Wake and Wave Reports: - Cardno Modelling Report - Mulgor ......America's Cup 36 Coastal Processes...

America's Cup 36 Coastal Processes and Dredging Technical Report

Beca // 12 January 2018

3233847 // NZ1-14861405-218 0.218 //

Appendix D

Wake and Wave Reports: - Cardno Modelling Report - Mulgor Field Measurement

Report

Americas Cup Investigations Numerical Wave Modelling

9 January 2018 Cardno i

Americas Cup Investigations

Numerical Wave Modelling

59917161

Prepared for

Panuku Development Auckland

9 January 2018


© Cardno. Copyright in the whole and every part of this document belongs to Cardno and may not be used, sold, transferred, copied or reproduced in whole or in part in any manner or form or in or on any media to any person other than by agreement with Cardno.

This document is produced by Cardno solely for the benefit and use by the client in accordance with the terms of the engagement. Cardno does not and shall not assume any responsibility or liability whatsoever to any third party arising out of any use or reliance by any third party on the content of this document.

59917161 | 9 January 2018 ii

Contact Information Document Information

Registered Name

Cardno (NSW/ACT Pty Ltd

ABN 95 001 145 035

Level 9, 213 Pacific Highway

NSW 2065

Australia

www.cardno.com

Phone+612 9496 7823

Prepared for Panuku Development

Auckland

Project Name Numerical Wave Modelling

File Reference 59917161_R001A

Job Reference 59917161

Date 9 January 2018

Version Number B

Author(s):

Chris Scraggs

Principal Engineer

Effective Date 9/10/2018

Approved By:

Doug Treloar

Senior Principal Engineer

Date Approved 9/01/2018

Document History

Version Effective Date Description of Revision Prepared by Reviewed by

A 22/12/2017 Issued for Review CS PDT

B 09/01/2018 Draft Final CS PDT


59917161 | 22 December 2017 iii

Table of Contents

1 INTRODUCTION 1

2 Wave Penetration Investigations – Wynyard Basin 2

2.1 Model System and Setup 2

2.2 Existing Layout Results 3

2.3 Americas Cup – Option 3.4e (version 3, panel Option A) Results 4

2.4 Americas Cup – Option 3.4e (version 3, panel Option B) Results 5

2.5 1-year ARI Simulation Results 6

3 Wave Penetration Investigations - FFIRF 8

3.1 Model System and Setup 8

3.2 FFIRF – Existing Results 9

3.3 FFIRF – Developed Results 10

3.4 1-Year ARI Simulation Results 11

4 References 12

Appendices

Appendix A Data Review

Appendix B Waves in Hobson West Marina

Appendix C Waves in Freemans Bay

Tables

Table 2-1 Modelled wave heights in the existing layout 3

Table 2-2 Option 3.4e (version 3, panel Option A) 4

Table 2-3 Modelled wave heights in the option 3.4e v3, Panel Option B simulations 5

Table 2-4 Modelled wave heights in the 1-year ARI simulations 7



Table 3-3 Modelled 1-year ARI significant wave heights 11

Figures

Figure 1.1 Locality Plan, Regional Context

Figure 1.2 Locality Plan, Americas Cup and FFIRF

Figure 2.1 Model grid extent and bathymetry, Wynyard Basin Area

Figure 2.2 Existing layout wave panels and reflection and transmission coefficients

Figure 2.3 Wake wave modelling results, Existing layout

Figure 2.4 Wynyard Basin Model extraction locations


59917161 | 22 December 2017 iv

Figure 2.5 Americas Cup Option 3.4e - panel Option A, Reflection and transmission coefficients

Figure 2.6 Wake wave modelling results, Americas Cup Option 3.4e - panel Option A

Figure 2.7 Modelled change in wave height, Americas Cup Option 3.4e - panel Option A

Figure 2.8 Americas Cup Option 3.4e - panel Option B, Reflection and transmission coefficients

Figure 2.9 Wake wave modelling results, Americas Cup Option 3.4e - panel Option B

Figure 2.10 Modelled change in wave height, Americas Cup Option 3.4e - panel Option B

Figure 2.11 1 year ARI wave modelling results

Figure 3.1 Model grid extent and bathymetry, FFIRF Model

Figure 3.2 FFIRF Wake wave modelling results, Existing Layout (300 to 345 Degrees)

Figure 3.3 FFIRF Wake wave modelling results, Existing Layout (0 to 45 Degrees)

Figure 3.4 FFIRF Model Extraction Locations

Figure 3.5 FFIRF Layout, Reflection and transmission coefficients

Figure 3.6 FFIRF Wake wave modelling results, Developed Layout (300 to 345 Degrees)

Figure 3.7 FFIRF Wake wave modelling results, Developed Layout (0 to 45 Degrees)

Figure 3.8 FFIRF modelled change in wave height, 300 to 345 Degrees

Figure 3.9 FFIRF modelled change in wave height, 0 to 45 Degrees

Figure 3.10 1 year ARI wave modelling results, FFIRF Model


59917161 | 22 December 2017 1

1 INTRODUCTION

Development Auckland has engaged Cardno to undertake numerical wave modelling investigations of a region of Auckland Harbour that includes at least Hobson West Marina (operated by Panuku) and the Viaduct Basin. This area is being considered for Americas Cup berthing and servicing, including the basin between the Halsey Pier and Wynyard. Additionally, because some vessels would then need to be relocated from the eastern Wynyard area to the western Wynyard-Westhaven area, wave modelling investigations were required there as well.

The Hobson marina areas are afforded some protection by concrete wave screens installed on the Halsey Pier (western and northern sides) and the Hobson Pier (northern side). However, there are remaining wave penetration problems, caused mainly by bow/stern waves generated by passing ferry traffic. Both the eastern and western Wynyard berthing areas would require new breakwaters (wave screens), piers and decking.

The specified scope of work incorporated the following tasks:-

> Undertake a thorough review of the available data and reports relevant to these sites and advise whether

or not additional data would be beneficial; and the nature and extent thereof of that additional data

collection work;

> Set up a numerical wave modelling system of the existing Hobsons marina and the Wynyard –

Westhaven facilities. Initial model simulations to verify the model using existing/new wake data. This

could be done only in a qualitative manner because of the complex incoming ferry wave structure and

response of the marina basins;

> From assessment of available and project specific wave data, determine appropriate wave model

boundary conditions;

> Together with Auckland Council, BECA and Tonkin & Taylor, develop a range of mitigation options and

present to Development Auckland for assessment;

> Undertake a range of simulations to investigate these options, taking special note of potential worsening

of conditions within the study area and beyond in other harbour areas

> Prepare a factual report on the outcomes.

Figures 1.1 and 1.2 describe the overall site.

This report describes the data, model systems and methods, and then the outcomes of this investigation.

In terms of wave direction, waves are described as ‘coming from’. Note that ferry waves can come from a large range of directions at one time within this overall study area and this characteristic complicates the selection of solutions.

A number of wake monitoring campaigns have been undertaken historically and as part of this project. An overview and review of these different monitoring campaigns are presented in Appendix A, with supplementary data in Appendices B and C.


59917161 | 22 December 2017 2

2 Wave Penetration Investigations – Wynyard Basin

2.1 Model System and Setup

In order to investigate the propagation of ferry waves into the Wynyard Basin, wave penetration modelling was undertaken using the SWASH Wave model system developed by Deltares. Initial investigations used the MIKE-21 BW model developed by DHI, but that system did not handle the short period waves well. These are phase resolving models and they require small grid sizes and time steps. SWASH includes refraction, shoaling, diffraction, bed friction, wave breaking and frequency-direction spectral input. It can include partial and full wave reflectivity – rock breakwaters, attenuators and vertical walls. The model used in this investigation used available bathymetric data provided by Panuka and later, by Beca. The model extent covered a sufficient extent of Auckland Harbour to investigate incident waves from 330o to 75o TN. Waves coming from directions further west than 330o TN are blocked by Wynyard Wharf. These directions encompass the great majority of wave directions determined by Mulgor (2017b) for Freemans Bay. The model domain and bathymetry applied to the Wynyard Basin investigations is presented in Figure 2.1

Each SWASH simulation was run for about 30 minutes of prototype time; allowing the first 10 minutes to establish dynamic equilibrium, before selecting the last 20 minutes for wave analysis. Partial wave reflection was adopted within the marina for foreshore areas protected by rock armour revetment walls, with a wave reflection coefficient of approximately 0.4. Vertical walls were specified as having a reflection coefficient of 0.9. Boundary wave generation in the simulations was set up specifying a time-series of water level boundary fluctuations described by a JONSWAP spectrum with the following shape parameters:

γ= 7.7 – narrow band of wave periods

σa = 0.07

σb = 0.09

Directional spreading of incident waves was set as a maximum of 10 degrees.

Wave penetration modelling was conducted at a water level of Mean Sea Level (1.9 m relative to Auckland CD).

Note that ferry wake waves arrive in intermittent bursts of about 12 to 20 waves, whereas the wave modelling has applied steady-state waves, albeit with a very narrow spectral width. Hence, in some areas of the harbour the incident-reflected wave structure will be too high, notably seaward of Hobsons Marina for the Existing layout.

Numerical wave penetration modelling was undertaken to assess the transformation of the ferry wake as it propagates into the designated berth areas. The modelling has simulated wave agitation within the existing harbour layout and then assessed the changes in wave conditions arising from the proposed harbour works – both within the berth areas and beyond, where increases in wave heights may not be acceptable. A range of developed layouts for the Wynyard Basin were tested and shared with the project team during the project. This report presents the final sets of results.

For the developed ‘final’ layouts, an incident wave height 0.45m, (representative of the maximum wave height in the wake train) with 5 seconds period coming from directions between 30ºN and 75ºN, in 15º increments (total of four directions), was adopted. Note that the extent and character of the existing wave screens was taken from the as-constructed plans for the Halsey Pier (outer western and northern ends) and Hobsons Pier (outer northern end). The wave screen panels extend to within 1m of the seabed – about. Hence some small amount of wave energy can pass beneath the screens, depending upon wave period and tide levels. The transmission/reflection conditions were set-up within the model using numerical porosity – for a 5 seconds wave period. The extent and porosity magnitude is determined from numerical wave flume investigations undertaken before setting up the full model system.

The results presented in this report should be interpreted as the ‘maximum wake wave height’, or Hmax. Based on field investigations and laboratory testing undertaken for similar work in Sydney Harbour, relationships between the average, significant and maximum ferry waves are:

Have = 0.5*Hmax

Hs = 0.9*Hmax (average of highest 1/3 waves in a wake train)

With Hmax being the wave heights presented in the wave-wake tables and figures attached to this report.


59917161 | 22 December 2017 3

2.2 Existing Layout Results

To provide a reference case for comparison, wave penetration into the existing berth areas was simulated first. The existing berth areas include the existing partially transmittive wave panels that extend to 1m above the seabed. The transmission and reflection coefficients for these panels were set at 0.15 and 0.9, respectively.

Figure 2.2 describes this layout, and the results are presented in Figure 2.3. Modelled wave heights have been extracted at the locations presented in Figure 2.4 which are tabulated in Table 2-1.

