height as a different series. Following the definitions in Section 4.4.3 flow into the reef was designated positive and flow out through the gaps was negative.

Like velocity, discharge across the reef tended to increase with both increasing water depth and wave height. However, the discharge during the lower wave height simulations peaked at less than the simulated maximum water depth. This was followed by a decrease in discharge across the reef and through the gaps to almost zero at the highest water level. In contrast, the discharge over the reef continued to increase with water depth for the run when H=1.55m.

At the lowest water level for both wave heights, flow through the wider Gap 2 was about 0.5m3s-1m-1, while the flow out of gap 1 was almost zero. Flow through the gaps increased as water depth increased. The per-meter flow through the gaps, at Ho=1.34m, was approximately the same at the still water depths of 0.05 and 0.35m. It was also approximately the same volume for the Ho = 1.55m and hr = 0.35m water depth run.

65 Results and Analysis

However, a successful simulation was not run at hr = 0.05m and Ho=1.55m and thus no comparisons could be made with this scenario.

As the water level increased, the flow through Gap 1 increased and was eventually greater than the flow through Gap 2 at water levels greater than about 0.5m. This was the reverse of the situation at the lowest water level.

Discharge per m over the reef and through the gaps, H =1.34m o 1 Gap 1 Gap 2 m Reef ( 0.5

m

1r) - 0 1em -p 3 s e g -0.5 r a h c s -1 i D

-1.5

-2 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Still Water Depth at Reef Crest, meters

Figure 4.14 Discharge per meter through gaps and over reef at a wave height of 1.34m

66 Results and Analysis

Discharge per m over the reef and through the gaps, H =1.55m o 1

m ( 0.5

m Gap 1

1r) Gap 2 - 0 Reef 1em -p 3 s e g -0.5 r a h c -1 s i D -1.5

-2 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Still Water Depth at Reef Crest, meters

Figure 4.15 Per Meter Discharge Across Reef and Through Gaps at a wave height of 1.55m

4.5.2 Total Discharge

The total discharge across the reef at each water level was plotted in Figure 4.16. The two wave heights were plotted as different series. Total discharge was calculated by summing the interpolated values of discharge along the entire reef line. This did not include the discharge through the gaps.

The total discharge increased less per unit depth at shallower depths than deeper depths when the wave height was 1.55m. As expected from the velocity results for the summer case (Ho =1.34m), the maximum discharge occurred at 0.65m. It was slightly greater (~150m3s-1) than the discharge at 0.65m for the winter simulation. The maximum

67 Results and Analysis discharge for the wave height of 1.55m for the simulated water depths occurred at the highest water level. At the same water depth, the total discharge for the Ho = 1.34m was very slightly negative. Greater discharge occurred during the 1.55m wave height simulation at either end of the range of water depths. In between however, the greater wave height had slightly less flow than the 1.34m wave height.

Total Discharge Across the Reef Top 2500

2000 m

, 1500 1e H =1.55m -g o s H =1.34m 3r o a 1000 h c s i 500 D

0

-500 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Still Water Depth at Reef Crest, meters

Figure 4.16 Total Discharge Across the Reef Top

68 Results and Analysis

4.6 Flushing Times

One of the observations this study was based on was the relative importance Hearn et al. (1986) ascribed to wave forcing on flushing at Ningaloo. For the purpose of their calculations, flushing was defined as “the average time taken for a particle released within one of the channel regions to exit through the reef line” (Hearn et al. 1986). The validity of the assumption that wave flushing was more important than wind or tidal flushing was checked using the modelled wave driven circulation. Hearn et al.’s (1986) methods were used to recalculate wind and tidal flushing times for the idealized lagoon. Then the wave driven flushing time was calculated using the modelled rate of discharge across the reef. This was carried out to determine if the relative importance of each type of forcing was maintained.

The volume of the lagoon was calculated at the high, mean and low water depths. The lagoon was divided into three sections, the backreef lagoon, reef flat and the reef crest, based on the bottom bathymetry. The volume of each section was calculated as depth x width x length. The results of the calculations are summarized in Table 4.2 to Table 4.4.

Table 4.2 Volume Calculations at Low Water Level Depth (m) Width (m) Length (m) Volume (m3)

Lagoon 2.05 1400 4000 114.8x105

Reef Flat 0.05 250 4000 0.5 x105

Reef Crest -0.15 100 4000 0

Total 115.3x105

69 Results and Analysis

Table 4.3 Volume Calculations at Mean Water Level Depth (m) Width (m) Length (m) Volume (m3)

Lagoon 2.55 1400 4000 143x105

Reef Flat 0.55 250 4000 5.5x105

Reef Crest 0.35 100 4000 1.4x105

Total 149.9x105

Table 4.4 Volume Calculations at High Water Level Depth (m) Width (m) Length (m) Volume (m3)

Lagoon 3.15 1400 4000 176.4x105

Reef Flat 1.15 250 4000 11.5 x105

Reef Crest 0.95 100 4000 3.80 x105

Total 191.7x105

4.6.1 Wind Driven Flushing

Hearn et al. (1986) estimated a mean annual wind-driven current of 0.15ms -1, which they considered likely to be an overestimate. Therefore, in their wind-driven flushing estimates they used an order of magnitude current speed estimate of 0.1ms-1 (Hearn et al. 1986). From the description of their methods, it appears they simply chose a typical travel distance from within a lagoon to a gap and assumed the particle would travel at a constant speed along that travel path. Although this is a questionable method of calculating wind driven flushing, for comparison the same method has been used here. So, assuming a travel path of 4 kilometers, from one end of the lagoon to the other, gives a wind driven flushing time of about 12 hours. This calculation probably under estimates the wind driven flushing time.

