Chapter 6 Wave Energy, Bathymetry and Sediments

CHAPTER 6 WAVE ENERGY, BATHYMETRY AND SEDIMENTS

The seaward extent of each beach system has been identified in terms of the offshore bathymetry "and pattern of sediments. The beach systems all display a seaward fining textural gradient indicating a common response to orthogonal wave power. Shore normal wave-sediment inter action can be accounted for in terms of the null-point theory, However, the point of incipient sediment motion for most beach systems is determined by a sediment bedrock interface rather than a textural discontinuity. Differences in bathymetry along the coast imply a complex relationship between wave energy, bathymetry and sediment distribution. A simple expression of this relationship is given in Figure 6-1.

FIGURE 6-1 WAVE BATHYMETRY INTERACTION

BEDROCK BATHYMETRY -^ WAVE CLIMATE

DEPOSITIONAL BATHYMETRY ^- SEDIMENT PATTERNS

In this chapter, wave energy values are calculated for each beach in an attempt to define the distribution of energy along the coast and the relationship with bathymetry and sediments. A model of offshore bathymetry and sediment patterns is proposed for the Sydney coast.

Wave Energy Distribution

Two factors govern the available wave energy at each

beach, the deep water wave characteristics and the bathymetry, The deep water wave characteristics, although temporarily variable, have been defined for the Sydney coast in Chapter 3 86 and comprise a dominant long period south easterly swell of 12 seconds, with secondary waves from the East and Northeast quarters. The deepwater wave energy is redistributed upon entering shallow water, due largely to refraction, diffraction, shoaling and bed friction caused by the impedence of orbital water motion by the sea bed. For a wave with a period of 12 seconds, shallow water energy redistribution begins at 112 metres depth according to equations 2 and 3.

Equation 2 - Wave Length.

Lo = Co T

Equation 3 - Shallow Water d < L/2 where Lo is the deep water wave length, Co is the deepwater wave velocity (g/"Tf 2) . T is the wave period and d is the shallow water depth.

For a planar sediment rich coast with a uniform sand ramp offshore, energy distribution along the coast is relatively uniform. On a coast where the offshore bathymetry and shoreline is irregular, energy is unevenly distributed. This is simply the result of a sedimentary coast adjusting to the dominant wave conditions, whereas wave energy must adjust on a rocky irregular coast.

Accurate calculation of wave energy at a shoreline depends upon the wave theory applied and knowledge of the bathymetry. A measure of wave refraction which is considered to be proportional to energy received at the shoreline, is the standard means of wave energy calculation, (Wiegel, I964) (Johnson and Eagleson, 1966), (Holmes, 1975). Where refraction is the impedence of orbital water motion by the sea bed, bending the wave crests parallel to the bottom contours as a result of changes to wave velocity and wave length. Refraction is determined using the theory developed by 87

Johnson, et al, (1948) and Arthur, et al, (1952), which employs orthogonals that graphically represent energy travelling at right angles to the wave crests. This theory is based upon several assumptions listed in Appendix 4> the most pertinent being that energy is conserved between the orthogonals. For a given set of wave conditions the ortho gonals are projected shoreward according to the predicted wave velocities and wave lengths at specified depth contours.

The orthogonals indicate the distribution of energy, given by

Equation 4«

So Equation 4* Energy = s"b~

/So Kr Jsb

Where So is the deepwater spacing of orthogonals and Sb is the spacing of orthogonals at the break point, Kr is the refraction coefficient which gives a measure of wave height and is the square root of energy. Thus areas of high waves are marked by converging orthogonals and areas of lower waves by diverging orthogonals. In addition to this quantative measure, orthogonals illustrate the role of bathymetry in redistributing energy.

All methods of wave energy calculation are limited by the level of available bathymetric data. The only available bathymetric map of the Sydney coast is the R.A.N. Map AUS 197, giving wide contour intervals and sparse spot depths. The detailed bathymetric charts compiled for this study, covering a major portion of the Sydney coast, permit an accurate measure of wave energy within the limits of present theory.

In an attempt to represent the wave conditions characteristic of the Sydney coast, a wave period of 12 seconds was chosen with directional fronts from the South

East, East and North East quadrants, since the 12s period is 88 the mean of the most common range of periods and these directions are the major directional peaks. (See Chapter 3)» Furthermore, Davies (1958), Wright (1970) and Bryant (1976), have shown that for the S.E. Australian coast, beach plan alignment and mean settling velocity gradings are best correlated with 10-12s S.E. swell waves.