Table 2-1 Modelled wave heights in the existing layout

Point

Co-ordinates (NZTM 2000) Maximum Wave Height, Hmax (m)

Easting (m) Northing (m) 30º 45º 60º 75º

Probe #1 1,757,137 5,921,467 0.72 0.63 0.63 0.51

Probe #2 1,757,122 5,921,581 0.73 0.61 0.62 0.40

Probe #3 1,757,193 5,921,539 0.75 0.68 0.59 0.60

Probe #4 1,757,413 5,921,518 0.82 0.62 0.56 0.55

Probe #5 1,757,254 5,921,273 0.65 0.69 0.79 0.33

Probe #6 1,757,181 5,921,239 0.52 0.55 0.68 0.24

Inshore 1 1,756,882 5,921,665 0.46 0.62 0.71 0.61

Inshore 2 1,756,970 5,921,538 0.48 0.69 0.63 0.68

Inshore 3 1,757,097 5,921,491 0.70 0.51 0.86 0.68

Inshore 4 1,756,816 5,921,553 0.54 0.71 0.53 0.65

Inshore 5 1,756,874 5,921,531 0.64 0.49 0.43 0.70

Inshore 6 1,756,907 5,921,510 0.45 0.31 0.38 1.06

Inshore 7 1,756,883 5,921,456 0.39 0.26 0.49 0.66

Inshore 8 1,756,844 5,921,409 0.34 0.23 0.36 0.51

Inshore 9 1,756,797 5,921,364 0.43 0.25 0.35 0.47

Inshore 10 1,756,731 5,921,389 0.45 0.44 0.36 0.40

Inshore 11 1,756,669 5,921,415 0.23 0.79 0.30 0.46

Inshore 12 1,756,709 5,921,459 0.26 0.69 0.54 0.50

Inshore 13 1,756,742 5,921,497 0.31 0.73 0.55 0.62

Inshore 14 1,756,776 5,921,532 0.45 0.69 0.60 0.80

Inshore 15 1,757,155 5,921,433 0.59 0.53 0.70 0.48

Inshore 16 1,757,361 5,921,396 0.71 0.84 0.55 0.42

Inshore 17 1,756,936 5,921,251 0.24 0.25 0.24 0.18

Inshore 18 1,756,845 5,921,210 0.16 0.18 0.19 0.19

Inshore 19 1,756,993 5,921,201 0.11 0.13 0.16 0.11

Inshore 20 1,756,918 5,921,327 0.22 0.25 0.23 0.19

Inshore 21 1,756,951 5,921,360 0.25 0.25 0.37 0.21

Inshore 22 1,756,991 5,921,383 0.24 0.32 0.35 0.24

Inshore 23 1,757,024 5,921,372 0.34 0.38 0.40 0.25

Inshore 24 1,757,063 5,921,358 0.27 0.37 0.53 0.17

Inshore 25 1,757,127 5,921,355 0.57 0.55 0.53 0.22

Inshore 26 1,757,169 5,921,339 0.34 0.44 0.60 0.25

Inshore 27 1,757,188 5,921,321 0.58 0.58 0.44 0.25

Inshore 28 1,757,264 5,921,268 0.73 0.63 0.80 0.32

Inshore 29 1,757,190 5,921,231 0.38 0.54 0.58 0.22

Inshore 30 1,757,143 5,921,242 0.37 0.44 0.99 0.41

Inshore 31 1,757,063 5,921,269 0.48 0.50 0.52 0.35


59917161 | 22 December 2017 4

2.3 Americas Cup – Option 3.4e (version 3, panel Option A) Results

Figure 2.5 describes this layout, which includes seaward development of the Halsey Street and Hobsons Piers, two wave panel breakwaters in the water area between Halsey Street Pier and Wynyard Wharf and breakwater protection for the western side of the waterway between Hobsons and Princess Pier. Reflection and transmission coefficients applied to this layout are presented in Figure 2.5.

Results are presented in Figures 2.6 and 2.7 in terms of wave heights and difference plots comparing the layout to the existing layout. Table 2-2 presents the modelled wave heights at the extraction locations for the layout 3.4e (v3), panel option A simulations.

Table 2-2 Option 3.4e (version 3, panel Option A)

Point



Probe #1 1,757,137 5,921,467 0.69 0.60 0.46 0.54

Probe #2 1,757,122 5,921,581 0.66 0.55 0.54 0.40

Probe #3 1,757,193 5,921,539 0.68 0.62 0.59 0.61

Probe #4 1,757,413 5,921,518 0.88 0.61 0.57 0.55

Probe #5 1,757,254 5,921,273 0.59 0.65 0.83 0.35

Probe #6 1,757,181 5,921,239 0.10 0.10 0.09 0.09

Inshore 1 1,756,882 5,921,665 0.36 0.62 0.64 0.52

Inshore 2 1,756,970 5,921,538 0.44 0.55 0.70 0.67

Inshore 3 1,757,097 5,921,491 0.60 0.48 0.84 0.71

Inshore 4 1,756,816 5,921,553 0.36 0.83 0.54 0.42

Inshore 5 1,756,874 5,921,531 0.55 0.30 0.19 0.21

Inshore 6 1,756,907 5,921,510 0.23 0.15 0.10 0.12

Inshore 7 1,756,883 5,921,456 0.18 0.10 0.09 0.13

Inshore 8 1,756,844 5,921,409 0.27 0.10 0.11 0.16

Inshore 9 1,756,797 5,921,364 0.31 0.17 0.16 0.16

Inshore 10 1,756,731 5,921,389 0.24 0.15 0.09 0.10

Inshore 11 1,756,669 5,921,415 0.23 0.13 0.08 0.12

Inshore 12 1,756,709 5,921,459 0.19 0.11 0.08 0.09

Inshore 13 1,756,742 5,921,497 0.20 0.14 0.12 0.10

Inshore 14 1,756,776 5,921,532 0.30 0.18 0.12 0.10

Inshore 15 1,757,155 5,921,433 0.55 0.46 0.57 0.45

Inshore 16 1,757,361 5,921,396 0.74 0.82 0.56 0.42

Inshore 17 1,756,936 5,921,251 0.11 0.11 0.09 0.08

Inshore 18 1,756,845 5,921,210 0.12 0.12 0.12 0.07

Inshore 19 1,756,993 5,921,201 0.07 0.08 0.07 0.04

Inshore 20 1,756,918 5,921,327 0.11 0.13 0.09 0.08

Inshore 21 1,756,951 5,921,360 0.14 0.10 0.11 0.10

Inshore 22 1,756,991 5,921,383 0.15 0.13 0.13 0.11

Inshore 23 1,757,024 5,921,372 0.15 0.18 0.16 0.12

Inshore 24 1,757,063 5,921,358 0.17 0.18 0.15 0.12

Inshore 25 1,757,127 5,921,355 0.32 0.25 0.15 0.13

Inshore 26 1,757,169 5,921,339 0.08 0.07 0.08 0.07

Inshore 27 1,757,188 5,921,321 0.10 0.09 0.07 0.08

Inshore 28 1,757,264 5,921,268 0.66 0.65 0.78 0.35

Inshore 29 1,757,190 5,921,231 0.07 0.08 0.08 0.11

Inshore 30 1,757,143 5,921,242 0.09 0.08 0.09 0.11

Inshore 31 1,757,063 5,921,269 0.20 0.19 0.14 0.09


59917161 | 22 December 2017 5

2.4 Americas Cup – Option 3.4e (version 3, panel Option B) Results

Figure 3.9 describes this layout, which is the same as described in Section 2.3, however, with a differing panel layout. The locations of the panels and the associated reflection and transmission coefficients applied to this layout are presented in Figure 2.8.

Results are presented in Figures 2.9 and 2.10 in terms of wave heights and difference plots comparing the layout to the Existing layout. Table 2-3 presents the modelled wave heights at the extraction locations for the Layout 3.4e (v3), panel Option B simulations.

Table 2-3 Modelled wave heights in the option 3.4e v3, Panel Option B simulations

Point



Probe #1 1,757,137 5,921,467 0.72 0.61 0.48 0.60

Probe #2 1,757,122 5,921,581 0.73 0.58 0.56 0.46

Probe #3 1,757,193 5,921,539 0.72 0.65 0.63 0.63

Probe #4 1,757,413 5,921,518 0.88 0.61 0.59 0.58

Probe #5 1,757,254 5,921,273 0.63 0.70 0.84 0.39

Probe #6 1,757,181 5,921,239 0.06 0.08 0.07 0.09

Inshore 1 1,756,882 5,921,665 0.37 0.62 0.66 0.53

Inshore 2 1,756,970 5,921,538 0.47 0.58 0.83 0.71

Inshore 3 1,757,097 5,921,491 0.67 0.46 0.86 0.76

Inshore 4 1,756,816 5,921,553 0.36 0.83 0.54 0.42

Inshore 5 1,756,874 5,921,531 0.54 0.30 0.20 0.20

Inshore 6 1,756,907 5,921,510 0.22 0.15 0.11 0.12

Inshore 7 1,756,883 5,921,456 0.18 0.10 0.10 0.13

Inshore 8 1,756,844 5,921,409 0.27 0.10 0.11 0.16

Inshore 9 1,756,797 5,921,364 0.31 0.18 0.18 0.17

Inshore 10 1,756,731 5,921,389 0.23 0.15 0.09 0.10

Inshore 11 1,756,669 5,921,415 0.23 0.13 0.09 0.12

Inshore 12 1,756,709 5,921,459 0.19 0.11 0.09 0.10

Inshore 13 1,756,742 5,921,497 0.19 0.15 0.13 0.11

Inshore 14 1,756,776 5,921,532 0.29 0.18 0.12 0.10

Inshore 15 1,757,155 5,921,433 0.56 0.49 0.63 0.53

Inshore 16 1,757,361 5,921,396 0.74 0.83 0.57 0.44

Inshore 17 1,756,936 5,921,251 0.12 0.13 0.11 0.10

Inshore 18 1,756,845 5,921,210 0.13 0.15 0.15 0.09

Inshore 19 1,756,993 5,921,201 0.08 0.10 0.08 0.06

Inshore 20 1,756,918 5,921,327 0.12 0.14 0.11 0.09

Inshore 21 1,756,951 5,921,360 0.16 0.12 0.13 0.11

Inshore 22 1,756,991 5,921,383 0.17 0.15 0.16 0.14

Inshore 23 1,757,024 5,921,372 0.17 0.21 0.18 0.13

Inshore 24 1,757,063 5,921,358 0.19 0.21 0.19 0.15

Inshore 25 1,757,127 5,921,355 0.33 0.30 0.21 0.18

Inshore 26 1,757,169 5,921,339 0.09 0.08 0.06 0.06

Inshore 27 1,757,188 5,921,321 0.09 0.07 0.05 0.05

Inshore 28 1,757,264 5,921,268 0.70 0.66 0.80 0.37

Inshore 29 1,757,190 5,921,231 0.06 0.06 0.06 0.11

Inshore 30 1,757,143 5,921,242 0.10 0.09 0.06 0.08

Inshore 31 1,757,063 5,921,269 0.22 0.23 0.16 0.07


59917161 | 22 December 2017 6

2.5 1-year ARI Simulation Results

The model was applied to simulate the transformation of the 1-year ARI wind wave conditions as they propagate into the harbour. This has been simulated using the same model setup as that described in Section 2.1, however, the boundary specification has been amended to:

γ= 2.0 – wide band of wave periods to describe a developing sea state

σa = 0.07

σb = 0.09

Tp = 3.0 s


The boundary significant wave height was set as 0.6m, with the main direction from the north (i.e. 0º TN). Due to the short period (3 seconds), and the numerical dispersion inherent in phase resolving models at low periods such as SWASH, the boundary significant wave height was increased to 0.75m to ensure a 0.6m significant wave height propagated into the model without excessive dispersion and under-propagation of the specified boundary wave height.

The simulations have been undertaken for the existing case, as well as the two Americas Cup Option 3.4e layouts. The results of these simulations are presented in Figure 2.11 and tabulated in Table 2-4.

Note that the results presented for the 1-year ARI simulations are Significant Wave Height, because this is more applicable to a sea state.


59917161 | 22 December 2017 7

Table 2-4 Modelled wave heights in the 1-year ARI simulations

Point

Co-ordinates (NZTM 2000) Significant Wave Height, Hs (m)

Easting (m) Northing (m) Existing Panel Option A Panel Option B

Probe #1 1,757,137 5,921,467 0.57 0.54 0.57

Probe #2 1,757,122 5,921,581 0.61 0.58 0.61

Probe #3 1,757,193 5,921,539 0.59 0.56 0.57

Probe #4 1,757,413 5,921,518 0.71 0.69 0.70

Probe #5 1,757,254 5,921,273 0.49 0.37 0.38

Probe #6 1,757,181 5,921,239 0.40 0.07 0.08

Inshore 1 1,756,882 5,921,665 0.36 0.34 0.35

Inshore 2 1,756,970 5,921,538 0.54 0.52 0.55

Inshore 3 1,757,097 5,921,491 0.55 0.52 0.55

Inshore 4 1,756,816 5,921,553 0.34 0.33 0.33

Inshore 5 1,756,874 5,921,531 0.37 0.30 0.30

Inshore 6 1,756,907 5,921,510 0.41 0.10 0.10

Inshore 7 1,756,883 5,921,456 0.38 0.13 0.14

Inshore 8 1,756,844 5,921,409 0.32 0.19 0.18

Inshore 9 1,756,797 5,921,364 0.30 0.20 0.20

Inshore 10 1,756,731 5,921,389 0.38 0.13 0.13

Inshore 11 1,756,669 5,921,415 0.33 0.05 0.05

Inshore 12 1,756,709 5,921,459 0.35 0.08 0.08

Inshore 13 1,756,742 5,921,497 0.33 0.10 0.10

Inshore 14 1,756,776 5,921,532 0.31 0.10 0.10

Inshore 15 1,757,155 5,921,433 0.59 0.56 0.58

Inshore 16 1,757,361 5,921,396 0.67 0.65 0.65

Inshore 17 1,756,936 5,921,251 0.09 0.05 0.06

Inshore 18 1,756,845 5,921,210 0.08 0.05 0.07

Inshore 19 1,756,993 5,921,201 0.05 0.03 0.03

Inshore 20 1,756,918 5,921,327 0.10 0.06 0.07

Inshore 21 1,756,951 5,921,360 0.14 0.06 0.08

Inshore 22 1,756,991 5,921,383 0.14 0.07 0.09

Inshore 23 1,757,024 5,921,372 0.18 0.11 0.13

Inshore 24 1,757,063 5,921,358 0.17 0.09 0.10

Inshore 25 1,757,127 5,921,355 0.44 0.34 0.40

Inshore 26 1,757,169 5,921,339 0.32 0.07 0.09

Inshore 27 1,757,188 5,921,321 0.34 0.09 0.11

Inshore 28 1,757,264 5,921,268 0.51 0.42 0.43

Inshore 29 1,757,190 5,921,231 0.41 0.08 0.07

Inshore 30 1,757,143 5,921,242 0.40 0.11 0.13

Inshore 31 1,757,063 5,921,269 0.26 0.17 0.19


59917161 | 22 December 2017 8

3 Wave Penetration Investigations - FFIRF

3.1 Model System and Setup

In order to investigate the propagation of ferry waves into the FFIRF Basin, wave penetration modelling was undertaken using the SWASH Wave model system developed by Deltares. The model used in this domain used available bathymetric data provided by Panuka and later, by Beca. The model extent covered a sufficient extent of western Wynyard and Westhaven Marina within Auckland Harbour to investigate incident waves propagating from 300o to 45o TN. Waves coming from directions further west than 300o TN are unlikely to propagate into the FFIRF Wharf. The model domain and bathymetry applied to the FFIRF investigations is presented in Figure 3.1.