70 Results and Analysis

4.6.2 Tidal Flushing

A standard calculation for the tidal flushing of an enclosed water body is the volumetric ratio time,

V τ = T Equation 4-3 volume ∆V

Where ∆V is the volume difference between high and low water, V is the mean volume of the water body and T is the tidal period. So, for the values given in Table 4.3, this yields a τvolume of 24 hours for the idealized lagoon.

However, in shallow water systems, the incoming tidal prism does not mix completely due to the formation of a front between the incoming tide and the water inside the lagoon. Mixing across this front depends on the density difference between the water bodies and the strength of any forcing driving mixing. The coefficient for this process is poorly known and so an accurate mixing time is difficult to calculate (Hearn et al. 1986). In addition, there may be re-circulation of water back into the lagoon. Empirically, a return coefficient, ‘r’ varying from zero (no re-entry) to one (total return) can be included to represent this aspect of the flushing process. This gives a τtide that depends on τvolume and r. Hearn et al. (1986) used a typical value of r=0.5.

τ τ = volume Equation 4-4 tide 1− r

This increases τvolume to about two days.

4.6.3 Wave Driven Flushing

Hearn et al. (1986) calculated a wave driven flushing time by assuming that flow occurs inwards across the reef and into deep channels where it is then guided out through breaks in the reef. They calculated a range of final exit velocities through the reef break and used these to determine how long the lagoon would take to empty (Hearn et al. 1986). This yielded a range of flushing times from 5 to 23 hours.

71 Results and Analysis

Table 4.5 Discharge Over the Reef at each Water Level Water Depth at Reef Crest Summer m3s-1 Winter m3s-1 0.95 -45.3 2073 0.65 1467.3 1322 0.35 821.7 703 0.05 311 - -0.15 90.5 210 Mean 530 1077

The modelled data was used to recalculate the flushing time. This was based on the amount of water coming into the lagoon over the reef (Table 4.5). Flushing time was simply calculated as

Disch arg e τ = Equation 4-5 wave Volume Using the mean values of discharge across the reef into the lagoon and the mean water volume of the lagoon (Table 4.3) yielded a flushing time of about 4 hours in winter. This increased to about 8 hours in summer.

72 Discussion

5 Discussion

5.1 Wave Setup

The magnitude of the maximum wave-setup was affected by changes in water level and wave height. There was approximately 3cm difference between the modelled maximum and minimum setup. The maximum setup was about 5cm and the minimum setup was about 2cm. In general, the magnitude of the setup increased as the water depth decreased. This gave good agreement with other experimental and modelled results. For example, according to Gourlay (1996a), the magnitude of wave setup increases as the water depth over the reef decreases for a given wave height and period.

At a given water depth and wave period, the wave setup increases as the incident wave height increases (Gourlay 1996a). The divergence between setup values at different wave heights appears to be greatest at the lowest and highest water levels. At the lowest water depth, when the water level was below the reef crest, waves broke on the reef front. Effectively, the waves were breaking on a very steep beach. Consequently, the force balance producing wave setup was not identical to the force balance for waves breaking on the reef top. When the water level is below the reef crest, setup on the reef flat occurs from overtopping by wave run-up. Relative run-up will depend on the roughness and the permeability of the reef face (Gourlay 1996a). This implies adjusting the permeability and roughness of the model reef could change the magnitude of the setup produced at low water levels.

At the upper end of the depth range, the difference in setup with wave height can probably be attributed to a reduction in wave breaking intensity. At the highest water level, when the water was almost a meter over the top of the reef, the 1.34m wave was not breaking as strongly as the 1.55m wave. This changed the force balance governing the conservation of momentum, reducing the increase in pressure required to balance the gradient in radiation stress.

73 Discussion

Although not simulated in this study, when the reef is submerged, there is a threshold value of the offshore wave height Ho below which there is no setup. Gourlay (1996a) ∪ suggested this value was Ho 0.4hr . For the range of water depths considered in the model simulations, this relationship yields an offshore wave height of approximately 0.46m. Wave heights less than this threshold value would not produce set-up. This is a very small swell height for the Northwest Cape region. According to the WNI percentage occurrence data (WNI 2000), a significant swell wave height of 0.4 is exceeded more than 99% of the time in both summer and winter. However, if the water depth over the reef was increased to 2m, the threshold wave height required to produce setup would increase to 0.8m. This threshold is still exceeded more than 85% of the time (WNI 2000). This implies a situation where no setup over the reef occurs is comparatively rare at Ningaloo.