Figures 6-2, 6-3 and 6-4 show the plots of paired orthogonals for 12s S.E., E. and N.W. waves corresponding to each beach. The paired orthogonals were projected to the point on the shore corresponding to the sampling traverses (Figure 1-2). Clearly, the overall solid boundary con figuration of the coast, trending S.S.W.-N.N.W. permits the South East orthogonals to meet the shore with minimal dis persion of energy compared to the orthogonals from the East and North East. This is borne out by the alignment of the beach plans to the South East. The dominance of the South East swell is supported by the symmetry of the sand bodies described in Chapter 4« Eight beaches either have symmetric beach systems, suggesting the valley long axes are normal to the South East or they thicken to the North suggesting that the S.E. waves concentrate sand to the North of the East trending valleys, such as at Bungan. At South Narrabeen, Whale and Palm Beach, the sand bodies are recessed behind large southern headlands and thicken to the South, suggesting that the East and North East orthogonals are more effective. This phenomenon may be characteristic of the sediment bodies associated with zeta-form beaches.

The irregular nature of the offshore bathymetry and shoreline has a profound effect upon the orthogonals. Where rock is dominant both offshore and along the shoreline the wave rays converge, producing high concentrations of energy on associated beaches, such as at North Narrabeen, Bungan and 89 Figure 6-2 Wave orthoKonals for a 12 second south east swell. 90

Figure 6-3 Wave orthogonals for a 12s east swell. Figure 6-4- Wave orthogonals for a 12s north east swell. 92

Avalon. However, where massive headlands project offshore the wave rays converge on these leaving shadow areas of strongly divergent orthogonals, such as at Manly, Dee Why and South Narrabeen. The refraction coefficients calculated for each beach are presented in Table 6-1, listing the beaches in order of decreasing energy.

TADLE 6-1 REFRACTION COEFFICIENTS AND FINE PARTICLE

CUT-OFF TOINTS

BEACH Kr Finns cut-off- AVALON 1.25 1.82 BUNGAN 1.15 1.82 NARRABEEN 1.04 1.77 NEWPORT 0.95 1.44 WHALE 0.78 1.97 CURL CURL 0.77 1.92 BRONTE 0.73 2.05 MONA VALE NTH 0.81 2.26 MONA VALE STH 0.73 2.12 MONA VALE STH 0.55 2.20 PALM BEACH 0.66 2.48 BOND I 0.55 2.20 DEE WHY 0.53 2.38 MANLY 0.51 2.65

The refraction coefficients represent a weighted average for the three wave front directions, S.E., E. and N.E. since the occurrence of these fronts is unevenly

distributed, The weighting is as follows: A0% S.E., 33? E. and 1~1% N.E., based on the wave rider buoy data for the period 1972-1975 (Refer Figure 3-1). The distribution of wave energy at the break point for the 12 beaches is remarkably different, showing an energy gradient along the coast from the high energy beaches, Avalon, Narrabeen, Bungan and Newport to the moderate energy 93 beaches, Bondi, Dee Why and Manly. It is stressed that these values correspond to the sampling traverses and therefore coefficients calculated at other sections of the wider beaches may be expected to differ. This is demonstrated at Mona Vale where refraction coefficients corresponding to the north, middle and south traverses show that wave height increases along the beach from South to North. Reference to the plot of orthogonals shows this is largely due to the offshore extension of Turimetta headland, causing the dominant S«E» wave rays to diverge. Nevertheless, the energy gradient along Mona Vale beach is small compared to the overall distribution of wave energy along the coast. This demonstrates that the gross configuration of the Sydney coast effectively encourages perpendicular approach of the dominant S.E. wave rays, giving rise to orthogonal wave power rather than longshore wave power. The distribution of orthogonal wave power is apparent on two levels. Within a beach system energy increases from south to north and along the coast, gross irregularities of the bathymetry and the shoreline are responsible for extreme differences in wave energy between beaches.

Wave Energy Distribution and Sediments The plot of orthogonals and the table of refraction coefficients for the 12 Sydney beaches confirm quantatively the inferences made in Chapter 5» that wave energy is unevenly distributed along the Sydney coast. This has significant implications for the role of wave energy in the pattern of sediments and the seaward boundary zones identified for each beach.

The range in grain sizes between beaches presented in Table 5-2 and the dominance of orthogonal wave power along the coast suggests that wave energy is responsible for the size sorting of particles along the coast. If wave energy is 94 responsible for the textural differences within and between beaches, there should be a correlation between the mean diameter grain size at the break point and the refraction co-efficients at the break point for the 12 beaches. The refraction coefficient at the break point is considered to be more closely related to wave-induced sediment motion than the energy coefficient, since the horizontal boundary layer flow is a function of wave height and wave length. This is supported by the good empirical trends between grain size and bed velocities established by Komar and Millar (1973)» where the laminar boundary layer flow required to move grain diameters smaller than 1.0 phi is given by equation 5«

Ration 5' (pLpfgD - 0.30 (do/D)'

Where ps is the grain density, p is the fluid density, D is the grain diameter and do is the shallow water orbital diameter and Urn is the maximum horizontal component of orbital velocity near the bed in cm per sec. A comparison of refraction and energy coefficient plots against grain size confirms that wave height is more closely related to sediment movement than simply energy.