Each SWASH simulation was run for about 30 minutes of prototype time; allowing the first 10 minutes to establish dynamic equilibrium, before selecting the last 20 minutes for wave analysis. Partial wave reflection was adopted within the marina for foreshore areas protected by rock armour revetment walls, with a wave reflection coefficient of approximately 0.4. Vertical walls were specified as having a reflection coefficient of 0.9. Boundary wave generation in the simulations was set up specifying a time-series of water level boundary fluctuations described by a JONSWAP spectrum with the following shape parameters:

γ= 7.7 – narrow band of wave periods

σa = 0.07

σb = 0.09

Tp = 5.0 s


Wave penetration modelling was conducted at a water level of Mean Sea Level (1.9 m relative to Auckland CD).

Numerical wave penetration modelling was undertaken to assess the transformation of the ferry wake as it propagates into the designated berth areas. The modelling has simulated wave agitation within the existing harbour layout and then assessed the changes in wave conditions arising from these harbour works – both within the berth areas and beyond, where increases in wave heights may not be acceptable. A range of developing layouts for the FFIRF Basin were tested and the results shared with the project team during the project. This report presents the final sets of results.

For the developed ‘final’ layouts, an incident wave height 0.45m (representative of the maximum wave height in the wake train) with 5 seconds period coming from directions between 300ºN to 45ºN, in 15º increments (total of eight directions) was adopted.


59917161 | 22 December 2017 9

3.2 FFIRF – Existing Results

To provide a reference case for comparison, wave penetration into the Existing Layout was simulated first. The model includes the whole Westhaven basin, outer breakwaters and the existing wave screen. The model has assumed that these are non-transmittive structures with a reflection coefficient of 0.4 for the breakwaters and revetments and 0.9 for the existing screen.

The results are presented in Figures 3.2 and 3.3. Modelled wave heights have been extracted at the locations presented in Figure 3.4, which are tabulated in Table 3-1.


Point


Easting (m) Northing (m) 300º 315º 330º 345º 0º 15º 30º 45º

FFIRF 1 1,756,633 5,921,771 0.32 0.53 0.42 0.42 0.44 0.50 0.43 0.20

FFIRF 2 1,756,621 5,921,781 0.32 0.53 0.42 0.45 0.43 0.45 0.54 0.29

FFIRF 3 1,756,610 5,921,792 0.32 0.52 0.43 0.45 0.44 0.44 0.51 0.38

FFIRF 4 1,756,598 5,921,804 0.34 0.52 0.43 0.43 0.44 0.43 0.43 0.38

FFIRF 5 1,756,587 5,921,813 0.34 0.51 0.43 0.43 0.43 0.44 0.41 0.36

FFIRF 6 1,756,618 5,921,754 0.23 0.49 0.46 0.46 0.45 0.51 0.40 0.17

FFIRF 7 1,756,607 5,921,764 0.22 0.47 0.46 0.48 0.44 0.47 0.54 0.26

FFIRF 8 1,756,595 5,921,776 0.23 0.47 0.46 0.48 0.45 0.44 0.53 0.37

FFIRF 9 1,756,582 5,921,788 0.23 0.46 0.45 0.47 0.46 0.44 0.43 0.41

FFIRF 10 1,756,570 5,921,798 0.24 0.46 0.45 0.46 0.44 0.46 0.41 0.38

FFIRF 11 1,756,601 5,921,744 0.18 0.39 0.53 0.49 0.46 0.53 0.45 0.18

FFIRF 12 1,756,586 5,921,759 0.17 0.38 0.52 0.47 0.49 0.44 0.58 0.32

FFIRF 13 1,756,567 5,921,776 0.18 0.37 0.48 0.45 0.45 0.46 0.42 0.44

FFIRF 14 1,756,584 5,921,725 0.12 0.27 0.51 0.46 0.48 0.55 0.45 0.17

FFIRF 15 1,756,568 5,921,740 0.12 0.26 0.49 0.45 0.51 0.47 0.60 0.29

FFIRF 16 1,756,550 5,921,758 0.13 0.28 0.45 0.44 0.44 0.46 0.43 0.50

FFIRF 17 1,756,578 5,921,704 0.09 0.18 0.40 0.49 0.58 0.50 0.32 0.12

FFIRF 18 1,756,564 5,921,718 0.09 0.19 0.38 0.48 0.53 0.55 0.53 0.20

FFIRF 19 1,756,544 5,921,736 0.10 0.20 0.38 0.45 0.43 0.51 0.60 0.44

FFIRF 20 1,756,551 5,921,692 0.07 0.14 0.29 0.50 0.45 0.60 0.45 0.13

FFIRF 21 1,756,533 5,921,709 0.08 0.14 0.27 0.47 0.37 0.50 0.70 0.29

FFIRF 22 1,756,517 5,921,724 0.08 0.16 0.26 0.44 0.39 0.36 0.34 0.61

FFIRF 23 1,756,540 5,921,679 0.07 0.11 0.23 0.44 0.42 0.56 0.50 0.12

FFIRF 24 1,756,521 5,921,696 0.07 0.12 0.22 0.40 0.40 0.47 0.70 0.31

FFIRF 25 1,756,504 5,921,712 0.07 0.14 0.22 0.37 0.44 0.33 0.27 0.62


59917161 | 22 December 2017 10

3.3 FFIRF – Developed Results

Figure 3.5 describes this layout. This layout includes development of the 108 Hamer St Yard, northern wharf with a double panel breakwater, and floating pontoons and open wharves.

Results are presented in Figures 3.6 to 3.9 in terms of wave heights and wave-height difference plots comparing this layout to the Existing Layout. Table 3-2 presents the modelled wave heights at the extraction locations for the FFIRF simulations.


Point


Easting (m) Northing (m) 300º 315º 330º 345º 0º 15º 30º 45º

FFIRF 1 1,756,633 5,921,771 0.15 0.27 0.31 0.35 0.38 0.43 0.35 0.17

FFIRF 2 1,756,621 5,921,781 0.16 0.28 0.33 0.39 0.37 0.40 0.48 0.25

FFIRF 3 1,756,610 5,921,792 0.19 0.32 0.33 0.39 0.38 0.36 0.42 0.32

FFIRF 4 1,756,598 5,921,804 0.24 0.39 0.35 0.38 0.40 0.39 0.37 0.31

FFIRF 5 1,756,587 5,921,813 0.33 0.47 0.38 0.38 0.39 0.41 0.38 0.33

FFIRF 6 1,756,618 5,921,754 0.23 0.40 0.31 0.23 0.17 0.13 0.09 0.07

FFIRF 7 1,756,607 5,921,764 0.23 0.40 0.31 0.25 0.17 0.14 0.09 0.07

FFIRF 8 1,756,595 5,921,776 0.24 0.42 0.33 0.27 0.20 0.16 0.11 0.08

FFIRF 9 1,756,582 5,921,788 0.24 0.43 0.36 0.32 0.25 0.20 0.14 0.11

FFIRF 10 1,756,570 5,921,798 0.23 0.43 0.43 0.44 0.40 0.36 0.27 0.21

FFIRF 11 1,756,601 5,921,744 0.15 0.31 0.34 0.21 0.15 0.11 0.08 0.06

FFIRF 12 1,756,586 5,921,759 0.16 0.32 0.38 0.27 0.19 0.15 0.10 0.07

FFIRF 13 1,756,567 5,921,776 0.18 0.35 0.47 0.40 0.34 0.28 0.19 0.13

FFIRF 14 1,756,584 5,921,725 0.13 0.28 0.50 0.33 0.22 0.15 0.10 0.07

FFIRF 15 1,756,568 5,921,740 0.13 0.27 0.50 0.42 0.33 0.23 0.14 0.09

FFIRF 16 1,756,550 5,921,758 0.12 0.25 0.45 0.44 0.46 0.40 0.27 0.17

FFIRF 17 1,756,578 5,921,704 0.09 0.19 0.44 0.40 0.28 0.17 0.10 0.07

FFIRF 18 1,756,564 5,921,718 0.09 0.18 0.40 0.47 0.37 0.25 0.14 0.09

FFIRF 19 1,756,544 5,921,736 0.09 0.18 0.36 0.46 0.45 0.40 0.26 0.15

FFIRF 20 1,756,551 5,921,692 0.08 0.14 0.28 0.54 0.44 0.31 0.17 0.08

FFIRF 21 1,756,533 5,921,709 0.08 0.14 0.27 0.43 0.44 0.43 0.28 0.16

FFIRF 22 1,756,517 5,921,724 0.08 0.13 0.25 0.44 0.37 0.44 0.37 0.26

FFIRF 23 1,756,540 5,921,679 0.07 0.11 0.23 0.43 0.48 0.38 0.21 0.10

FFIRF 24 1,756,521 5,921,696 0.07 0.11 0.22 0.39 0.42 0.46 0.32 0.19

FFIRF 25 1,756,504 5,921,712 0.07 0.12 0.21 0.37 0.42 0.37 0.37 0.28


59917161 | 22 December 2017 11

3.4 1-Year ARI Simulation Results

The model was applied to simulate the transformation of the 1-year ARI wind wave conditions as they propagate into the FFIRF facility. This process has been simulated using the same model setup as described in Section 3.1, however, the boundary specification has been amended to:

γ= 2.0 – wide band of wave periods to describe a developing sea state

σa = 0.07

σb = 0.09

Tp = 3.0 s


The boundary significant wave height was set as 0.6m, with the main direction from the north (i.e. 0º TN). Due to the short period (3 seconds), and the numerical dispersion inherent in phase resolving models at low periods such as SWASH, the boundary significant wave height was increased to 0.75m to ensure that a 0.6m significant wave height propagated into the model without excessive dispersion.

The simulations have been undertaken for the existing and developed cases. The results of these simulations are presented in Figure 3.10 and tabulated in Table 3-3.

Note that the results presented for the 1-year ARI simulations are Significant Wave Height, because this is more applicable to a sea state.

Table 3-3 Modelled 1-year ARI significant wave heights

Point

Co-ordinates (NZTM 2000) Significant Wave Height, Hs (m)

Easting (m) Northing (m) Existing Developed

FFIRF 1 1,756,633 5,921,771 0.49 0.44

FFIRF 2 1,756,621 5,921,781 0.48 0.42

FFIRF 3 1,756,610 5,921,792 0.50 0.46

FFIRF 4 1,756,598 5,921,804 0.53 0.49

FFIRF 5 1,756,587 5,921,813 0.52 0.51

FFIRF 6 1,756,618 5,921,754 0.48 0.12

FFIRF 7 1,756,607 5,921,764 0.50 0.14

FFIRF 8 1,756,595 5,921,776 0.46 0.16

FFIRF 9 1,756,582 5,921,788 0.47 0.21

FFIRF 10 1,756,570 5,921,798 0.48 0.39

FFIRF 11 1,756,601 5,921,744 0.47 0.22

FFIRF 12 1,756,586 5,921,759 0.48 0.27

FFIRF 13 1,756,567 5,921,776 0.45 0.36

FFIRF 14 1,756,584 5,921,725 0.47 0.27

FFIRF 15 1,756,568 5,921,740 0.43 0.32

FFIRF 16 1,756,550 5,921,758 0.47 0.40

FFIRF 17 1,756,578 5,921,704 0.39 0.24

FFIRF 18 1,756,564 5,921,718 0.41 0.31

FFIRF 19 1,756,544 5,921,736 0.43 0.36

FFIRF 20 1,756,551 5,921,692 0.37 0.29

FFIRF 21 1,756,533 5,921,709 0.44 0.37

FFIRF 22 1,756,517 5,921,724 0.42 0.38

FFIRF 23 1,756,540 5,921,679 0.36 0.30

FFIRF 24 1,756,521 5,921,696 0.41 0.35

FFIRF 25 1,756,504 5,921,712 0.40 0.37


59917161 | 22 December 2017 12

4 References

AS3962 (2010): Standards Australia. Guidelines for Design of Marinas.