When the modelled results were compared to Gourlay’s (1996a) experimental results, it appeared FUNWAVE could be seriously underestimating wave setup. While this should not be ruled out, it is also possible that differences between the constraints placed on flow in his experiments and the modelled scenario might be significant. Gourlay’s (1996a) two scenarios involved different flow restrictions. The so-called “fringing reef” scenario only allowed water to exit the lagoon during the backwash phase of wave breaking. The “platform reef” scenario allowed flow to occur out of the lagoon at the back of the lagoon. It was then re-directed back to the “ocean” in the wave flume through side channels that were separated from the central flume by solid walls. In contrast, the return flow out of the lagoon in the model was not constrained. This led to an uneven setup profile along the reef-line in the long-shore direction. Gourlay (1996a) found setup was reduced when water was not trapped in the lagoon, by an amount at least equal to the velocity head of the wave generated flow across the reef. This implies reducing constraints on flow by including breaks in the reef would continue to reduce wave setup.

However, despite variability in the magnitude of setup, the approximate location of maximum setup was the same for each simulation. The maximum wave setup always occurred at the leeward end of the surf zone. This agrees with the conservation of

74 Discussion momentum theory and experimental observations made by Gourlay (1996b). That is, the maximum wave set-up should occur at the back of the reef flat where the wave breaking process was complete (Gourlay 1996a). However, the point of maximum set down shifted progressively towards the lagoon as the water depth decreased. This may be explained by differences in magnitude of radiation stress and depth gradients across the reef flat.

5.2 Wave Induced Currents and Discharge

Modelled current speeds reached a maximum of 0.5ms-1across the reef and 1ms-1 through the outflow channels. However, it is difficult to compare these values directly to currents recorded at other locations around the world as reef profile can have a significant affect on wave dynamics (Gourlay 1996b, Lugo-Fernandez 1998). However, as order of magnitude estimates, the modelled values seem to match reported current speeds quite well. For example, Hearn et al. (1986) reported that current speeds of up to 1ms-1 in outflow channels were recorded in Guam. Landward flow over the reef was measured at 0.3ms-1 (Hearn et al 1986). It is possible that the velocity measurements may be underestimates given the particular reef profile given Gourlay’s (1996a) reported experimental setup values were larger than the setup values modelled by FUNWAVE. If setup is underestimated then it is likely velocity will also be underestimated.

The modelled velocity profiles showed that the velocity at the front of the reef and through the outflow channels increased with water depth and wave height. This agreed with the trend identified in the experimental results of Gourlay (1996a), who observed that velocity increased as incident wave height increased at a given water depth. He also observed that wave generated flow increased as wave period increased. Unfortunately, the wave period used in the two sets of simulations was not the same so the effects of increasing wave height could not be completely isolated from the effect of increasing period. However, the two wave periods used in the model simulations differed by only one second. When a linear fit was applied to the raw results and non-dimensionalized results, the R2 values of 0.75 and 0.77 were approximately the same. This suggests that

75 Discussion relative differences in modelled results are probably more likely to be due to different wave height than wave period.

Discharge was calculated using the modelled velocities and still water depth at the reef crest. Discharge increased as the water depth increased for a given wave height, in accordance with the experimental results of Gourlay (1996a). However, it increases to a maximum value before starting to decrease (Gourlay 1996a). This implies there would be tidal modulation of the rate of discharge at frequencies of particular tidal constituents. This has been observed at other locations, including John Brewer Reef (Symonds et al. 1995) and in Japan (Kraines et al. 1998).

The results of modelling were analyzed after the simulation had reached a steady state condition for a discrete water level. The simulated time for this to occur was about one hour, which is the same the length of time quoted by van Rijn (1990) to establish equilibrium conditions for wave setup. However, water levels are not static in the natural environment. The tidal cycle causes a cyclic change in water level over a 12 or 6 hour time period. These changes in water level and non-monochromatic sea-states introduce considerable variability into the forcing on wave driven flow. This aspect of wave driven flow dynamics was not examined. However, these effects are probably significant, given observations such as those by Roberts (1980), who reported variations of 50% around the mean speed of surge currents into the lagoon at timescales of 1 to 2 minutes (Lugo- Fernandez 1998).

Currents over the reef showed considerable spatial variability both across and along the reef. A swell direction that is not normal to the reef line creates asymmetry in outflows. Initial runs, not discussed in this report, were carried out with wave crests approaching perpendicular to the reef. The currents produced in these simulations were considerably more symmetrical than those produced when the waves approached at an angle. This implies that in a real coral reef gradients in radiation stress are probably significant in the

Sxy direction, rather than purely the Sxx direction. This implies theoretical models such as

76 Discussion that proposed by Symonds et al. (1995) may need further development if they are to be applied to reef environments that show variability in both the x and y direction.

Interaction between waves and currents in shallow water near the coast may affect wave characteristics (van Rijn 1990). A current opposing the waves yields increased wave heights and reduced wave lengths effectively steepening the wave, possibly to the point of breaking (van Rijn 1990). This situation occurs at the ocean side of the gaps where the outflow currents exit the lagoon. This could explain the set down in the gaps and the occurrence of breaking at the front of the gaps.