Figure 6-5 gives the plot of mean diameter grain size at the break point against the refraction coefficients at the break point for the 12 beaches. The relationship shows a very good positive correlation of increasing grain size with increasing wave height, giving a correlation coefficient of r = 0.78, significant at the 99^ level. The beaches displaying the lower refraction coefficients, Dee Why, Manly and the south end of Mona Vale have the smallest grain sizes. The beaches displaying moderate refraction coefficients, mid Mona Vale - north Mona Vale, Palm Beach, Whale, Bronte, Bondi and Curl Curl have characteristically moderate grain 95

Figure 6-5 The relationship between mean diameter grain size at the break point and refraction coefficients at the break poinfr.

1.0 NEW

NA« ' BUM "/ • M '•cc

8?" Mvfortf)

0 2.0 0-W • •

3.0 . r= 0.786 1.0 2.0 Kr

Figure 6-6 The relationship between the fines cut-off particle size and the refraction coefficients at the break point.

1.0

NEW

NflK • SUM AV

lcc 0 2.0 • * MV(MI>0 Bon PB w D-W

MV (»TH)

3.0

r= 0„782 1.0 2.0 Kr 96 sizes. It is significant that at Mona Vale Beach the correlation for the south, middle and northern sectors is almost linear. This confirms that the longshore variations in grain size are strongly related to longshore-variations in wave height, increasing from South to North and thus, that orthogonal wave power is dominant. The coarsest beaches, Newport, North Narrabeen, Avalon and Bungan have the highest refraction coefficients.

Figure 6-5 shows that variations in orthogonal wave power along the coast are responsible for the variations in grain sizes, both within a beach and between beaches. However, wave energy determines the point in the grain size distribution at which the finer material is removed, rather than the grain size of the coarse tail. If this mechanism applies to size sorting at Sydney beaches a correlation between the fines cut off point for the size distributions and the refraction coefficients should approximate the plot in Figure 6-5• Using the technique reported by Visher (1969)> the grain size at which the finer particles have been removed, has been cal culated for each sample at the break point (Table 6-1, column 3).

Figure 6-6 shows that the correlation is exceptionally good for grain sizes determined at the tail of the dis tributions and given the limitations of the wave theory. The correlation coefficient r = O.78, significant at the 99/v level supports the idea that variations in wave height are responsible for the size sorting of grains both along the Sydney coast and along individual beaches by removing the finer particles to areas of lower energy. Thus, producing grain size distributions that reflect the intensity of wave energy input.

These results support the few other studies made of this phenomenon, along the SoE. Australian coast (Bryant, 1976), 97

(Rosenburg, 1974), at Chcsil Beach, Dorset, (King, 197*0, Half Moon Bay, California (Bascom, 1951), Monterey Bay, California (Johnson and Eagelson, 1966), and Start Bay, Devon (Hails, 1975), that where orthogonal wave power is dominant and sediment supply does not interfere, the beach particle sizes are sorted alongshore according to the distribution of wave height.

The wave-sediment distribution relationship outlined for the Sydney coastline implies that the null-point mechanism at each beach system operates within the grain size-wave power conditions of that beach system. Reference to Figure 5-1, showing the grain size-depth plots and Table 5-2 showing the average grain sizes across the nearshore zone, indicate that the coarser higher energy beaches are coarse across the beach system and the finer lower energy beaches are fine across the beach system. This implies that the sand bodies associated with each beach reflect the wave-sediment relationships at the break point. However, if a large energy gradient occurs between the break point and the seaward boundary, grain sizes would be expected to reflect this, such as at Curl Curl. This steep energy gradient normal to shore would be expected where the orthogonals are widely spaced offshore but divergent at the break point. At Curl Curl this may be related to the offshore extension of North Head.

The null-point theory specifies that the point of in cipient sediment motion at a beach system, and thus the sea ward boundary depends upon the wave conditions and the particle size. Theoretically it may be expected that wave energy determines the width of the active zone, where higher higher energy beaches would have the widest active zones and lower energy beaches the narrowest active zones, given a fairly uniform sediment distribution. However, the point of incipient sediment motion must be further inshore for coarser particles and further offshore for finer particles. 98

For the Sydney beach systems where grain size and wave conditions vary considerably between beaches, the width of the active sediment zone must be a function of the inter relationship between wave energy, particle size, subaqueous slope and the occurrence of bedrock outcrops. If the width of the active zone is measured by the depth at which the sequence of seaward fining grain size is terminated offshore, then it can be seen from Figure 5-1 and Table 5-1 that no simple relationship exists. The higher energy beach systems vary in active zone width from 14 metres depth at Narraboen to 26 metres depth at Dungan, suggesting that at Bungan the wave energy input is the main determinant of the active zone width whereas at Narrabeen the coarse grain size must be dominant. At a low energy beach such as Bondi, the active zone width is greater than at Narrabeen, suggesting that the finer grain size is the determinant of the active zone width. These relationships are complicated by the interference of bedrock in the profile which influences the width of the active zone for 8 beach systems. Figure 6-7 illustrates the effect of each factor on the active zone width, showing that wave energy has a positive relation ship with grain size and with the active zone width, whereas grain size has a negative relationship with the active zone width.

