Coastal Engineering and Wave Modeling Report: 6110ENG Assignment 2

This report details a wave modeling project focused on the Moreton Bay and the Port of Brisbane, addressing the need for accurate wave climate predictions for the port's upgrade and expansion. The study utilizes the MIKE 21 SW model to simulate wave conditions, considering wind data from the Bureau of Meteorology. The project involves data pre-processing, spectral wave model establishment, and analysis of wave characteristics, including height, direction, period distributions, and spectral parameters. The report presents the application of design formulas to determine wave heights and stability coefficients crucial for coastal structure design. The findings offer essential design data for the construction of marine structures and are valuable for future coastal projects in Moreton Bay. This project underscores the importance of accurate wave predictions in coastal engineering, impacting both the safety and the economic aspects of marine infrastructure development.

Wave Modeling
(Report)
Author
Institutional Affiliation

I. INTRODUCTION
A. Project
The Moreton Bay is one of the most crucial coastal resources in Queensland. The bay is
situated at the eastern coast of Austarlia and its distance from central Brisbane is 14 kilometers.
Southeast of Queensland is the Brisbane River which is the longest with a length of
approximately 344 km. The Brisbane Port serves a very important function of coordinating large
ship traffic crossing the northern section of the bay.
In order to facilitate the functions of the bay, the port is to undergo upgrade and
extension. Such a project within a water body requires preliminary investigations on the climatic
conditions of the area be done. While upgrading and expanding the port, various marine
structures will be erected to facilitate the functions of the port. The construction of marine
structures needs an accurate prediction of the wave climate of the area in order to determine the
precise design data for the structures [1].
The Figure 1 below shows the Moreton Bay and the location where the Port of Brisbane
which is to be upgraded and expanded. The Moreton bay does not have much available historical
wave monitoring data; however, the Bureau of Meteorology provides a summary and averages of
the Rose of Wind direction versus Wind speed in km/h for the Brisbane area from the year 1950
to 2000 [2].
The objective of this task is to predict the design wave conditions by using MIKE 21 SW.
Among the tasks accomplished in the project include the preparation and pre-processing of the
required data, establishment of a spectral wave model using the calibrated model parameters
provided, and analysis of the results of the wave conditions including the wave height/direction
and period distributions in the entire bay and the wave characteristics at the Port of Brisbane.

Figure 1. Brisbane River and Moreton Bay [3]
B. Model and Design Formula
The project was accomplished through the provided “Key Model Parameters” indicated
in the next section of the report. In order to carry out the entire project, a complete simulation of
the Morten Bay area was conducted using the provided wind conditions data and the wave output
parameters given. After the simulation, an in-depth analysis of the wave data was done and the
results recorded as indicate in the results section of this report. Some of the primary design
aspects considered and analysed during project execution include the developed wave
height/direction, the period distributions of the wave, the wave characteristics at the location
where the port is to be upgraded and expanded, and the developed wave spectral parameter. All
these key details are necessary for the construction of any marine structure [4] [5] [6]. Hence, the

need for analysis and presentation of accurate results to the construction firm undertaking the
task.
C. Key Model Parameters
The Figure 1 above is a satellite image of the location of the Port of Brisbane that is to be
expanded and upgraded. Other essential data/parameters that are provided for the project are the
50 year ARI design wind which is within the project domain. The data provided in the Wind
Roses is as indicated in the attached document: both the direction and speed of wind in km/h.
Accurate design data for coastal structures heavily relies on the accurate prediction of the
design waves [7]. Safe structures and the development of economic structural designs are
dependent above all on the reliability and accuracy of the basic design parameters [8]. The Port
of Brisbane to be upgraded and expanded is a coastal structure. Therefore, all the necessary and
essential data for its design should be taken into account for the safe and economical design of
the structure [9]. The accuracy of the design of any coastal structure determines both the social-
economical and safety aspects of the structure [10] [11]. For instance, the construction of a high
crested coastal structure is rendered to be almost completely safe; however, the cost implication
for such a development could be extremely high. Also, socio-economically, such structures
become visual obstructions to the view of the sea, yet such views are tourist attractions which
have considerable economic value. However, if a structure is design with a low crest level, its
safety should be put into consideration. In order to achieve all these, accurate wave predictions
of the area/region should be done – the objective of this project/spectral wave predictions [12].
The following are some of the design parameters that were used in the development of
the design:
i. Bathymetry data – from pre-generated file of “Moreton_Bathy.mesh”.