There is of waves over the reef line. Refraction occurs when waves approach bottom contours at an angle. One end of the wave experiences the bottom and is slowed, the other end of the wave curves to become parallel to the reef more slowly. This was shown by waves reaching gauge locations at different times along the reef line. Waves arrive at Gauges 1 and 2 a few seconds before they reach Gauges 3, 4 and 5. This implies waves are not normal to the reef when they reach the gauges on the reef crest. This reinforces the earlier point that the assumption that waves break normal to the reef made by other modelling approaches (Prager 1991, Kraines et al. 1998) may not be valid.

Inspection of aerial photographs suggests that only inflow occurring within about one lagoon width of a break takes the shorter route of a direct arc out through the break without reaching the inshore channel (Hearn et al. 1986). In the modelled scenario, the distance where inflow took the shorter route was longer, almost double the gap width. This is probably due to a combination of omitted topographical effects and forcings. As the water moves into the lagoon, the wave induced velocity decreases. Hearn et al. (1986) suggested by that wind forcing becomes more important closer to shore. The omission of wind forcing could explain why the water does not flow further into the lagoon before entering an outflow current.

77 Discussion

5.3 Flushing Times

The relative magnitudes of the re-calculated values of flushing agree with the values originally calculated analytically by Hearn et al. (1986). That is, the most rapid flushing would occur under a purely wave-driven flushing regime. Tidally driven flushing was the slowest flushing mechanism and purely wind driven flushing was estimated to take roughly double the wave driven flushing time. However, the method used to calculate wind driven flushing was highly questionable. A better method would have been to use the calculated wind driven velocity to calculate a discharge rate. However, this is only likely to increase the estimated wind driven flushing time. So, the modelling of wave driven flow has confirmed the importance of wave driven flushing at Ningaloo Reef.

Although wave pumping is almost certainly the most important factor in flushing of Ningaloo lagoons, it can not be considered alone if accurate predictions of flushing time are required. For example, tidal currents may modulate flushing times. Wave driven outflow currents may be blocked at flood tide or strengthened at ebb tide (Prager 1991). Wind driven currents may strengthen wave driven currents if they act in the same direction or weaken them if the wind driven currents act in the opposite direction. Swell waves of less than a meter would also slow wave driven velocities. This might then reduce the importance of wave driven flushing relative to tidal and wind forcing.

The effective flushing time for a reef at Ningaloo could be slowed by re-circulation of water from outflow currents back over the reef top. This question is currently unquantified, and is usually approximated using an empirical re-circulation coefficient (Hearn et al. 1986). The velocity vector field results (Appendix B) show the occurrence of re-circulation. It might be possible to use this type of modelling approach to quantify the increase in effective flushing time caused by re-circulation.

The formation of density gradients due to tidal intrusion of water with different temperature and salinity characteristics might also slow mixing between oceanic and lagoonal waters and consequently increase flushing times. The rate of mixing across the front will depend on the strength of the density gradient and wave conditions. As

78 Discussion

FUNWAVE is vertically integrated, and assumes uniform water body characteristics, density gradients can not be included in the model.

Determining accurate flushing times is important for risk analysis of contaminant dispersal. This is becoming increasingly important at Ningaloo due to proposed developments, such as the Coral Coast Resort development (EPA 1995). Increased boating pressure might damage coral, not just by direct physical damage caused by moorings, but also through biological imbalance caused by discharge of sullage. More accurate flushing calculations could be developed using a coupled model, incorporating realistic wave forcing and the effect of density gradients, wind and tides.

5.4 Influence of Other Factors

Numerical modelling of a problem, especially one that is not fully parameterized, requires assumptions and approximations be made. The results of numerical modelling should be appraised in view of the factors that have been left out, as well as those that have been controlled for. In this case, these variables include bottom friction, real sea- states and wave period.

5.4.1 Wave Period

The model runs were not controlled for the effect of wave period on setup or velocity. The winter and summer simulations used different wave periods, but as they also used different wave heights, inferences on the effect of wave period alone on setup or velocity cannot be drawn. This is unfortunate, as Gourlay (1996a) has shown that wave period affects wave setup. In his experimental work, it appeared that wave setup increased with increasing wave period until a limiting condition was reached. It was not possible to determine conclusively if this limiting condition was reached at wave periods of 13 or 14s.

79 Discussion

5.4.2 Bottom Friction

Bottom friction can have a significant effect on wave-breaking processes. It can affect the type of breaker by reducing the wave height or changing breaking location (Lugo- Fernandez 1998). It is relatively straightforward to measure friction in the absence of swell. Under these conditions, it has been determined that coral has a very high drag coefficient, up to two orders of magnitude higher than normal ocean shelves. However, there is currently no information about frictional stresses under large wave conditions (Hearn 1999). In addition, bottom friction is likely to be spatially variable over a coral reef. This complicates the incorporation of friction into a two dimensional model. However, given that a friction factor is related to current speed in Symonds et al.’s (1995) theoretical model, it is probably an important variable and requires more calibration.