FIGURE 6-7

seaward boundary particle size

active zone width +

wave energy.

The Relationship between Wave Energy, Grain Size and the Active Zone Width 99

It is concluded that the width of the active zone for

Sydney beach systems is not simply a function of wave energy or a balance between wave energy and particle size. An im balance of these forces can produce a narrow active zone for high energy beaches and a relatively wide active zone for low energy beaches. Commonly, the beach active zone is restricted by the outcrop of bedrock.

A Model of Offshore Bathymetry and Sediment Patterns for

Sydney Beaches

The bathymetric surveys and the sediment analyses reported in Chapters 4 and 5 and the wave energy relationships presented in this Chapter have demonstrated that the seaward boundary zone of the beach systems ranges between 14 m and 26 m depth.

This zone is marked either by a textural discontinuity or rock outcrop, distinguishing the seaward fining nearshore sediments from the coarse innershelf material. The sand bodies associated with each beach system may be classified morphologically into three types; an open sand ramp, a sand funnel and a sand pocket, based on the degree of restriction by submerged rock. The majority of beaches have restricted sand bodies due to low sediment availability and are composed characteristically of quartz and shell particles in almost- equal quantities. Of the 12 beach systems studied, only Bondi and Bronte show evidence of a significant sediment input.

This material is quartz sand derived from Pleistocene dunes that comprise these coastal catchments.

The beach systems are not only texturally graded normal to shore, conforming to the null-point theory, but are size graded along the coast both within a beach system coarsening to the north and between beach systems, indicating negligible movement of a material along the roas!:. Correlation of grain 100 sizes at the break point and wave energy values calculated for the same location show that there is a significant positive relationship between the mean size of the particles and the fines cut-off point and the wave heights at each beach. Coarser grains are associated with higher energy beaches and finer grains with lower energy beaches. Within a beach system, coarsening to the north relates to increasing wave heights to the north, confirming that the Sydney beaches are swash aligned due to dominant South Easterly orthogonal wave power.

The large variation in Avave energy distribution along the coast is due to the irregular rocky shoreline and offshore bathymetry. Energy is concentrated at some sections and spread at others. The variation in wave energy distribution and sediment size along the coast can be significant in determining the location of the seaward boundary zone of a beach system. Wave energy alone is not responsible for the width of the active zone, rather a complex inter-relationship exists between wave energy, grain size and bedrock bathymetry. In fact the bedrock bathymetry influences the width of the active zone at eight beach systems.

Figure 6-8 provides a model summary of the offshore bathymetry and sediment patterns of Sydney beaches, illustrating the relationship between the dominant S.E. wave rays and the bathymetry, sand body morphology and textural gradients. 101

Figure 6-8

A Model of Offshore Bathymetry and Sediment Patterns for Sydney Beaches.

5.E. ORTHOfrOM metres

Beach Active Zone. Textural Gradient shore normal and longshore. Mean Diameter Grain Sise: 0 1.0- 0 2.75

O O Inner Shelf coarse sand. o o a Mean Diameter Grain Size: 0 0.6 - 0 1.75

>i Rock

Land, 101

Figure 6-8

A Model of Offshore Bathymetry and Sediment Patterns for Sydney Beaches.

Beach Active Zone. Textural Gradient shore normal and longshore. Mean Diameter Grain Size: 0 1.0- 0 2.75

Inner Shelf coarse sand. Mean Diameter Grain Size: 0 0.6 - 0 1.75

I Rock

Land, 10?-

APPENDIX 1 CHART COMPILATION

Figure A - 1

J.M. IIANN

M.W.S.D.B,

A.D. SHORT

R.A.N

J.M. HANN

I M.W.S . D . B. \ J J.M. IIANN

0 i— Km

Figure A - 1 shows the coverage of the respective surveys used for the compilation of Charts ! nnd 2. Two levels of confidence or survey accuracy are apparent.