PIANC (2016): Guidelines for Marina Design, Parts I & II. Report No. 149.

Mulgor (2017a): Waves in Hobson West Marina.

Mulgor (2017b): Waves in Freemans Bay.


59917161 | 22 December 2017 13


FIGURES

59917161 Jan 2018N:\Projects\599\FY17\161_Hobson West Marina Wave Modelling\


Locality PlanRegional Context

Figure 1.1



Locality PlanAmericas Cup and FFIRF

Figure 1.2



Model grid extent and bathymetryWynyard Basin Area

Figure 2.1



Existing layout wave panelsand reflection and transmission coefficients

Figure 2.2



Wake wave modelling resultsExisting layout

Figure 2.3



Wynyard Basin Model extraction locations

Figure 2.4



Americas Cup Option 3.4e − panel Option AReflection and transmission coefficients

Figure 2.5



Wake wave modelling resultsAmericas Cup Option 3.4e − panel Option A

Figure 2.6



Modelled change in wave heightAmericas Cup Option 3.4e − panel Option A

Figure 2.7



Americas Cup Option 3.4e − panel Option BReflection and transmission coefficients

Figure 2.8



Wake wave modelling resultsAmericas Cup Option 3.4e − panel Option B

Figure 2.9



Modelled change in wave heightAmericas Cup Option 3.4e − panel Option B

Figure 2.10



1 year ARI wave modelling results

Figure 2.11



Model grid extent and bathymetryFFIRF Model

Figure 3.1



FFIRF Wake wave modelling resultsExisting Layout (300 to 345 Degrees)

Figure 3.2



FFIRF Wake wave modelling resultsExisting Layout (0 to 45 Degrees)

Figure 3.3



FFIRF Model Extraction Locations

Figure 3.4



FFIRF LayoutReflection and transmission coefficients

Figure 3.5



FFIRF Wake wave modelling resultsDeveloped Layout (300 to 345 Degrees)

Figure 3.6



FFIRF Wake wave modelling resultsDeveloped Layout (0 to 45 Degrees)

Figure 3.7



FFIRF modelled change in wave height300 to 345 Degrees

Figure 3.8



FFIRF modelled change in wave height0 to 45 Degrees

Figure 3.9



1 year ARI wave modelling resultsFFIRF Model

Figure 3.10


59917161 | 22 December 2017 15


APPENDIX

DATA REVIEW


59917161 | 22 December 2017 16

As part of Cardno’s wave modelling engagement, two previous ferry and wind wave assessment reports were reviewed. They were:-

Hobson West Marina: Wave Measurement. Report prepared for Ports of Auckland by Beca CarterHollings & Ferner Ltd in 2000

Effect of Ocean Waves on the Viaduct Marina, Auckland. Thesis prepared by Stephen William Curriefor fulfilment of Master of Civil Engineering, The University of Auckland, 2014.

A.1 Beca Carter et al

DOBIE pressure-recording wave gauges were installed at the seaward end of Wynyard Wharf and the south-east corner of the Hobson West Marina. About 1 month of data was obtained in January-February, 2000. Recording bursts of 3.5 minutes at intervals of 30 minutes were obtained. Analyses were undertaken more for wind waves than ferry wake. However, additional ferry wake observations were made on 10 and 11 February during early morning calm periods. Visual and video recordings were made. The outcome was that wind waves in the south-east corner of the marina appear to be attenuated by about 50%. The observed wave heights were assessed to be ‘good’ in terms of AS3962. Some analysis of the wave data recorded within the marina was undertaken to relate observed waves to ferry passages. However, there is no detail on wave periods and no detail on pressure corrections for deployment depth of transducers. Moreover, events identified as ferry wave cases were analysed using wind wave processing methods; and that approach can under-estimate ferry wave heights.

A.2 Currie Thesis

Two Nortek Aquadopp current meters were applied for short periods – one kept in the same location outside of the marina for the duration of the sampling exercise. These instruments recorded X & Y currents over periods of about 10 to 20 minutes. Periods of sea waves and ferry waves were identified and were considered separately. The records were linearly de-trended to remove tide and then analysed using zero up-crossing and spectral methods, thereby leading to wave heights being described in terms of significant wave height. This parameter is not suited to ferry wave analysis because these waves occur as short groups of waves. A second spectral analysis approach was applied also. Currie also undertook some numerical wave modelling; mainly for wind waves – the main direction of his studies. He advised that incident ferry waves have significant heights up to 0.25m with periods between 4 and 6 seconds. He notes that no ferry waves exceeded a height of 0.15m within the marina – being a threshold that was considered at that time to define acceptable ferry wave heights affecting moored pleasure craft.

A.3 Summary

Both authors effectively advised that ferry wave conditions within the marina are acceptable for berthed vessels; however, it is known that this is not the case. More recent advice from PIANC (2016), together with the experience of the marina operators and users, suggests that this is not the case – especially in terms of day-to-day at-berth vessel motions caused by ferry waves. Penetration of ferry waves into the marina areas depends upon ferry wave incident direction (likely to be very variable) and wave period. Furthermore, there is some uncertainty in incident wave height, given the lack of clarity in depth-pressure correction methods applied and the adoption of the significant wave parameter to describe these heights.

The numerical wave modelling is very dependent on wave period for assessment of methods that provide improved protection from ferry waves entering the marina. Onsite observation by Cardno suggests a common ferry wave period of 3 to 3.5 seconds and incident heights (seaward of the marina entrance), up to about 0.3m (individual, higher waves). Preliminary wave modelling of the existing layout showed that there is significant internal reflection of these waves from existing vertical walls.

A.4 Ferry Wave Re-analysis

The Auckland University wave data recorded at the site seaward of the entrance was re-analysed by Cardno using a time-series approach, and correcting for pressure attenuation with depth. This data has been processed assuming that the depth at the site is about 5m more than the gauge readings (i.e. about 7m at high tide).

There are three periods when boat wake is evident, as shown by the boxes in the top graph shown in Figure 2.1. The tide is rising over this period of time.

The water level data has been extracted for each of these periods, de-trended (i.e. removed the tide), and a zero up-crossing analysis performed to extract individual wave heights and periods. Each of these periods is


59917161 | 22 December 2017 17

presented in Figure A.1, with the three analysis periods presented in separate panels, and with the analysed portions shown in orange.

This re-analysis indicates that the average incident wake wave period is between 3.5 and 4.5 seconds. Once corrected for pressure attenuation (factors of 1.33, 1.40 and 1.46 were applied assuming 4.5 seconds wave periods), the largest wake waves for each wave train were 46cm, 33cm and 43cm (refer Table A-1). Note that the plots are ‘uncorrected’. For Wake 1 the maximum height is about 0.35m (in figure) x 1.33 = 0.46m. However, the data is complex and will include incident wakes from a number of ferries and some reflected wave energy from the marina wave-screen walls. On the other hand, the instrument was deployed about 40m seaward of the marina entrance and coherence will be low at a little more than 1 wavelength distance from the wall. These wave heights appear a little higher than observed, but the more common waves in each train are smaller.

Table A-1 Re-Analysed Ferry Wake Data – Seaward of Hobson West Marina Entrance

Wave Train 1 Wave Train 2 Wave Train 3

Maximum Wave Height (m) 0.46 0.33 0.43

Average Wave Period (s) 4.5 4.3 4.2

Period of Maximum Wave (s) 4.5 3.7 4.3

A.5 Additional Data

The forgoing discussion addressed the lack of reliable data and the importance of data to this investigation. Hence Cardno discussed this issue with Council (Philip Wardale), together with prospective groups who could provide reliable data collection methods and analyses. They were Shearwater (Jonathan Duffy) and Mulgor (Derek Goring). These people undertook recent similar data collection and analyses studies for Port of Marlborough at Waikawa. Three pressure instruments were deployed in an array within Hobsons Marina that allowed estimation of wave directions, periods and heights. Wavelet theory and first order pressure/depth correction was used to analyse individual waves/periods (Mulgor 2017a). A second deployment and data analysis task was undertaken in October 2017; placing a three-probe array of pressure transducers in Freemans Bay immediately outside the entrance to Hobsons Marina and generally where an initial Americas Cup harbour area might be developed. One additional probe was placed on the seaward end of Princess Pier and two others, one each side of Hobsons Pier. Figures 2.2 and 2.3 describe the deployment locations.

Mulgor reports have been included as Appendices B and C.

A.5.1 Mulgor – Hobsons Bay

Mulgor (2017a) describes the installation, insitu-calibration and results determined from the deployment of three pressure transducer wave probes within Hobsons Bay. Analysis of this data was complicated by complex nature of marina wave trains caused by multiple ferry movements and reflections from marina walls. Results included wave heights (individual), wave periods and directions.

Mulgor undertook what was described as an event analysis, in which individual wave heights that exceeded an adopted threshold (0.25m in this case) at Pile #2 were identified. Note, that should a lower threshold, such as 0.1m, have been adopted, then many more ‘events’ would have been identified. Mulgor identified three patterns of marina waves, but the two most important arose from waves entering the marina through the main entrance and those entering the marina by propagating from the ferry operations area and under the Princess and Hobsons wharves.

Typically, waves entering the marina through its entrance had periods of about 4 seconds, whereas those propagating beneath the wharves exhibited periods from 4.5 to 6.5 seconds. Other waves were determined to have been caused by vessel movements within the marina areas (up to 0.49m on one occasion). However, most commonly, it was not possible to determine a specific group – most likely as a result of waves being caused by more than one ferry or the presence of some wind wave energy. In one instance a wave height of 0.49 m was recorded, probably as a result of combined incident and reflected waves.


59917161 | 22 December 2017 18

A.5.2 Mulgor – Freemans Bay

This deployment was undertaken over a period of only about five days because of the urgency of investigations required for Americas Cup planning. Similar methods of wave data analysis were allied to Mulgor (2017b) data. In this case wave conditions were affected less by wave reflections and an event threshold of 0.35m was adopted.Wave directions were determined to be from 40o to 70o TN, typically, but with incident of 35o and one of 106o TN. However, in many cases the wave data was too complex for Mulgor to determine wave direction.

Maximum individual wave heights did not exceed 0.55m at any of the three Freemans Bay wave recorders. Wave periods were more commonly about 4 seconds, up to 4.5 seconds, but wave periods in the order of 6 seconds (Mulgor 2017a), were not identified in Freemans Bay. The cause of this outcome is not understood.

In addition to the three wave probes deployed in Freemans Bay, three similar wave probes were deployed, one on the western, seaward end of Princes Pier and one each on the eastern and western sides of mid-Hobsons Pier in order to describe wave heights entering Hobsons Marina under these wharves from the Auckland ferry terminal operations area. Of the waves recorded during the deployment period, the largest waves, ≈0.37m, occurred at the seaward end of Princes Pier, with smaller waves, up to 0.3m and 0.25, at the eastern and western sides of Hobsons Pier.

These results are consistent with Cardno’s data re-analysis – Section A.4. Hence, incident wave periods are likely to be up to 5 seconds, typically.

Up to this time, a highest, common wave period of 6 seconds was applied to much of the Americas Cup wave modelling because longer wave periods penetrate more effectively into the marina berths and the Mulgor (2017a) data pointed to the incidence of these waves.

From the time of the Freemans Bay report, a common, higher wave period of 5 seconds was adopted. This wave period was associated with a common, higher wave height of 0.45m, though higher waves were recorded over the five days of deployment. This wave height is designated as a maximum wave height, Hmax.

Note that for ferry wave investigations, rather than wind waves, and based on our experience using recorded ferry waves (single vessel site) and data from a towing tank at Australian Maritime College, an indicative Hs/Hmax relationship for ferry waves is around 0.9. Those analyses were undertaken as part of ferry wave investigations in Sydney Harbour. Note also that in the case of ferry waves, Hs is better designated H1/3 – average of the highest one-third of waves in a train of ferry waves, about 10 to 15 waves.



Measured wake wavesAukland University Data

Appendix A.1



Mulgor measurementsDeployment 1 − In Hobsons Bay

Appendix A.2



Mulgor measurementsDeployment 2 − In Freemans Bay

Appendix A.3


59917161 | 22 December 2017 19


APPENDIX

WAVES IN HOBSON WEST MARINA

09-Nov-2017

Waves in Hobson West Marina

1. Introduction

The objective of this study was to measure the waves generated by ferries passing Hobson West

Marina and penetrating to berths within the marina to assist with marina wave climate

investigations.