5.4.3 Irregular Waves

Irregular waves, particularly if accompanied by wave groups may produce setup conditions significantly different to those produced by regular waves (Gourlay 1996a). For example, Seelig (1983) found irregular waves of a given significant wave height created less setup than monochromatic waves with the same wave height. FUNWAVE does have the capability to model a real-sea wave . It could potentially be used to determine if using a monochromatic wave field is an invalid assumption in modelling wave driven dynamics over a coral reef.

80 Conclusions

6 Conclusions

This study conducted a preliminary investigation of wave driven circulation over an idealized version of a Ningaloo Reef lagoon. In particular, it examined differences in wave setup and wave driven velocities at a range of water levels and wave conditions using a numerical model.

The magnitude of the maximum wave-setup was affected by changes in water level and wave height. In general, the magnitude of the setup increased as the water depth decreased. From comparison with experimental work, it appears that FUNWAVE predicts the location of setup and setdown accurately, but it may underestimate setup. Alternatively, it is possible that permitting lateral flow decreases the maximum wave setup over the reef top when compared to the experimental scenarios, where flow was constrained in the y-direction.

Modelled current speeds reached a maximum of 0.5ms-1across the reef and 1ms-1 through the outflow channels. It was difficult to assess the accuracy of these values due to a lack of field data and realistic bathymetry. However, as estimates of velocities over an idealized reef, the modelled values seem to match current speeds reported at various locations around the world quite well.

The relative magnitudes of the re-calculated values of flushing agree with the values originally calculated analytically by Hearn et al. (1986). That is, the most rapid flushing occurred under a purely wave-driven flushing regime. Modelling showed the water level and wave conditions had a significant effect on the rate of wave driven flushing. In particular, the relative submergence of the reef when compared to wave height is important in determining the velocity and rate of flushing. The rate of discharge across the reef slows when the breaking ratio of water depth to wave height is exceeded. This contributed to flushing being twice as fast in the winter as the summer scenario, despite a wave height difference of just 20cm.

81 Conclusions

Other outcomes included the possibility that FUNWAVE might be useful in quantifying re-circulation from outflow gaps back into the reef. This could improve flushing estimates by quantifying the proportion of lagoonal water that re-enters the lagoon over the reef. However, to calculate flushing properly, the moderating effects of wind and tides need to be incorporated. This would require coupling a wave model such as FUNWAVE to a 3-D hydrodynamic model.

The spatial variability shown by the model along the reef line demonstrates observations of current speed and direction will be affected by the location of measurements. This makes it important to understand spatial variability in current speed when planning fieldwork for model verification.

In conclusion, FUNWAVE has provided a useful tool for investigating the dynamics of wave driven flow over a coral reef. However, as the model has not been validated against experimental results or real observations, it is impossible to evaluate the error involved in the modelled current speeds and wave setup.

82 Recommendations

7 Recommendations

The scope of this study was limited and highly idealized. It focused on only one aspect of the forces driving water circulation around a simplified coral reef. Although wave pumping has been identified as the dominant forcing mechanism at Ningaloo, other factors such as wind and horizontal density gradients may also contribute to the overall rate of flushing and circulation. The recommendations for further work can be divided into two parts. First, further investigation of FUNWAVEs’ usefulness in modeling circulation around a coral reef is discussed. Second, incorporation of other forcings to develop better predictions of flushing time is suggested.

7.1 FUNWAVE and Wave-driven circulation

A more realistic bathymetry reflecting the actual bottom contours of particular lagoon would improve the accuracy of modelled results. The surface structure of the reef might also influence the energy dissipation across the reef through the groove and spur structures. To resolve these structures the size of the model grids would have to be reduced. This would cause either an increase in computational time, which is already long, or a decrease in the maximum size of the domain. A realistic bathymetry would also include the deep channels that typically exist in back-reef lagoons. This is an aspect of circulation that was neglected in the study of flow across the reef, although it has been identified as the location of the greatest mass flux within the reef (Hearn et al 1986).

A major strength of FUNWAVE is its ability to take a directional wave field as an input. This allows it to better reflect the complexity of a real sea-state. So, the wave field should be changed from a monochromatic field to a more realistic directional spectrum to show if variability in the wave field creates variability in wave driven currents.

83 Recommendations

The friction factor used in the modeled runs was at the high end of the typical range suggested in the FUNWAVE 1.0 Manual (Kirby et al 1998). However, this was probably an underestimate by at least one order of magnitude (Gourlay 1996a). Bottom friction might have a significant effect on wave flow at shallow depths. However, the friction factor should not be increased throughout the model domain. Increased friction would need to be localized over the top of the reef and on the reef face. The rest of the domain should be left with a lower friction factor typical of a sandy sea floor. This would provide a more accurate representation of the influence of friction of wave driven flow.

7.2 Other Forcings

A wave model can only describe one aspect of the forces driving circulation around a coral reef. Tidal direction and wind strength, as well as wave height and water depth will moderate the strength of wave driven currents within the lagoon. These forcings could be incorporated into modeling of circulation around a coral reef by coupling the wave model to 3-D hydrodynamic model.