1. P.W.D., M.W.S.D.B., A.D. Short and J.M. Hann

2. Royal Australian Navy (R.A.N.)

All soundings have been reduced to Hydrographlc datum, or

0.0 at the Fort Denison tide gauge. APPENDIX 2 Survey lines for outfall studies, 103 (M.W.S.D.B.,1976)

Turimetta Head

North Head

Bondi APPENDIX 2 cont. Survey lines for outfall studies, 104 (M.W.S.D.B.,1976)

JtOCK

3000 4000 5000 7000 DISTANCE (m)

SURVEY LINE 2 - TURIMETTA HEAD 0

20 - E

40 J;

100 1000 2000 3000 4000 5000 DISTANCE tm)

SURVEY LINE 109 -NORTH HEAD

s«^IL

1000 4000 5000 0000 DISTANCE (•»)

SURVEY LINE 9-NORTH HEAD

1000 2000 3000 4000 5000 7000 DISTANCE (»)

SURVEY LIME 13 - BONDI

3000 4000 5000 DISTANCE (n )

SURVEY LINE 14 - BONDI 105

APPENDIX 3a SEDIMENT CHARACTERISTICS TOTAL SAMPLE

BEACH SAMPLE MEAN RELATIVE DIAM. SORTING SKEWNESS KURTOSIS CaCo- IRON TO DATUM GRAIN STAIN. /- (METRES) SIZE 0

(s) AVALON +5.0 1.43 0.25 0.02 1.10 37.7 Strong

+ 1.0 1.38 0.28 -0 . 2 1 1.56 53.0 s

-2.5 1.45 0.25 0.07 1.08 44.0 s

-5.? 1.48 0.2.6 0.05 1 .20 45.0 s

-10.0 1.27 0.36 0.01 . 1.04 58.0 s

-15.0 1.59 0.29 0.05 1.14 45.0 s

-19.0 2.03 0.41 0.08 1.10 47.0 s

-37.0 O.84 0.28 -0.14 1.35 58.0 s

(") BONDI + 1.0 1.66,- 0.39 -0.05 1.34 6.6 VJeak 0.0 1.79 0.32 -0.21 1.21 5.0 w

-4-0 1.95 0.26 0.19 1.11 5.0 w

-12.0 2.0.T 0.31 -0.08 1.15 20.0 w

-20.0 2.09 0.29 -0.03 1.07 11 .8 w

-25.0 2.07 0.28 0.07 1 .07 6.7 w (m) -30.0 1.75 0.2§ 0.30 1.53 5.0Moderate

BRONTE + 1 .0 1.28 0.3 2 -0.16 1.15 8.0 w

-2.0 1.60 0.24 -0.14 1.22 7.0 w

-9.0 1.76 0.30 0.01 1.05 8.0 w

-14.0 1.90 0.38 -0.14 1.11 16.0 w

-19.0 2.08 0.30 -o.oi 1.14 10.0 w

-31.0 1.76 0.29 0.34 1 .50 5.0 m

BUNGAN +6.o 1.48 o.iG 0.19 l.li 20.0 s

+ 1.0 1.47 0.24 0.20 1.69 25.0 s

-1.0 1.46 0.30 0.12 1.54 32.0 s

-4.0 1.57 0.41 -0.11 1.44 37.0 s

-8.0 1.61 0.35 0.15 1.13 36.0 s

-12.0 1.78 0.34 -0.04 1-57 34.5 s

-18.0 1.67 0.4 3 0.08 1 .24 37.0 s

-25.0 1.87 0.38 0.0" 1.17 3?.0 s

-44.0 1 . °o 0.15 0.26 0.8o 39.0 s 106 • • cont•

BEACH SAMPLE MEAN RELATIVE DIAM. SORTING SKEWNESS KURTOSIS CaCo, IRON TO DATUM GRAIN at 0 STAIN. (METRES) SIZE

CURL CURL +5.0 1.51 0.25 0.0 1.08 11.0 s

+ 1.0 1.22 0.31 -0.18 0.82 12.8 s

-1.5 1.63 0.33 0.05 0.92 17.0 m

-4.5 1.73 0.37 -0.04 1.04 33.0 m

-9.5 1.97 0.37 -0.09 1.07 49.0 m

-14.5 2.34 0.36 -0.10 1.06 46.0 m

-19.5 2.36 0.34 -0.18 1.23 37.0 m -24.5 2.48 0.30 -0.18 1.21 29.5 w -39.0 1.18 0.21 0.23 1.27 28.6 m