2. Instrumentation

Three RBR wave sensors were deployed, as shown in Figure 1. The purpose of the three

instruments was to determine the wake direction by triangulation. The locations and details of the

instruments are presented in Table 1. The instruments were programmed to sample continuously

and the clocks were synchronised.

Table 1. Wave gauges, locations (Mount Eden 2000), height above bed, and depth at mid-tide.

Brand Sampling Easting m Northing m Height m Depth m

Pile #1 RBRduet 4 Hz 399880.0 804220.3 3.17 2.776

Pile #2 RBRsolo 2 Hz 399800.6 804255.0 3.75 2.844

Pile #3 RBRsolo 2 Hz 399844.7 804306.3 3.29 2.872

The instruments were placed as close to the surface as practicable so as to reduce the attenuation of

short period waves.

The details of the triangle formed by the wave gauges are presented in Table 2.

Table 2. Definition of triangle between wave gauges

Length m Angle ºN

Pile #1 to Pile #2 86.62 293.6

Pile #1 to Pile #3 92.98 337.7

Pile #3 to Pile #2 67.62 220.7

The trigonometry involved in calculating the bearing of a wave crest is presented in Appendix I and

is briefly described in Section 3.3, along with a caveat for its use.

Waves in Hobson West Marina 2

Figure 1. Locations of the three wave gauges.


3. Data and Methods

The data were downloaded from the instruments and placed in netCDF files for easy access.

3.1 Calibration

Since the instrument calibrations were two or three years out of date, a calibration was done against

the tide – if the instruments give the correct measurements for the tidal wave, which has a range of

more than 3 m, we infer that they will work correctly for much shorter period, smaller amplitude

waves.

The tide was forecast using the tidal constituents from the nearby Ports of Auckland tide gauge and

compared to 15-min means from Pile #1, high-pass filtered to eliminate meteorological effects. The

comparison showed that data are within ±0.12 m at the 95% confidence level. For a site inside a

harbour where compound- and over-tides are significant, this error is about as good as one can

expect. Indeed, a sensitivity test in which the measured data were scaled by factors between 0.95

and 1.05 showed that there was no justification for using a factor other than 1.00. Thus, the

calibration of the instrument Pile #1 was assumed to be correct.

To check the calibration of the other two instruments, the 15-min data were plotted against each

other, as shown in Figure 2 (in which the individual data are plotted as points), indicating that

factors of 1.0101 and 1.0077 need to be applied to data from Piles #2 and #3 respectively to match

the data at Pile #1.

Figure 2. 15-min data from Piles #2 and #3 (displaced upwards by 1 m for clarity) plotted against

data from Pile #1.

1 1.5 2 2.5 3 3.5 4 4.5 51

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Pile #2Slope = 1.0101

Pile #3Slope = 1.0077

Sea Level at Piles #2 and #3

Se

a L

eve

l a

t P

ile #

1


3.2 Data Processing

The record was split into windows of 20-min length and each of these windows was transformed to

the frequency domain so that depth correction could be applied. Depth correction accounts for the

attenuation of the wave signal with depth that occurs with pressure transducers. The correction

factor is given by:

λ=cosh(kh)cosh (kz i)

(1)

where h is the water depth, zi is the height of the instrument above the bed (its invert level), and k is

the wave number calculated from the dispersion relation for each frequency in the transformed

window. 20-min windows were chosen because there are a reasonable number of waves in the

sample and the change in depth due to the tide is not too large.

For short period waves, the depth correction given by Equation (1) can become very large, so a

limit was imposed given by:

f cutoff >0.45√g /h (2)

where f is frequency and g is the acceleration of gravity. This ensured that the correction was

restricted to less than 10. Waves with frequency above the cutoff were set to zero.

The depth correction was applied frequency-by-frequency to the transformed signal, then the

spectral wave parameters (significant wave height, Hsm, average period, Tm1, etc) were calculated

from the spectral moments. The transformed signal with depth correction was then inverse-

transformed back into the time domain and a zero-crossing analysis was carried out to extract the

individual waves in each window.

3.2 Calculating Wake Angle

The trigonometry for calculating the wake angle is presented in Appendix I. By assuming that the

wake is moving at a constant speed (the “group velocity”), the distance travelled between Probe 2

and Probe 1 (calculated by the wave speed times the time of travel) is matched to the actual

distance. This is repeated between Probe 3 and Probe 1, and by solving the resulting simultaneous

equations, the angle of attack is inferred.

The analysis depends upon the same wave train passing all three recorders without dispersing,

which is not always the case. Nevertheless, some events will provide reliable data.


4. Results

4.1 Wave Spectra

The overall mean wave spectra are shown in Figure 3, which represent the means over 1,000

ensembles. They show the main energy lies in a band between 4 and 8 s period, with little energy in

the swell band (8 to 25 s). The essentially constant energy in the long wave band (> 25 s) indicates

white noise, which implies that the waves in this band are random.

The presence of the bumps in energy at Piles #2 and #3 at 54 s could indicate seiche between the

harbour entrance and the opposite (SW) side of the marina. The energy at this period at Pile #2 is

twice the energy at Pile #3, which is consistent with a fundamental seiche mode having a node at

the entrance and an antinode at the other end. However, the energy in this seiche is an order of

magnitude less than the wave energy, so it is probably insignificant.

Figure 3. Overall mean wave spectra, before depth correction has been applied.

The areas under the spectra (i.e. variances) and periods at the spectral peak are listed in Table 3. The

variances are similar, with energy at Pile #2 being a few percent higher than at the other two piles.

The period at Pile #1 is considerably shorter than the periods at the other two piles.

Table 3. Variance and peak periods from the spectra (Figure 2).

Pile #1 Pile #2 Pile #3

Variance mm2 94.0 102.3 90.2

Peak Period s 4.71 7.14 6.18

100

101

102

10−8

10−7

10−6

10−5

10−4

10−3

Period s

PS

D m

2 s

Pile #1

Pile #2

Pile #3


The distribution of wave energy with time is shown in Figure 4, which presents the total energy

each day. The figure shows reduced energy at weekends and Fridays generally having the most

energy.

Figure 4. Daily wave energy.

4.2 Overall Statistics

The wave heights in 20-min windows are shown in Figures 5a and b for significant, Hsm, and

maximum, Hmx, wave heights respectively. There is a distinct diurnal pattern, with low wave heights

in the early morning, followed by a peak at about 9 am and another peak at 5pm corresponding to

the morning and evening rush-hours. Notice that in the weekends (e.g., 30-Sep and 01-Oct) the

peaks are less pronounced.

0

0.005

0.01

0.015

Pile #1

0

0.005

0.01

0.015

Pile #2

29−Sep 02−Oct 05−Oct 08−Oct 11−Oct 14−Oct 17−Oct−20170

0.005

0.01

0.015

Pile #3

Da

ily E

ne

rgy m

2

Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon


Figure 5a. Significant wave heights in 20-min windows for the period of record.

28−Sep 29−Sep 30−Sep 01−Oct 02−Oct−170

0.05

0.1

0.15

0.2

0.25

02−Oct 03−Oct 04−Oct 05−Oct 06−Oct−170

0.05

0.1

0.15

0.2

0.25


0.05

0.1

0.15

0.2

0.25


0.05

0.1

0.15

0.2

0.25


0.05

0.1

0.15

0.2

0.25

Sig

nific

ant W

ave H

eig

ht m

Pile #1

Pile #2

Pile #3


Figure 5b. Maximum wave heights in 20-min windows for the period of record.

28−Sep 29−Sep 30−Sep 01−Oct 02−Oct−170

0.1

0.2

0.3

0.4

0.5


0.1

0.2

0.3

0.4

0.5


0.1

0.2

0.3

0.4

0.5


0.1

0.2

0.3

0.4

0.5


0.1

0.2

0.3

0.4

0.5

Maxim

um

Wave H

eig

ht m

Pile #1

Pile #2

Pile #3


4.3 Event Analysis

To examine the waves in more detail, an event analysis was undertaken. This involved identifying

individual waves greater than a threshold at a particular pile and assuming the event extended for an

interval either side of the maximum. Pile #2 was chosen as the indicator and a threshold of 0.25 m

was used and it was assumed that there was at least 100 s between wake events. Figure 6 shows a

typical day of record with the events at Pile #2 marked.

Figure 6. Individual wave heights for a typical day of record, with events identified at Pile #2

annotated.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Pile #1

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Pile #2

1

2 3

4

5

6

7

8

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Pile #3

Waves on 06−Oct−2017

Wave H

eig

ht m


Over the 18 full days of observations, there were 83 events when the wave height at Pile #2 (where

response was largest) exceeded 0.25 m. Examination of these events revealed that there are four

different patterns. One of each of these occurred on 06-Oct-2017, as shown in Figures 7a to d.

Figure 7a shows the wave pattern that we expected to see. A wake enters the marina, hitting Pile #3

first, followed by Pile #2 and then Pile #1. Using the peaks indicated by the cyan squares, and

inserting the times between them into the equations in Appendix I, we find that the bearing of the

line of crests is 84.0º from N, meaning the waves are coming from 354.0º N through the entrance.

The peak for Pile #1 could be the one indicated, or it could be the peak before. If we use the one

before, the direction becomes 349.4º, which is only 4.6º different, indicating that the angle

calculations are not particularly sensitive to which crest is chosen.

Figure 7a. Waves at the three piles for Event 5 on 06-Oct-2017. For clarity, the sequences for Piles

#2 and #3 have been displaced downwards by 0.2 m. The cyan squares indicate the peak wave crest

used for calculating the angle of attack.

−50 −40 −30 −20 −10 0 10 20 30 40 50−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

Time s from 06−Oct−2017 14:06:16

Sea L

evel m

H = 0.373 m at Pile #2

Pile #1 Pile #2 Pile #3 Reference Wave


In fact, the pattern shown in Figure 7a occurred only nine times in the 83 events. Many more events

had a pattern like that shown in Figure 7b, where there was a strong response of short period waves

at Pile #2, but little activity at the other two piles, and the wave periods at these piles were

somewhat longer. On 08 and 09-Oct (Saturday and Sunday) there were 6 events like the one shown

in Figure 7b, which implies that they correspond to recreational vessels that were moored near Pile

#2, rather than passing ferries.

Figure 7b. Waves at the three piles for Event 6 on 06-Oct-2017. For clarity, the sequences for Piles

#2 and #3 have been displaced downwards by 0.2 m.

−50 −40 −30 −20 −10 0 10 20 30 40 50−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

Time s from 06−Oct−2017 17:16:18

Sea L

evel m

H = 0.329 m at Pile #2



The third pattern is shown in Figure 7c. In this event, the wake started at Pile#1 and propagated to

Piles #2 and #3. For this case, the wave direction is from 122.3º N, indicating that the ferry wake

came through the piers between Hobson West and Princess Wharves near Pile #1 and propagated

NW across the marina.

Figure 7c. Waves at the three piles for Event 2 on 06-Oct-2017. For clarity, the sequences for Piles

#2 and #3 have been displaced downwards by 0.2 m. The cyan squares indicate the peak wave crest

used for calculating the angle of attack.

−50 −40 −30 −20 −10 0 10 20 30 40 50−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

Time s from 06−Oct−2017 08:55:28

Sea L

eve

l m

H = 0.254 m at Pile #2



The fourth pattern is indeterminate, as shown in Figure 7d: there are waves at Pile #2, but the

activity at the other two piles, if there is any, does not appear to be related to what is happening at

Pile #2. Jonathan Duffy of Shearwater Consulting Ltd, who was responsible for deployment and

recovery of the instruments noted that “when it is busy there is general 'slop' rather than

distinguishable wake waves” and this may correspond with the measurements shown in Figure 7d.

Note that for this example, the waves have shorter period at Pile #2, than the other piles, but they

not as short as those shown in Figure 7b.

Figure 7d. Waves at the three piles for Event 1 on 06-Oct-2017. For clarity, the sequences for Piles

#2 and #3 have been displaced downwards by 0.2 m.

Using the patterns shown in Figures 7a to d, the 83 events when the wave height at Pile #2 exceeded

0.25 m can be categorised into four groups:• Group A: Wake propagating into the marina through the entrance: 9 events;• Group B: Short period wake from nearby vessels: 26 events;• Group C: Wake entering through the Hobson West Pier and propagating NW across the

marina: 9 events; or• Group D: Indeterminate, possibly the superposition of multiple ferry wakes: 39 events.

The categorisation is subjective, based on the author's observation of each event. Unfortunately, no

objective way has been found to improve on this, yet.

Appendix II contains the maximum wave height and corresponding period for each of these events,

organised into the designated groups and Tables 4a to d contain the summary statistics.

Some points that arise from these tables are:

−50 −40 −30 −20 −10 0 10 20 30 40 50−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

Time s from 06−Oct−2017 08:29:20

Sea L

evel m

H = 0.282 m at Pile #2



1. Irrespective of the Group a wake falls into, the height of the maximum wave is almost

always at Pile #2, and the heights at the other two piles are about half of that.