Calibration and validation of any circulation model is essential if the coupled model is to be used for practical applications. This would make it useful for or ecological modeling of neutrally buoyant particles such as coral larvae.

84 Bibliography

8 Bibliography

Andrews, J.C., & Pickard, G.L. (1990) The of Coral Reef Systems, In Coral Reefs ed. Z. Dubinsky, Ecosystems of the World, Vol. 25, Elsevier

Chen, Q., Dalrymple, R.A., Kirby J.T., Kennedy, A.B., Haller, M.C. (1999) Boussinesq modeling of a system, Journal of Geophysical Research, Vol. 104 NoC9, pp20,617-20,637

Coral Coast Marina Development [31 August 2001] Coral Coast Resort, http://www.coralcoastresort.com.au, (28/9/01)

D’Adamo, N. and Simpson, C.J. (2001). Review of the oceanography of Ningaloo Reef and adjacent waters. Technical Report: MMS/NIN/NIN-38/2001. March 2001. Marine Conservation Branch, Department of Conservation and Land Management. (Unpublished report).

Gourlay, M.R. (1993) Wave Set-up and Wave-generated Currents on Coral Reefs, Proc. 11th Australasian Conference on Coastal and Ocean Engineering, pp479-484

Gourlay, M.R. (1996a) Wave set-up on coral reefs. 1. Set-up and wave generated flow on an idealized two dimensional horizontal reef Coastal Engineering, Vol. 27 pp161-193

Gourlay, M.R. (1996b) Wave set-up on coral reefs 2. Set-up on reefs with various profiles. Coastal Engineering, Vol. 28, pp17-55

Hardy, T.A., Mason L.B., McConochie J.D., (2000) A wave model for the Great Barrier Reef, Ocean Engineering, Vol. 28 pp45-70

Hearn, C.J., (1999), Wave-breaking hydrodynamics within coral reef systems and the effect of changing relative sea level, Journal of Geophysical Research, Vol. 104 no C12 15 December 1999, pp30007-30019

Hearn, C.J., Hatcher, B.G., Masini, R.J., Simpson, C.J. (1986) Oceanographic Processes on the Ningaloo Coral Reef, Western Australia, Center for Water Research, Environmental Report ED-86- 171, University of Western Australia

Horikawa, K. (1978) Coastal Engineering: An Introduction to Ocean Engineering, University of Tokyo Press, Tokyo

85 Bibliography

Johnson, David (2001) Center for Water Research, University of Western Australia, personal communication

Kirby, J.T., Wei, G., Chen, Q., Kennedy, A.B., Dalyrmple, R.A., (1998) FUNWAVE 1.0, Fully Non-Linear Boussinesq Wave Model Documentation and Users Manual, Research Report NO. CACR –98-06, Center for Applied Coastal Research, University of Delaware, Newark DE, USA

Kraines, S.B., Yanagi, T., Isobe, M., Komiyama, H. (1998) Wind-wave driven circulation on the coral reef at Bora Bay, Miyako Island, Coral Reefs, Vol. 17, pp133-143

Lugo-Fernandez, A., Roberts, H.H., Suhayda, J.N. (1998a) Wave transformations across a Caribbean fringing-barrier Coral Reef, Continental Shelf Research, Vol. 18, pp1099-1124

Lugo-Fernandez, A., Roberts, H.H., Wiseman, W.J. Jr., (1998b) Tide Effects on Wave Attenuation and Wave Set up on a Caribbean Coral Reef, Estuarine, Coastal and Shelf Science, Vol. 47, pp385-393

Massel S.R., Gourlay, M.R., (2000) On the modelling of wave breaking and set-up on coral reefs, Coastal Engineering, Vol. 39, pp1-27

Mann, K.H., (2000) Ecology of Coastal Waters With Implications for Management 2nd edition, Blackwell Science, Oxford

Naval Postgraduate School, (2000) State of Nearshore Processes Research: II: Report Based on the Nearshore Research Workshop, St. Petersburg, Florida September 14-16, 1998, Technical Report NPS- OC-00-001, Naval Postgraduate School, Monterey, 93943

Pattiaratchi, C. (2001) Hydrodynamics of Fringing Reef Systems, ARC Linkage Research Proposal

Pond S., and Pickard G.L. (1983) Introductory Dynamical Oceanography 2nd Edition, Pergamon Press, U.K.

Prager, E.J. (1991) Numerical simulation of circulation in a Caribbean-type backreef lagoon: a preliminary study, Coral Reefs, Vol. 10, pp177-182

86 Bibliography

Sanderson, P.G. (1996). Cuspate forelands of the west coast of Western Australia. Ph.D. Thesis. Department of Geography, University of Western Australia, Nedlands, Western Australia, 6009.

Save Ningaloo, [25 October 2001] Save Ningaloo Campaign, http://www.save-ningaloo.org (28/9/01)

Sorensen R.M., (1978) Basic Coastal Engineering, J.Wiley & Sons, 227pp.