DEE WHY + 1.0 0.99 0.56 -0.28 0.85 25.3 m -3.0 2.11 0.29 -0.15 1.38 26.8 w

-5.5 2.14 0.30 -0.19 1.25 39.5 w

-11.0 2.38 0.33 -0.09 1.32 39.7 w

-15.5 2.38 0.31 -0.10 1.22 54.5 m

-19.5 2.6f 0.29 -0.06 1.29 29.5 m

-41.0 1.29 0.19 0.09 1.41 17.5 s

MANLY + 1.0 1.55 0.32 0.12 1.13 21.0 w

-3.0 2.18 0.38 -0.21 0.86 34.0 w

-5.0 2.28 0.39 -0.21 1.02 29.5 w

-9.5 2.35 0.55 -0.03 1.27 34.0 w

-14.5 2.64 0.35 -0.12 1.02 24.0 w

-19.5 2.72 0.37 -0.07 1 . 27 24-0 w

MONAVALE + 5.0 1.64 0.22 0.10 1.02 28.9 s

(MID.) + 1.0 1.09 0.35 -0.01 1.13 45.0 s

-1.5 1.93 0.35 -0.20 1.12 43.5 s -4.5 1.76 0.45 0.08 1 .18 37.0 s

-7.5 1.85 0.66 -0.07 1.82 43.5 s

-11.5 1.82 0.37 0.13 1.14 38.8 s

-19.5 2.12 0.52 -0.03 1.25 35.9 m

-39-0 1 -44 o.~3 -0.11 0.66 61.0 m lO*'

•••• confc«

BEACH SAMPLE MEAN RELATIVE DIAM. SORTING SKEWNESS KURTOSIS CaCo. IRON TO DATUM GRAIN % 3 STAIN. (METRES) SIZE

MONAVALE

(NORTH) + 1.0 0.75 0.51 -0.21 1.04 65.3 s -2.0 1.73 0.38 -0.03 1.11 48.9 s

-5.5 1.89 0.45 -0.07 1.11 35.8 s -9.5 2.16 0.39 0.10 0.99 39.5 s

-14.5 1.85 0.35 -0.15 0.77 36.2 s

MONAVALE + 1.0 1.52 0.28 0.09 1.02 69.0 s (SOUTH) -3.0 2.22 0.31 0.09 0.98 36.0 s -6.0 1.72 0.28 -0.02 1.21 33.0 s

-11.0 2.08 0.43 0.04 1.00 58.5 s

-16.0 2.15 0.37 0.02 1.12 26.3 s

*NARRABEEN +5.0 1.25 0.29 0.05 0.72 24.0 (NORTH) + 1.0 1.00 0.26 -0.03 0.78 32.0 m WELLINGTON -2.0 1.40 0.31 -0.12 0.86 m STREET -4.0 1.35 0.33 -0.06 1.11 36.0 -6.0 1.60 0.39 .0.01 0.62

-8.0 1.45 0.44 0.15 0.71 33.0

-10.0 1.55 0.32 0.55 1.16 -12.0 1.65 0.40 O.ll 0.72 36.0

-14.0 1.85 0.38 0.08 0.64

16.0 1.75 0.42 -0.13 0.71 34.0

-18.0 1.65 0.33 0.07 0.63 26.0 -20.0 1.48 0.40 0.08 0.70 22.0

-22.0 1.23 0.47 0.13 0.89 44.0

-24.0 0.60 0.31 0.05 0.79 58.0

-"All data for Narrabeen is from Short (in press).