2. There does not appear to be any correlation of wave height with Group: wakes of any height

can occur within any Group.

3. The period of the maximum wave is generally a good indicator of the Group (from the

median or mean):

a. Group A: 4 to 5 s

b. Group B: 2 to 3 s

c. Group C or D: 5 to 6 s

Table 4a. Group A: summary statistics of maximum wave height in each event.

Maximum Wave Height m Period of Maximum Wave in s

Pile #1 Pile #2 Pile#3 Pile #1 Pile #2 Pile#3

Maximum 0.238 0.373 0.289 6.21 5.08 5.40

Minimum 0.097 0.253 0.101 3.93 3.56 3.85

Median 0.168 0.297 0.172 4.38 4.19 4.65

Mean 0.162 0.301 0.191 4.74 4.14 4.72

Table 4b. Group B: summary statistics of maximum wave height in each event.



Maximum 0.154 0.488 0.269 7.08 3.96 4.93

Minimum 0.037 0.240 0.054 1.82 1.82 1.82

Median 0.082 0.265 0.126 3.68 2.23 2.63

Mean 0.092 0.283 0.134 3.58 2.58 2.98

Table 4c. Group C: summary statistics of maximum wave height in each event.



Maximum 0.215 0.355 0.177 7.42 7.49 7.41

Minimum 0.101 0.253 0.124 4.67 3.84 4.25

Median 0.145 0.281 0.149 6.49 6.21 5.82

Mean 0.152 0.293 0.150 6.39 5.73 5.89

Table 4d. Group D: summary statistics of maximum wave height in each event.



Maximum 0.277 0.369 0.217 9.63 9.20 9.83

Minimum 0.091 0.234 0.090 1.46 2.64 2.28

Median 0.149 0.282 0.158 5.43 5.09 5.44

Mean 0.164 0.286 0.158 5.54 5.39 5.69


5. Discussion

One of the more unusual events is shown in Figure 8. At the start of the event there were short

period waves, probably from vessel/s near Pile #2, but the short period waves were swamped by

three large oscillations of about 9 s period. These waves could be swell, but a group of only three

swell waves is unusual. Alternatively, they could be be the result of a large vessel (a barge maybe)

manoeuvring in the marina. They waves are reminiscent of the response of a large harbour to

tsunami waves – they could be the marina resonating as a result of chaotic interaction of wakes

from numerous vessels, but the periods appear to be too short for that. Nevertheless, this event

indicates the possibility of resonance and the consequent possibility of large amplitude waves as a

result.

In view of these observations, long-period oscillations of the marina should be investigated by

mathematical modelling.

Figure 8. Event with a few long-period waves.

−50 −40 −30 −20 −10 0 10 20 30 40 50−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

Time s from 08−Oct−2017 01:24:01

Sea L

evel m

H = 0.336 m at Pile #2



6. Conclusions

Analysis of data from three instruments deployed in Hobson West Marina for 18 days has revealed:• Mean wave energy is concentrated in the period range between 4 and 8 s.• The mean energy varies slightly from day-to-day during the week, but is lower at weekends.• Waves have a diurnal pattern, with peaks at around 9 am and 5 pm, corresponding to rush

hours.• There are 4 groups of wave pattern:◦ Waves propagating into the marina through the entrance;◦ Short period wakes from nearby vessels;◦ Wake entering the marina through the Hobson West piers, then propagating NW across

the marina; or◦ Indeterminate wave patterns.• The period of the waves is determined by the wave pattern, but waves of any height occur

within any wave pattern.• Long-period waves may need to be investigated.

Derek Goring

Mulgor Consulting Ltd.

[email protected]


Appendix I: Trigonometry

Calculation of the bearing of a wave crest given the time taken to propagate from 3 to 1 and 2 to 1,

assuming the wave speed, c, remains constant and the line of crests remains straight and parallel.

Matching the distances between the lines of wave crests with the travel time for those lines at speed

c gives:

c∆ t12=s12sin (ϕ− θ1)c∆ t 13=s13sin ϕ

Substituting for c:

s12

sin (ϕ− θ1)=s

13

∆ t12

∆ t13

sin ϕ

Whence:

ϕ=tan− 1[

− s12sin θ1

s13

∆ t12

∆ t13

− s12 cosθ1 ]


The bearing of the wave crests in degrees from North is:

ψ=90+θ13− ϕwhere θ13 is the angle from the x-axis of the line from 1 to 3, i.e., 67.7º.

For example, for Event 5 on 06-Oct-2017, ∆ t12 = 20.7 s and ∆ t13 = 39.4 s, whence using

s12 = 86.62 m, s13 = 92.98 m, and θ1 = 44.05º, we get:ϕ = -102.5º which is equivalent to +77.5º, and

Bearing ψ = 80.2º

The alignment is shown in Figure A1.

Figure A1. Alignment of wave crests for Event 5 on 06-Oct-2017.

Pile #1

Pile #2

Pile #3


Appendix II: Events

The following tables list all the events described in Section 4.3.

Table A.IIa. Group A events

Time Maximum Wave Height m Period of Maximum Wave in s

NZDT Pile #1 Pile #2 Pile #3 Pile #1 Pile #2 Pile #3

29-Sep 06:49 0.097 0.253 0.101 3.93 3.56 3.85

29-Sep 07:21 0.168 0.334 0.289 4.20 4.02 4.65

29-Sep 18:12 0.106 0.288 0.143 6.21 5.08 5.23

02-Oct 16:06 0.161 0.297 0.210 4.14 3.97 4.57

03-Oct 18:16 0.174 0.280 0.167 4.30 3.63 4.14

06-Oct 12:08 0.238 0.305 0.227 5.91 4.43 5.38

06-Oct 14:06 0.203 0.373 0.248 4.38 4.21 4.74

09-Oct 08:50 0.141 0.328 0.163 5.00 4.19 5.40

12-Oct 17:50 0.169 0.254 0.172 4.63 4.19 4.56


Table A.IIb. Group B events

Time Maximum Wave Height m Period of Maximum s


29-Sep 13:36 0.071 0.257 0.085 7.08 2.41 2.79

05-Oct 17:07 0.131 0.259 0.105 6.01 3.75 4.93

06-Oct 17:16 0.099 0.329 0.185 3.85 2.55 4.17

06-Oct 20:34 0.102 0.248 0.127 4.20 3.93 4.54

06-Oct 22:06 0.141 0.268 0.141 4.00 3.59 3.77

07-Oct 13:16 0.054 0.254 0.122 2.20 2.04 2.11

07-Oct 14:05 0.055 0.290 0.121 1.82 2.01 1.89

07-Oct 14:19 0.073 0.260 0.157 2.13 1.82 1.97

07-Oct 15:02 0.147 0.329 0.166 3.83 1.95 2.78

07-Oct 15:22 0.112 0.353 0.160 2.17 2.02 2.36

07-Oct 16:31 0.095 0.298 0.130 3.65 2.07 2.37

08-Oct 00:19 0.127 0.240 0.137 5.05 2.10 2.49

08-Oct 01:31 0.058 0.264 0.109 2.20 2.22 2.12

08-Oct 01:51 0.080 0.278 0.125 2.04 2.05 2.18

08-Oct 02:15 0.069 0.295 0.076 2.13 2.03 1.91

08-Oct 03:09 0.103 0.488 0.152 2.16 2.09 2.35

08-Oct 05:24 0.066 0.253 0.112 1.88 1.87 1.82

09-Oct 14:09 0.064 0.263 0.117 3.69 2.88 2.85

09-Oct 15:12 0.051 0.247 0.081 2.71 2.12 2.30

10-Oct 08:51 0.154 0.267 0.109 6.11 3.86 4.85

11-Oct 18:31 0.077 0.265 0.111 4.32 2.29 4.24

12-Oct 07:02 0.037 0.250 0.054 4.73 2.24 2.27

13-Oct 21:06 0.145 0.254 0.269 3.50 3.66 3.70

15-Oct 20:44 0.064 0.282 0.155 3.89 3.35 3.78

16-Oct 09:16 0.085 0.265 0.135 3.67 2.33 2.77

16-Oct 18:19 0.140 0.297 0.246 4.18 3.96 4.22


Table A.IIc. Group C events



29-Sep 16:40 0.196 0.309 0.177 6.50 5.90 5.60

30-Sep 09:29 0.123 0.294 0.146 7.25 7.16 7.41

01-Oct 01:23 0.191 0.280 0.169 7.42 7.49 7.20

02-Oct 18:05 0.107 0.253 0.149 6.49 6.35 5.82

04-Oct 06:50 0.101 0.355 0.124 4.67 4.15 4.25

04-Oct 12:14 0.133 0.268 0.153 5.41 3.84 4.36

04-Oct 17:05 0.145 0.339 0.134 7.29 3.88 4.55

06-Oct 08:55 0.215 0.254 0.158 6.06 6.21 6.43

14-Oct 18:53 0.156 0.281 0.145 6.44 6.62 7.36

Table A.IId. Group D events



29-Sep 14:27 0.149 0.280 0.090 5.40 6.25 6.21

29-Sep 17:05 0.155 0.239 0.167 4.15 4.09 4.98

02-Oct 12:05 0.183 0.286 0.206 4.53 4.01 4.66

02-Oct 17:43 0.130 0.297 0.176 6.46 5.68 7.18

03-Oct 08:11 0.142 0.302 0.214 6.53 6.77 6.66

03-Oct 17:25 0.210 0.286 0.104 6.98 6.31 2.95

03-Oct 18:43 0.145 0.262 0.122 4.42 3.56 2.94

04-Oct 17:24 0.161 0.238 0.149 5.06 3.79 6.09

05-Oct 07:54 0.095 0.252 0.111 4.33 3.92 3.40

05-Oct 08:26 0.194 0.369 0.148 5.23 4.24 4.65

05-Oct 15:35 0.120 0.253 0.111 5.48 4.20 5.89

06-Oct 08:29 0.209 0.282 0.127 5.18 3.95 4.64

06-Oct 09:09 0.127 0.258 0.128 5.19 5.93 5.81

07-Oct 11:52 0.095 0.289 0.137 2.22 2.64 2.28

08-Oct 01:24 0.151 0.305 0.187 9.63 9.20 9.83

09-Oct 08:10 0.243 0.353 0.196 4.86 4.25 5.18

09-Oct 09:20 0.146 0.357 0.158 1.46 3.97 3.57

09-Oct 10:42 0.143 0.322 0.175 4.08 4.23 4.56

09-Oct 12:55 0.172 0.307 0.166 6.50 6.66 7.33

09-Oct 14:57 0.131 0.282 0.163 9.04 8.16 8.02


09-Oct 16:03 0.148 0.288 0.193 5.76 2.79 4.95

10-Oct 08:25 0.185 0.365 0.182 4.42 4.01 4.82

10-Oct 14:26 0.131 0.257 0.148 6.47 7.51 7.55

11-Oct 06:46 0.094 0.264 0.118 4.03 3.53 3.91

11-Oct 13:26 0.175 0.271 0.167 6.87 7.05 7.83

11-Oct 17:46 0.187 0.260 0.213 4.80 4.55 4.55

12-Oct 14:03 0.138 0.255 0.127 5.45 5.75 6.41

13-Oct 07:28 0.106 0.279 0.130 4.67 3.44 4.26

13-Oct 14:22 0.237 0.279 0.186 5.43 6.20 5.40

13-Oct 14:54 0.147 0.286 0.193 6.84 6.82 7.39

13-Oct 15:22 0.147 0.293 0.191 6.46 6.77 6.48

13-Oct 15:52 0.191 0.234 0.139 7.30 8.30 9.58

13-Oct 16:54 0.224 0.295 0.209 5.49 6.87 6.54

14-Oct 14:56 0.277 0.275 0.110 8.19 7.52 7.34

14-Oct 17:08 0.226 0.276 0.196 6.57 7.71 7.96

15-Oct 14:32 0.091 0.298 0.115 3.06 3.82 3.54

15-Oct 15:54 0.177 0.308 0.133 6.41 6.62 6.72

16-Oct 07:10 0.148 0.291 0.158 6.20 5.09 5.44

16-Oct 14:05 0.262 0.250 0.217 4.70 4.13 4.54


59917161 | 22 December 2017 22


APPENDIX

WAVES IN FREEMANS BAY

12-Dec-2017

Waves in Freemans Bay

1. Introduction

The objective of this study was to measure the waves generated by ferries passing Freemans Bay to

assist with marina wave climate investigations.

2. Instrumentation

2.1 Initial Deployment

Six RBR wave sensors were deployed, as shown in Figures 1a and b. The purpose of Probes 1 to 3

was to determine the wake direction by triangulation. The other three locations were chosen as

strategic points to compare the wave heights. The details of the instruments are presented in Table

1. The instruments were programmed to sample continuously and the clocks were synchronised:

Probes #1 to #3 within 1 s, Probes #4 to #6 within a few seconds. The initial deployment was from

17-Nov-2017 17:20 to 23-Nov-2017 12:49.