Stejskal, I.V. (2000) Obtaining Approvals for Oil and Gas Projects in Shallow Water Marine Areas in Western Australia using an Environmental Risk Assessment Framework, Spill Science and Technology Bulletin, Vol. 6 no. 1, pp69-76

Symonds G., Black K., Young I.R., (1995) Wave-driven flow over shallow reefs, Journal of Geophysical Research, Vol. 100 no C2 15 February 1995, pp2639-2648

Taylor, J.G., Pearce, A.F., (1999) Ningaloo Reef currents: implications for coral spawn dispersal, zooplankton and whale shark abundance, Journal of the Royal Society of Western Australia, Vol. 82, pp57- 65

Van Rijn, L.C., (1994) Principles of Fluid Flow and Surface Waves in Rivers, , and , Aqua Publications, Netherlands

Wolanski, E., Delesalle B., Dufour V., Aubanel A., (1993) Modeling the fate of pollutants in the Tiahura Lagoon, Moorea, French Polynesia, Proc 11th Australasian Conference on Coastal and Ocean Engineering, pp583-588

Yamamoto, H., Kayanne, H., Yonekura, N., Nakamura, H., and Kudo, K. (1998) Water circulation in a fringing reef located in a monsoon area: Kabira Reef, Ishigaki Island, Southwest Japan. Coral Reefs, Vol. 17, pp89-9

87 Appendices

88 Appendix A

Appendix A FUNWAVE2D datafile, FUNWAVE2dpt.data

Details of coefficients used in modelling c*** if idout is set to 1 (eta and mean currents) then itdel is reset internally to be 2*dominant wave period

$data1 ibe = 2 imch = 2 a0 = 0.5 h0 = 15.0 tpd = 12.0 dx = 10.0 dy = 20.0 dt = 0.5 mx = 301 ny =201 nt = 7201 itbgn = 3000 itend = 6001 itdel = 20 itscr = 10 itftr = 200 theta = 45.0 cbkv = 0.35 delta = 0.02 slmda = 20.0 isltb = 60 islte = 301 $end

$data2 isrc = 31 jsrc = 1 cspg = 10.0 cspg2 = 0.0 cspg3 = 0.0 ispg = 21 10 1 1 ngage = 5 ixg = 35 45 180 270 290 iyg = 123 123 123 123 123 itg = 5001 cbrk = 1.2 ck_bt = 0.004 c_dm = 0.05 isld = 1 idout = 2 idft = 0 $end

$data3 f1n = 'dpdata.cacr' f2n = 'inwdata.cacr' f3n = 'specmat.spec' f4n = 'gauges.out' f5n = 'end.out' f6n = 'means.out' f7n = 'timeseries.out' $end

$data4 ihotsave=0 errorcrit=0.0001 ipb=1 iaverno=5 shorecf=1.8 shorefilt=0.8 $end

$ptrack npar = 0 npstart=1000 pstrtx= 110 110.5 110 110.5

89 Appendix A pstrty= 10 10 10.5 10.5 $end

90 Appendix B

Appendix B

Mean Velocity Field at t= 56min, h =0.95m, H =1.34m r o 3000 222

2500

2000

1500 2 2 2

2 2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

Mean Velocity Field at t= 58min, h r=0.95m, H o=1.55m 3000 222

2500

2000

1500 2 2 2

2

2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

91 Appendix B

Mean Velocity Field at t= 56min, h =0.65m, H =1.34m r o 3000 22 2

2500

2000

1500 2 2

2 2 2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

Mean Velocity Field at t= 58min, h r=0.65m, H o=1.55m 3000 222

2500

2000

1500 2 2 2 2

2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

92 Appendix B

Mean Velocity Field at t= 56min, h =0.35m, H =1.34m r o 3000 222

2500

2000

1500 2 2 2 2

2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

Mean Velocity Field at t= 58min, h =0.35m, H =1.55m r o 3000 22 2

2500

2000

1500 2 2 2

2

2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

93 Appendix B

Mean Velocity Field at t= 56min, h r=0.05m, H o=1.34m 3000 222

2500

2000

2 1500 2 2 2

2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

94 Appendix B

Mean Velocity Field at t =56min, h =-0.15m, H =1.34m r o 3000 222

2500

2000

2 2 1500 2 2

0 0 0 0 2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

Mean Velocity Field at t =58min, h =-0.15m, H =1.55m r o 3000

222

2500

2000

2 2 1500 2 2

0 0 0 0 2 2

1000

500

1.0 m/s

0 4000 3500 3000 2500 2000 1500 1000 500 0 Distance Along the Reef Line, meters

95 Appendix C

Appendix C

Velocity Contours

s Magnitude of Velocity Field, H =1.34m, h =0.95s r o r e 1 t 4000 e m 3000 0.5 , e c n 2000 0 a t s i 1000 -0.5 D

-1 500 1000 1500 2000 2500 3000 Distance, meters (A) s Magnitude of Velocity Field, H =1.55m, h =0.95s r o r e 1 t 4000 e m 3000 0.5 , e c n 2000 0 a t s i 1000 -0.5 D