Wellington St,

T Whetherill St. 108

i ••• cont•

BEACH SAMPLE MEAN RELATIVE DIAM. SORTING SKBWNESS KORTOSI^ CeCo. IROK TO DATUM GRAIN STAIN* (METRES) SIZE

NARRABEEN +7.0 1.25 0.20 0.0 19.0

(SOUTH) +1.0 1.25 0.34 0.02 28.0 m

WHETHERILL -2.0 1.35 0.34 0.01 m

STREET -4.0 1.57 0.14 1.50 32.0

-6.0 1.70 0.32 0.01 27.5

-8.0 1.65 0.33 0.11

-10.0 1.83 0.35 -0.03 30.0

-12.0 1.75 0.31 0.15

-14.0 1.85 0.30 0.00 30.0

-16.0 "1.75 0.27 0.00

-18.0 1.63 0.25 0.04 22.0

-20.0 1.44 0.44 0.27 35.0

-22.0 0.94 0.36 0.16 75.0

-27.5 0.36 0.09

-30.0 0.70 0.28 0.04 88.0

-33.0 1.10 0.46 0.10 89.0

NEWPORT + 1.0 1.41 0.21 0.22 1,.0 4 31.5 s

0.0 1.07 0.35 -0.26 1 .51 44.0 s

-5.0 1.52 0.26 -0.06 1 .07 42.0 s

-9.0 1.60 0.26 -0.04 1 .07 42.0 s

-14.0 1.60 0.25 0.07 1 .03 32.0 s

-22.0 0.64 0.51 0.06 1 .07 80.0 s

-32.0 0.64 0.39 0.11 1 .02 62.0 s

PALM BEACH +1.0 1.58 0.31 -0.20 1 ,37 29.0 s

- -1.5 1.86 0.39 -0.85 1 .07 54.5 s

-5-5 1.96 0.41 0.08 1 .09 50.5 s

-n.5 2.17 0.41 -0.12 0 .96 53.7 s

-19-5 2.2 3 0.37 0.02 1 .01 30.5 s

-33.0 1 .42 0.33 -0.21 1 .12 5.5 s 109

• • • • cot it •

BRACK SAMPLE HBAH RELATIVE DXAM. -PORTING ^KE^&E^ KtJRTOSr? CaCo,, TO DATUM <2RAXN (METM5

WHALE + 1.0 1.48 0.31 -0.03 1.12 54.0 s

-3.0 1.88 0.36 -0.10 0.92 44.5 s -5.5 1.88 0.47 -0.09 1.14 49.0 s

-9.5 2.04 0.47 0.00 1.05 50.7 s •17.5 2.41 0.44 -0.11 1.08 30.4 s 31.0 2.13 0.30 -0.10 1.38 23.3 s 110

APPENDIX 3b SEDIMENT CHARACTERISTICS CARBONATE REMOVED

BEACH SAMPLE MEAN RELATIVE DIAM. SORTING SKEWNESS KURTOSIS TO DATUM GRAIN (METRES) SIZE

AVALON +5.0 1.42 0.24 0.04 1.35

+ 1.0 1.53 0.23 0.09 1.22

-2.5 1.57 0.19 0.15 1.08

-5.2 1.48 0.29 0.17 1.05

-10.0 1.35 0.24 0.01 1.32

-15.0 1.74 0.41 0.24 1.19

-19.0 2.14 0.23 -0.02 0.97

-37.0 0,95 0.25 -0.01 2.00

BONDI +1.0 1.68 0.31 •0.14 1.31

0.0 1.79 0.34 -0.21 1.04

-4.0 2.00 0.28 0.01 1.20

-12.0 2.08 0.28 0.26 1.06

-20.0 2.11 0.29 0.1? 0.88

-25.0 2.02 0.31 0.07 1.07

-30.0 .1.72. 0.24 0.33 1.18

BRONTE + 1.0 1.35 0.26 0.01 1.12

-2.0 1.48 0.30 -0.02 1.09

-9.0 l.8l 0.29 0.04 1.04

-14.0 1.96 0.32 0.02 1.13

-*9.0 2.15 0.30 0.04 1.02

-31.0 1.70 0.24 1.32 1.15

BUNG AN + 6.0 1.53 0.20 0.15 1.00

-1.0 1.50 0.21 0.13 1.08

-1.0 1.62 0.26 0.00 1.08

-4.0 1.74 0.29 0.04 1.02

-8.0 1.83 0.29 0.0? 1.08

-12.0 2.02 0.32 0.01 1.06

-18.0 1.85 0.37 0.05 0.98

-25.0 1.95 0.37 0.05 0.98

-44.0 1 • ~V , 0.17 0.19 1.23 Ill

•. • • corvt •

BEACH SAMPLE MEAN RELATIVE DIAM. SORTING SKEWNESS KURTOSIS TO DATUM GRAIN (METRES) SIZE

CURL CURL +5.0 1.57 0.29 0.08 1.04 +1.0 1.30 0.27 0.01 1.05 -1.5 1.53 0.30 0.15 1.07 -4.5 1.79 0.38 0.16 1.08 -9.5 1.76 0.45 0.24 1.25 -14.5 2.60 0.28 -0.09 1.17 -19.5 2,47 0.35 -0.14 1.13 -24.5 2.29 0.32 -0.08 1.00 -39.0 1.09 0.17 0.30 1.56

DEE WHY +1.0 1.32 0.42 -0.20 1.10 -3.0 2.06 0.34 0.03 1.11 -5.5 2.12 0.30 -0.14 1.21 -11.0 2.45 0.28 0.13 l.ll -15.5 2.57 0.25 0.29 1.04 -19.5 2.59 0.26 0.30 0.93 -41.0 1.25 0.16 0.22 1.39

MANLY +1.0 1.54 0.30 0.14 1.04 -3.0 2.26 0.42 -0.26 1.31 -5.0 2.33 0.39 -0.19 1.18 -9.5 2.42 0.40 -0.24 1.30 -14.5 2.60 0.30 -0.27 1.23 -19.5 2.63 a.36 -0.16 1.80

MONAVALE +5.0 I.58 0.25 -0.00 1.22 (MID) +1.0 1.15 0.30 0.03 1.10 -1.5 1.89 0.30 -0.07 0.93 -4.5 1.85 0.32 -0.21 1.05 -7.5 2.03 0.39 0.03 0.97 -11.5 1.94 0.34 0.07 1.08 -15.0 7.15 0.41 0.12 1.09 -19.3 n.32 0.40 0.09 0.90 -39.0 °.3i 0.51 _o.ro o.ao 112

* * • • cont.