Table 1. Wave gauges, locations (Mount Eden 2000), height above bed, and depth at mid-tide.

Serial No Sampling Easting m Northing m Height m Depth m

Probe #1 083200 4 Hz 399831.9 804447.7 0.96 4.828

Probe #2 041265 2 Hz 399815.6 804560.5 0.06 6.667

Probe #3 041264 2 Hz 399886.9 804519.8 0.04 5.061

Probe #4 041401 4 Hz 400107.2 804503.3 4.83 2.921

Probe #5 085500 4 Hz 399952.5 804255.3 4.98 2.025

Probe #6 085504 4 Hz 399880.0 804220.3 3.16 2.874

The instruments were placed as close to the surface as practicable so as to reduce the attenuation of

short period waves.

The details of the triangle formed by the wave gauges shown in Figure 1a are presented in Table 2.

Table 2. Definition of triangle between wave gauges

Length m Angle ºN

Pile #1 to Pile #2 113.99 351.8

Pile #1 to Pile #3 90.71 37.3

Pile #3 to Pile #2 82.14 299.7

The trigonometry involved in calculating the bearing of a wave crest is presented in Appendix I and

is briefly described in Section 3.3, along with a caveat for its use.

Waves in Freemans Bay 2

Figure 1a. Locations of the three wave gauges used for triangulation.


Figure 1b. Location of six wave gauges in Freemans Bay.


2.2 Second Deployment

At midday on 23-Nov, the instruments were recovered, the data were extracted, and the instruments

were re-deployed. The instrument at Probe #1 (Serial No. 083200) was thought (erroneously) to be

malfunctioning, so it was withdrawn and was replaced by the instrument from Probe #4 (Serial No.

041401). Unfortunately, this instrument malfunctioned at 05:11 on 26-Nov-2017, meaning that no

data are available at Probe #1 from this time onwards.

The details of the second deployment are listed in Table 3.

When Probes #4 and #5 were re-attached to the piles, their position was slightly lower down the pile

than for the first deployment (they measured greater depths) and this is reflected in the changed

heights shown in Table 3. Probes #1, #2, and #3 were bottom mounted, so their heights above the

bed did not change.

Table 3. Wave gauges used in second deployment.

Serial No Sampling Start Finish Height m

Probe #1 041401 4 Hz 23-Nov 17:20 26-Nov 05:11 0.96

Probe #2 041265 2 Hz 23-Nov 17:20 01-Dec 07:55 0.06

Probe #3 041264 2 Hz 23-Nov 17:20 01-Dec 07:55 0.04

Probe #4 - - - - -

Probe #5 085500 4 Hz 23-Nov 17:20 01-Dec 07:55 4.59

Probe #6 085504 4 Hz 23-Nov 17:20 01-Dec 07:55 2.69

3. Data and Methods

The data were downloaded from the instruments and placed in netCDF files for easy access.

3.1 Calibration

Since the instrument calibrations were two or three years out of date, a calibration was done against

the tide – if the instruments give the correct measurements for the tidal wave, which has a range of

more than 3 m, we infer that they will work correctly for much shorter period, smaller amplitude

waves.

The tide was forecast using the tidal constituents from the nearby Ports of Auckland tide gauge and

compared to 15-min means from Probe #1, filtered to eliminate meteorological effects. The

comparison showed that data are within ±0.12 m at the 95% confidence level. For a site inside a

harbour where compound- and over-tides are significant, this error is about as good as one can

expect. Indeed, a sensitivity test in which the measured data were scaled by factors between 0.95

and 1.05 showed that there was no justification for using a factor other than 1.00. Thus, the

calibration of the instrument Probe #1 was assumed to be correct.

To check the calibration of the other five instruments, the 15-min data were regressed against the

data from Probe #1, resulting in the factors listed in Table 3. In each case, the coefficient of

determination, r2, was 1.0000. Considering that there may be small variations in the tide between

the locations, these factors are so close to unity that we may assume the instrument calibrations are

accurate, so no correction was applied to the measurements.


Table 3. Regression factors for each probe relative to Probe #1.

Probe #1 Probe #2 Probe #3 Probe #4 Probe #5 Probe #6

1.00000 1.0068 1.0093 1.0072 0.9990 0.9991

3.2 Data Processing

The first step was to forecast the tide using the Port of Auckland constituents and subtract it from

the records to form a set of residuals. Each residual was split into windows of 20-min length and

each of these windows was transformed to the frequency domain so that depth correction could be

applied. Depth correction accounts for the attenuation of the wave signal with depth that occurs

with pressure transducers. The correction factor is given by:

λ=cosh(kh)cosh (kz i)

(1)

where h is the water depth, zi is the height of the instrument above the bed (its invert level), and k is

the wave number calculated from the dispersion relation for each frequency in the transformed

window. 20-min windows were chosen because there are a reasonable number of waves in the

sample and the change in depth due to the tide is not too large.

For short period waves, the depth correction given by Equation (1) can become very large, so a

limit was imposed given by:

f cutoff >0.282√g /h (2)

where f is frequency and g is the acceleration of gravity. This ensured that the correction was

restricted to less than 10. Waves with frequency above the cutoff were set to zero.

The depth correction was applied frequency-by-frequency to the transformed signal, then the

spectral wave parameters (significant wave height, Hsm, average period, Tm1, etc) were calculated

from the spectral moments. The transformed signal with depth correction was then inverse-

transformed back into the time domain to provide a depth-corrected time series.

Wave heights were processed in a different way. The individual waves were extracted from the

record using a zero-crossing analysis, then depth-correction was applied to each wave in turn using

its period and the water depth. The depth correction factor, λ, had a threshold of 10 and waves with

λ greater than the threshold were eliminated, along with short-period waves (2.5 s or less) that can

produce anomalous spikes in wave height.

To illustrate the effect of depth correction on a typical wake, consider Figure 3. It shows that the

amplitudes of the measured wake are only a quarter of the amplitude after depth correction.


Figure 3. Typical wake at Probe 2 comparing the signal before and after depth correction.

3.2 Calculating Wake Angle

The trigonometry for calculating the wake angle is presented in Appendix I. By assuming that the

wake is moving at a constant speed (the “group velocity”), the distance travelled between Probe 2

and Probe 1 (calculated by the wave speed times the time of travel) is matched to the actual

distance. This is repeated between Probe 3 and Probe 1, and by solving the resulting simultaneous

equations, the angle of attack is inferred.

The analysis depends upon the same wave train passing all three recorders without dispersing,

which is not always the case. Nevertheless, some events will provide reliable data.

An independent check on the calculations of wake direction would be advisable and this is being

undertaken using video records. At the time of writing, the results of this analysis were not

available.

−50 −40 −30 −20 −10 0 10 20 30 40 50−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Time s from 18−Nov−2017 06:30:01

Se

a L

eve

l m

Raw Signal

Depth Corrected


4. Results

4.1 Wave Spectra

The overall mean wave spectra are shown in Figure 4, which represent the means over 1,000 20-

minute ensembles for each probe. They show the main energy lies in a band between 3 and 10 s

period. The essentially constant energy in the long wave band (> 25 s) indicates white noise, which

implies that the waves in this band are random.

Figure 4. Overall mean wave spectra, before depth correction has been applied.

The areas under the spectra (i.e. variances) and periods at the spectral peak are listed in Table 4.

These represent overall averages and reflect the wave climate at each probe, rather than events,

which are considered in Section 4.3. The variances at Probes #3 and #4 are largest, indicating a

higher level of disturbance than the other probes, while the variance at Probe #6 inside the marina is

less than half these. The peak periods are essentially the same at each probe.

Table 4. Variance and peak periods from the spectra (Figure 3).

Probe #1 Probe #2 Probe #3 Probe #4 Probe #5 Probe #6

Variance mm2 109.1 86.5 159.6 145.1 93.0 62.2

Peak Period s 4.46 4.55 4.63 4.55 4.13 4.59

4.2 Overall Statistics

The significant wave heights in 20-min windows are shown in Figure 5 for Probe #3, which is

typical. There is a distinct diurnal pattern, with low wave heights in the early morning, one or more

100

101

102

10−8

10−7

10−6

10−5

10−4

10−3

10−2

Period s

PS

D m

2 s

Probe #1

Probe #2

Probe #3

Probe #4

Probe #5

Probe #6


peaks during the day, and reducing wave heights towards midnight. In the weekend, (18- and 19-

Nov) there is a single peak at 1500 , but during the working week there is a small peak at 0700 and

a stronger one at 1600 each day. Presumably, these peaks correspond to intense ferry activity in the

rush hours, with the direction of the ferries (arriving or departing) affecting the strength of the

effect.

Figure 5. Significant wave heights in 20-min windows at Probe #3 for the period of record.

4.3 Event Analysis

To examine the waves in more detail, an event analysis was undertaken. This involved identifying

individual waves greater than a threshold at a particular probe and assuming the event extended for

an interval either side of the maximum. Probe #2 was chosen as the indicator because that appears

to be the “busiest” location, and a threshold of 0.35 m was used. It was assumed that there were at

least 100 s between wake events. Figure 6 shows a typical day of record with the events at Probe #2

marked.

Figure 6. Individual wave heights for a typical day of record. Events with maximum wave height

greater than 0.35 m are circled.

A question has arisen as to why the wave heights shown in Figure 6 do not seem to correspond to

18−Nov 19−Nov 20−Nov 21−Nov 22−Nov 23−Nov−170

0.1

0.2

0.3

0.4

Sig

nific

ant W

ave H

eig

ht m

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time on 21−Nov−2017

Wa

ve

He

igh

t m

Probe # 2


those in Figure 5. The reason is that the individual wave heights shown in Figure 6 were calculated

using a wave-by-wave analysis, whereas the significant wave heights shown in Figure 5 were

calculated from the energy in 20-minute samples. Thus, Figure 5 shows averages, whereas Figure 6

shows specifics.

Over the 5 days of observations in the initial deployment, there were 32 events when the wave

height at Probe #2 exceeded 0.35 m, and in the additional 1.5 days of the second deployment, there

was one event. A listing of all 33 events is in Appendix II. Examination of these events revealed that

there are two different patterns. One of each of these are presented in Figures 7a and b.

Figure 7a shows a wave pattern that is straightforward to explain. A wake enters the bay and hits

Probe #3 first, followed by Probe #2 , then Probe #1. The time taken to travel from Probe #3 to

Probe #2 is 23 s and the time to Probe #1 is 8 s. Inserting these times into the equations in Appendix

I, we find that the wave direction is from 72º N.

Estimating which wave at Probes #1 and #3 correspond to the indicator wave at Probe #2 is not

easy: it could be one wave either way. Fortunately, however, the calculation is not particularly

sensitive to which wave is chosen. If the times are varied by ± 4 s (the period of the waves), the

resulting direction is changed by only ±5º.

There was essentially no response to this wake at Probes #4, #5, and #6. This is true for all other

events of this type as well.

Figure 7a. Waves at the six probes for Event 4 on 18-Nov-2017. For clarity, the sequences have

been displaced downwards by 0.2 m for each of Probes #2 to #6. The indicator wave is marked by a

magenta circle.

−50 −40 −30 −20 −10 0 10 20 30 40 50

−1

−0.8

−0.6

−0.4

−0.2

0

0.2 Probe

#1

#2

#3

#4

#5

#6

Time s from 18−Nov−2017 06:30:01

Sea L

evel m

H = 0.368 m at Probe #2


Table 5 lists the wave heights and periods for all the events like that shown in Figure 7a. The wave

directions are mainly from the NE to E. The maximum wave height is usually largest at Probe #2

(but not always) and the wave heights at Probes #4 to #6 are significantly less. The periods at

Probes #1 to #3 are similar for each event, but vary from 3.5 to 5 s between events, probably

corresponding to the particular ferry that generated the wake.

Table 5. Wave direction, wave heights and corresponding periods for events similar to that

shown in Figure 6a.