-1 500 1000 1500 2000 2500 3000 Distance, meters (B)

96 Appendix C

s r Magnitude of Velocity Field, H =1.34m, h =0.65s e o r t 4000 1 e m 3500

, 3000 0.5 e c 2500 n 0 a 2000 t 1500 s i 1000 -0.5 D 500 -1 500 1000 1500 2000 2500 3000 Distance, meters (A) s r Magnitude of Velocity Field, H =1.55m, h =0.65s e o r t 4000 1 e m 3500

, 3000 0.5 e c 2500 n 0 a 2000 t 1500 s i 1000 -0.5 D 500 -1 500 1000 1500 2000 2500 3000 Distance, meters (B)

97 Appendix C s r Magnitude of Velocity Field, H =1.34m, h =0.35s e o r t 4000 1 e m 3500

, 3000 0.5 e c 2500 n 0 a 2000 t 1500 s i 1000 -0.5 D 500 -1 500 1000 1500 2000 2500 3000 Distance, meters (A) s r Magnitude of Velocity Field, H =1.55m, h =0.35s e o r t 4000 1 e m 3500

, 3000 0.5 e c 2500 n 0 a 2000 t 1500 s i 1000 -0.5 D 500 -1 500 1000 1500 2000 2500 3000 Distance, meters (B)

98 Appendix C s r Magnitude of Velocity Field, H =1.34m, h =-0.15s e o r t 4000 1 e m

, 3000 0.5 e c n 2000 0 a t s i 1000 -0.5 D

-1 500 1000 1500 2000 2500 3000 s Distance, meters (A) r Magnitude of Velocity Field, H =1.55m, h =-0.15s e o r t 4000 1 e m

, 3000 0.5 e c n 2000 0 a t s i 1000 -0.5 D

-1 500 1000 1500 2000 2500 3000 Distance, meters (B)

99 Appendix D

Appendix D

Velocity at the Wave Gauges

Velocity at the Wave Gauges, h =0.95m, H =1.34m r o 2 Gauge 1 1 1 - s 0 m -1 0 10 20 30 40 50 2 Gauge 2 1 1 - s 0 m -1 0 10 20 30 40 50 2 Gauge 3 1 1 - s 0 m -1 0 10 20 30 40 50 2 Gauge 4 1 1 -s m 0 s m -1 , 0 10 20 30 40 50 2 1y -t Gauge 5 i 1 c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

100 Appendix D

Velocity at the Wave Gauges, h =0.95m, H =1.55m r o 2 Gauge 1 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 2 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 3 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 4 1 1 - s 0 ms m -1 , 0 10 20 30 40 50 2 1y -t Gauge 5 i 1 c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

101 Appendix D

Velocity at the Wave Gauges, h =0.65m, H =1.34m r o 2 Gauge 1 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 2 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 3 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 4 1 1 - ss 0 mm -1 , 0 10 20 30 40 50 2 1y -t Gauge 5 i 1 c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

102 Appendix D

Velocity at the Wave Gauges, hr=0.65m, Ho=1.55m 2 Gauge 1 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 2 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 3 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 4 1 1 -s ms 0 m -1 , 0 10 20 30 40 50 2 1y -t Gauge 5 i 1 c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

103 Appendix D

Velocity at the Wave Gauges, hr=0.35m, Ho=1.34m 2 Gauge 1 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 2 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 3 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 4 1 1 -s ms 0 m -1 , 0 10 20 30 40 50 2 1y -t Gauge 5 i 1 c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

104 Appendix D

Velocity at the Wave Gauges, h =0.35m, H =1.55m r o 2 Gauge 1 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 2 1 1 -s 0 m -1 0 10 20 30 40 50 2 Gauge 3 1 1 -s m 0 -1 0 10 20 30 40 50 2 Gauge 4 1 1 -s ms 0 m -1 , 0 10 20 30 40 50 2 1y -t Gauge 5 i 1 c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

105 Appendix D

Velocity at the Wave Gauges, h =0.05m, H =1.34m r o 2 Gauge 1 1 1 - s 0 m -1 0 10 20 30 40 50 2 Gauge 2 1 1 - s 0 m -1 0 10 20 30 40 50 2 Gauge 3 1 1 - s 0 m -1 0 10 20 30 40 50 2 Gauge 4 1 1 - s 0 sm m -1 , 0 10 20 30 40 50 2 1y -t Gauge 5 i 1 c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

106 Appendix D

Velocity at the Wave Gauges, h = -0.15m, H =1.34m r o 2 Gauge 1 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 2 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 3 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 4 1 1 -s m 0

s m -1 0 10 20 30 40 50 , 2 1y -t Gauge 5 1 i c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

107 Appendix D

Velocity at the Wave Gauges, h = -0.15m, H =1.55m r o 2

1 Gauge 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 2 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 3 1 1 -s m 0

-1 0 10 20 30 40 50 2 Gauge 4 1 1 -s m 0 s m -1 0 10 20 30 40 50 , 2 1y - t 1 Gauge 5 i c o 0 l e -1 V 0 10 20 30 40 50 Time, half seconds

108 Appendix A

109