BEACH SAMPLE MEAN RELATIVE DIAM. SORTING SKEWNESS KURTOSIS TO DATtm GRAIN (METRES) SIZE

MONAVALE +1.0 1.21 0.30 -0.35 1.83 (NORTH) -2.0 1.84 0.37 0.00 1.03 -5.5 2.06 0.43 -0.02 1.00 -9.5 2.23 0.41 0.13 0.88 -14.5 2.20 0.28 -0.11 0.89

MONAVALE +1.0 1.68 0.28 -0.17 1.06 (SOUTH) -3.0 1.96 0.33. -0.04 1.24 -6.0 1.78 0.26 -0.01 1.03 -16.0 2.25 0.36 0.23 0.94

NARRABEEN +5.0 1.30 0.28 0.05 (NORTH) +1.0 1.23 0.30 0.06 -2.0 1.25 0.35 0.00 -4.0 1.60 0.26 -0.04 -6.0 1.50 -8.0 0.40 0.17 -10.0 1.65 -12.0 0.36 0.12 -14.0 1.90 -16.0 1.72 0.38 -0.05 -18.0 1.58 0.35 -20.0 1.45 0.34 0.10 -22.0 0.95 0.30 0.02 -24.0 0.25 0.13 113

i • • • cof t& <

BEACH SAMPLE MEAN RELATIVE DIAM* SORTING SKEWNESS KtmTOSiS TO DATtft GRAIN (METRES) SIZE

NARRABEEN +7.0 1.40 0.20 0.00

(SOUTH) +1.0 1.43 0.22 0.10

-2.0 1.35 0.34 -0.05

-4.0 1.70 0.27 -0.08

-6.0 0.28 -0.05

-8.0 1.80

-10.0 0.34 0.35

-12.0 1.76

-14.0 0.30 0.22

-16.0 1.68

-18.0 1.30 0.22 0.08

-20.0 1.07 0.21 0.15

-22.0 0.34

-27.5 1.00

-30.0 0.50 0.15

-33.0 0.95 0.55 -0.13

NEWPORT +1.0 1.51 0.17 0.19 1.13

0.0 1.19 0.20 -0.15 1.44 -5.0 1.52 0.23 0.02 1.08 -9.0 1.65 0.24 0.01 l.Ol

-14.0 1.62 0.24 0.10 1.04 -22.0 0.12 0.66 0.32 1.00

-32.0 0.84 0.48 0.10 0.82

PALM BEACH +1.0 1.50 0.21 -I.85 1.26

-1.5 1.91 0.47 -0.24 1.51 -5.5 2.05 0.39 0.07 1.08

-11.5 2.25 0.34 0.01 l.Ol

-19.5 2.28 0.34 0.00 1.06 -33.0 1.13 0.39 -0.26 1.11 114

• • • • C0**fc •

BBACH SAMPLE MEAN RELATIVE DIAM. SORTI&G SIOWHESS KtfRTOSlf? TO OATW GRAIN (METRES) SIZE

WHALE +1.0 1.58 0.29 0.04 1.18

-3.0 1.95 0.33 -0.11 1.05

-5.5 1.92 0.37 0.11 0.93

-9.5 2.08 0.43 0.03 0.94 -17.5 2,51 0.43 -0.08 0.91 -31.0 2.14 0.26 0.04 1.42 115

APPENDIX 4

Assumptions made for the determination of wave energy by

refraction. (from Wiegel, 1964, PP 157)

1. that the velocity of the wave crests depends only on the

wave length and the still water depth under the crest at each

point;

2. the elements of the wave crest advance in a direction perpendicular to the crest line;

3. that the wave energy is confined between the orthogonals;

4. that the waves are long crested;

5. that the period is constant.

These assumptions, based on Snell's law that predicts the refraction of water gravity waves, have been found to be acceptable for a wide range of wave periods and bathymetric conditions (Wiegel, 1964) 116

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vol. 1 no. 3, 412 - 459- OFFSHORE BATHYMETRY CHAAT 1 Shark Point to Ben Buckler SURVEYED BY : R.A.N. M.W.S.D.B. J.M.HANN COMPILED BY: J.M.HANN CONTOUR INTERVAL 2m ON HYDROGRAPHIC DATUM SCALE: 1:25,000 ACCURACY: DERIH VALUES ±Q.^m LOCATION +I0.0m Increasing Seaward

/ \ BONDI BE^CH

BRONTE BEACH

SAND

SHARK POINT TflSMflN SEA

YL LflN/D

ROCK ;-/ SflMO PATCHES

kilometres I H H H H H I Thesis LG 712 .M4 • E2 no 125

MACOWA«E UNIVERSITY ti©fiABY OFFSHORE BATHYMETRY BflRRflrO JOEY North Head to Barranjoey surveyed by.- R.A.N. P.W.D. A.D.Short J.M.Hann compiled by: J.M.Hann Thesis LG 712 .H4 .E2 no 125

MAC