Date/Time Dirn Maximum Wave Height m Period s

#1 #2 #3 #4 #5 #6 #1 #2 #3

17-Nov 21:02 106 0.342 0.397 0.342 0.116 0.119 0.157 4.45 3.76 3.93

18-Nov 06:30 72 0.314 0.368 0.432 0.184 0.033 0.053 3.71 3.87 3.73

18-Nov 16:25 72 0.369 0.428 0.499 0.163 0.188 0.120 4.02 3.94 4.84

18-Nov 17:44 55 0.364 0.381 0.221 0.114 0.087 0.107 4.86 5.04 5.16

19-Nov 15:09 52 0.362 0.385 0.508 0.269 0.135 0.086 3.76 4.52 4.36

20-Nov 06:48 73 0.258 0.372 0.247 0.116 0.113 0.099 4.49 4.55 5.01

20-Nov 16:20 38 0.323 0.500 0.361 0.149 0.053 0.063 3.28 3.18 3.10

20-Nov 17:34 80 0.306 0.351 0.464 0.180 0.175 0.114 3.81 3.79 3.88

20-Nov 21:03 58 0.338 0.527 0.290 0.124 0.064 0.047 4.05 4.18 4.17

21-Nov 07:55 66 0.264 0.353 0.356 0.273 0.175 0.068 4.35 4.39 4.45

21-Nov 08:52 61 0.234 0.497 0.382 0.140 0.154 0.084 4.87 3.98 3.84

21-Nov 13:04 46 0.481 0.354 0.275 0.172 0.098 0.056 3.90 3.97 4.03

21-Nov 18:12 35 0.376 0.385 0.380 0.189 0.096 0.095 4.15 4.64 4.24

22-Nov 08:25 42 0.378 0.359 0.441 0.241 0.141 0.170 3.48 3.62 3.75

22-Nov 16:04 68 0.476 0.465 0.382 0.267 0.152 0.091 3.62 3.55 3.77

22-Nov 16:45 64 0.473 0.399 0.360 0.234 0.191 0.177 3.50 3.54 3.50

22-Nov 17:02 60 0.386 0.385 0.383 0.250 0.159 0.134 3.99 4.56 4.81

The event on 17-Nov has a direction of 106º, i.e., ESE, compared to all the other events when the

directions were north of east. Examination of the event shows waves arrived at Probe #1 before

Probe #2, which is consistent with waves from the south, so the event was anomalous, but not

necessarily spurious.


The pattern shown in Figure 7a occurred 17 times in the 33 events.

The other 16 events had a pattern like that shown in Figure 7b, which appears to be a smorgasbord

of wakes with no discernible correlation between one probe and another.

Figure 7b. Waves at the six probes for Event 1 on 17-Nov-2017. For clarity, the sequences have

been displaced downwards by 0.2 m for each of Probes #2 to #6. The indicator wave is marked by a

magenta circle.

4.4 Individual Wake Waves

The chaotic nature of the wakes in Figure 7b makes event analysis difficult. Therefore, an

alternative analysis was conducted on individual wake waves, which are shown in the cumulative

distribution function (CDF) in Figure 8, in this case for Probe #4. The figure shows that only 10%

of waves are larger than 0.075 m, and only 1% are larger than 0.15 m. Thus, for a large proportion

of the time, wake waves are essentially insignificant.

However, from time to time there are large wake waves and these are shown in the upper end of the

CDFs for all probes presented in Figure 9. The figure shows that the largest wake waves occur at

Probes #2 and #3. The other 4 probes have smaller wake wave heights.

The maximum measured wake height was 0.587 m at Probe #2. There were a few other wake

heights that were calculated as being higher (up to 1 m), but on examination they corresponded to

short-period waves (T < 3 s) with large depth-correction factors, so they were rejected as spurious.

−50 −40 −30 −20 −10 0 10 20 30 40 50

−1

−0.8

−0.6

−0.4

−0.2

0

0.2 Probe

#1

#2

#3

#4

#5

#6

Time s from 17−Nov−2017 18:14:34

Sea L

evel m

H = 0.413 m at Probe #2


Figure 8. CDF of individual wave at Probe #4.

Figure 9. Upper end of the CDFs, with x showing maximum wave heights for each probe.

0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

%age Greater Than

Wa

ve

He

igh

t m

10−3

10−2

10−1

100

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

%age Greater Than

Wa

ve

He

igh

t m

Probe #1

Probe #2

Probe #3

Probe #4

Probe #5

Probe #6


5. Discussion

In the earlier report on wakes in Hobson West Marina, periods of 6 s were recorded for wakes

coming through the entrance of the marina, yet for the deployment analysed here, the periods

outside the marina were much less (3.5 to 5 s).

In an effort to explain this, events at Probe #6 (inside the marina) were compared with the signal at

other probes, as shown in Figure 10, which is typical. The long period waves at Probe #6 appear to

show no correlation with the waves at the other probes. In my opinion, this indicates that the

oscillations in the marina are not propagating waves, but seiching (oscillation of the basin at its

natural frequency) which has been set up by multiple wakes from different directions. The seiche

only lasts for a few waves, which is consistent with my observations of seiche elsewhere.

Figure 10. Waves at the six probes for an event at Probe #6. For clarity, the sequences have been

displaced downwards by 0.2 m for each of Probes #2 to #6. The indicator wave is marked by a

magenta circle.

−50 −40 −30 −20 −10 0 10 20 30 40 50

−1

−0.8

−0.6

−0.4

−0.2

0

Probe

#1

#2

#3

#4

#5

#6

Time s from 21−Nov−2017 11:24:31

Se

a L

eve

l m

H = 0.302 m at Probe #6


6. Conclusions

Analysis of data from six instruments deployed in Freemans Bay for 13 days has revealed:• Mean wave energy is concentrated at around 4.5 s and its magnitude varies considerably

around the bay, with maximum just outside the Viaduct Harbour entrance (Probes #1 to #3).• Waves have a diurnal pattern, with peaks at around 7 am and 4 pm during the week,

corresponding to rush hours, but a single peak at around 3 pm during the weekend.• Two wake patterns were detected:◦ Wake waves propagating from the NE to E across the entrance to Viaduct Harbour;◦ Chaotic pattern of wake waves from various sources.• For 90% of the time, the waves throughout the bay are small.• For 1% of the time, the waves throughout the bay are larger than 0.1 m, and can be as large

as 0.59 m just outside the entrance to Viaduct Harbour.• No direction connection was found between wake events inside Hobson West Marina and

wakes outside.

Derek Goring

Mulgor Consulting Ltd.

[email protected]


Appendix I: Trigonometry

Calculation of the bearing of a wave crest given the time taken to propagate from 3 to 1 and 2 to 1,

assuming the wave speed, c, remains constant and the line of crests remains straight and parallel.

Matching the distances between the lines of wave crests with the travel time for those lines at speed

c gives:

c∆ t12=s12sin (ϕ− θ1)c∆ t 13=s13sin ϕ

Substituting for c:

s12

sin (ϕ− θ1)=s

13

∆ t12

∆ t13

sin ϕ

Whence:

ϕ=tan− 1[

− s12sin θ1

s13

∆ t12

∆ t13

− s12 cosθ1 ]


The bearing of the wave crests in degrees from North is:

ψ=270− θ13− ϕwhere θ13 is the angle from the x-axis of the line from 1 to 3, i.e., 112.3º.

For example, for the event in Figure 6a at 06:30 on 18-Nov-2017, ∆ t12 = -8 s and ∆ t13 = -31

s, whence using s12 = 113.99 m, s13 = 90.71 m, and θ1 = 45.58º, we get for the angle

between s13 and the line of wave crests:ϕ = 55.3º, and

Bearing ψ = 162.3º

The wave direction, which is 90º from the bearing of the wave crests, is 72º.

The alignment is shown in Figure A1.

Figure A1. Alignment of wave crests for the event at 06:30 on 18-Nov-2017.

Pile #1

Pile #2

Pile #3


APPENDIX II

Table II. Complete listing of events where the maximum wave height at Probe #2 exceeded 0.36 m. Wave direction is from ºN and NaN means

there was no discernible direction.

No Date/Time Dirn Maximum Wave Height m Corresponding Period s

Probe: 1 2 3 4 5 6 1 2 3 4 5 6

1 17-Nov 18:14:34 NaN 0.314 0.388 0.284 0.195 0.312 0.184 5.10 3.74 3.78 4.16 5.24 5.32

2 17-Nov 19:32:06 NaN 0.134 0.532 0.396 0.166 0.057 0.066 6.14 4.39 3.65 4.62 4.67 9.48

3 17-Nov 21:02:34 106 0.342 0.397 0.342 0.116 0.119 0.157 4.45 3.76 3.93 6.57 6.47 5.19

4 18-Nov 06:30:01 72 0.314 0.368 0.432 0.184 0.033 0.053 3.71 3.87 3.73 3.35 2.80 2.70

5 18-Nov 16:25:00 72 0.369 0.428 0.499 0.163 0.188 0.120 4.02 3.94 4.84 5.33 4.64 4.95

6 18-Nov 17:44:50 55 0.364 0.381 0.221 0.114 0.087 0.107 4.86 5.04 5.16 4.54 6.72 5.67

7 19-Nov 15:09:58 52 0.362 0.385 0.508 0.269 0.135 0.086 3.76 4.52 4.36 4.46 5.10 5.07

8 19-Nov 17:48:50 NaN 0.195 0.353 0.334 0.110 0.163 0.079 3.78 3.64 3.62 5.66 3.67 6.39

9 20-Nov 06:48:32 73 0.258 0.372 0.247 0.116 0.113 0.099 4.49 4.55 5.01 4.87 5.84 4.59

10 20-Nov 09:26:42 NaN 0.216 0.431 0.388 0.169 0.143 0.062 3.50 3.66 3.65 3.93 3.63 3.91

11 20-Nov 11:08:54 NaN 0.257 0.450 0.380 0.127 0.100 0.169 4.01 3.69 4.12 4.85 4.28 3.42

12 20-Nov 16:20:20 38 0.323 0.500 0.361 0.149 0.053 0.063 3.28 3.18 3.10 3.33 4.03 3.66

13 20-Nov 17:34:46 80 0.306 0.351 0.464 0.180 0.175 0.114 3.81 3.79 3.88 3.21 5.13 5.77

14 20-Nov 21:03:11 58 0.338 0.527 0.290 0.124 0.064 0.047 4.05 4.18 4.17 5.18 5.35 4.55

15 21-Nov 07:55:05 66 0.264 0.353 0.356 0.273 0.175 0.068 4.35 4.39 4.45 4.22 4.35 3.74

16 21-Nov 08:27:08 NaN 0.302 0.340 0.301 0.123 0.108 0.135 3.82 3.99 4.08 3.95 4.26 3.63


No Date/Time Dirn Maximum Wave Height m Corresponding Period s

Probe: 1 2 3 4 5 6 1 2 3 4 5 6

17 21-Nov 08:52:45 61 0.234 0.497 0.382 0.140 0.154 0.084 4.87 3.98 3.84 4.43 5.28 5.51

18 21-Nov 10:17:23 NaN 0.219 0.365 0.226 0.149 0.138 0.071 3.85 4.02 4.40 5.37 4.20 4.78

19 21-Nov 13:04:58 46 0.481 0.354 0.275 0.172 0.098 0.056 3.90 3.97 4.03 3.92 3.85 4.96

20 21-Nov 15:26:18 NaN 0.256 0.350 0.348 0.283 0.142 0.070 3.77 3.27 3.74 7.28 7.58 3.10

21 21-Nov 16:35:13 NaN 0.258 0.367 0.473 0.322 0.208 0.144 3.88 4.08 3.69 3.64 3.96 4.97

22 21-Nov 18:12:58 35 0.376 0.385 0.380 0.189 0.096 0.095 4.15 4.64 4.24 3.68 4.38 4.28

23 22-Nov 08:25:41 42 0.378 0.359 0.441 0.241 0.141 0.170 3.48 3.62 3.75 3.62 5.22 5.22

24 22-Nov 14:19:38 NaN 0.253 0.519 0.545 0.203 0.087 0.062 3.60 3.61 3.53 3.59 3.65 2.32

25 22-Nov 16:04:51 68 0.476 0.465 0.382 0.267 0.152 0.091 3.62 3.55 3.77 4.13 3.63 2.78

26 22-Nov 16:32:43 NaN 0.497 0.379 0.372 0.213 0.138 0.091 3.85 4.00 4.40 4.36 4.27 2.32

27 22-Nov 16:45:35 64 0.473 0.399 0.360 0.234 0.191 0.177 3.50 3.54 3.50 4.13 4.15 2.38

28 22-Nov 17:02:32 60 0.386 0.385 0.383 0.250 0.159 0.134 3.99 4.56 4.81 4.81 3.77 1.69

29 22-Nov 18:11:48 NaN 0.280 0.457 0.286 0.156 0.113 0.072 3.70 3.09 3.65 2.97 5.65 4.29

30 23-Nov 07:42:24 NaN 0.280 0.372 0.262 0.236 0.119 0.094 4.22 4.26 4.86 4.32 4.63 6.85

31 23-Nov 08:25:34 NaN 0.277 0.413 0.354 0.240 0.197 0.127 3.38 4.04 3.64 4.78 4.80 4.18

32 23-Nov 10:56:43 NaN 0.231 0.475 0.351 0.191 0.170 0.071 3.50 3.77 3.29 4.59 4.29 4.86

33 25-Nov 09:48:36 NaN 0.099 0.516 0.348 - 0.086 0.065 3.53 3.38 3.63 - 3.40 3.70


59917161 | 22 December 2017 25

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