Figure 2: Bathymetry data.
The study area of Moreton Bay’s geographical position of origin is 27.5255S
and153.0364E (Easting 503202.6966424, Northing 6954863.894501).
ii. The domain has Northern, Southern and Eastern and Brisbane river mouth open
boundaries.
iii. A MIKE 21 SW model has been developed and calibrated using the Moreton
Buoy data (Easting 519719, Northing 6985769). The following model parameters
will be applied:

a. Basic equations: Fully spectral formulation and Instationary formulation
b. Spectral discretization: 25 frequencies and 16 directions
c. Diffraction needs to be considered with smoothing factor and steps are 1 for both
d. Include quadruplet wave interaction
e. Constant wave braking index of 0.8
f. D50 sand size is 0.0002 m
g. No whitecapping
iv. The Port Brisbane is located at (Easting 520000, Northing 6973000).
v. Rose of wind direction versus wind speed information in four seasons is provided
in the file “040223-3pm-all.pdf”.
After modeling, the following are the results arrived at:
Direction of
Wind
N NW S SE
Speed of Wind 22.4 24.2 23.2 31.6
Significant
Height of the
Wave
6.434 6.234 6.04 6.32
Peak Period of
the Wave
15.22 12.162 12.24 16.34
D. Formulas Applied and the Methodology

In order to prepare and pre-process the required data, and also to establish the spectral
wave model, the parameters below were used in a pre-generated file of “Moreton_Bathy.mesh”
and the simulation run:
i. Time up, 100 steps and 1800 sec.
ii. Given wind speeds and directions,
iii. Boundary conditions as lateral boundary.
iv. Point series,
v. Area series
vi. Spectral series
The results obtained were recorded and anlysed in the results section that follows.
II. RESULTS
The MIKE 21 SW application was used to determine the spectral wave model. MIKE 21
SW is a software developed by DHI and it is a 3rd generation spectral wind wave model. This
model was used to stimulate the growth, decay, and transformation of the waves generated by the
wind, and the swells with the Port of Brisbane in Moreton Bay, which is under construction
(upgrade and expansion).
In order to obtain complete detailed data for the design of the coastal structure, a full
spectral and a directional decoupled parametric formulation was done and was part of this
analysis. The full spectral formulation has its basis on the wave action conservation equation,
defined in [13] and [14]. The directional decoupled parametric formulation, on the other hand, is
based on the equation of conservation of the wave action. In order to do parameterization, a
zeroth and 1st moment of wave action was introduced in the frequency domain. After that, small

scale and large scale applications of the basic conservation equations were formulated in the
Cartesian co-ordinates and the polar spherical co-ordinates respectively [15].
The following physical phenomena were obtained from a full spectral model:
i. The wave growth – this was as a result of the wind’s action.
ii. Wave-wave interactions (unswerving)
iii. There was no dissipation because there was no whitecapping from the given data.
iv. Bottom friction, however, resulted to dissipation.
v. Depth-induced wave breaking led to dissipation.
vi. Refraction and shoaling – a result of variations in depth.
vii. Interaction between waves and current.
viii. Effects of time-varying water depth, and
ix. Effects of coverage by ice on the wave field.
The cell-centred finite volume method was used to conduct the discretisation of the main
equation in the location and spectral space. The geographical domain in this project was the
Moreton bay. In this case, an unstructured mesh method was applied. The fractional step
technique was used to carry out the time integration, and in this case, a multi-sequence explicit
approach was used to propagate the wave action.
After simulation, the results in the figures below were obtained from the MIKE 21 SW
model based on the “Key Model Parameters” that were specified for the project:

Figure 3: Spectral Wave Model
Figure 4: Wave Height and Wave Direction Distribution

Figure 5: Wave Period Distributions

Figure 6: Wave Spectral Parameter
E. Formulas and Solutions
Design wave height,
H10 %=Hrms √−ln ( 0.1 )
Wave height at the breakwater,
Hb =γ b hb
Whereγb – Break criteria
-❑b HB−water depth at thetoe of Breakwater .
Hudsons Formula

Stability number,
Ns = H
∆ Dn 50
=( K D cot α ¿ ¿
1
3
 D50= H
∆ ¿ ¿
 ∆= ρs
ρw
−1
 W n 50= ρs g Dn 503
Calculations:
The results indicate that the maximum height is for the North direction-design height
Hence,
Significant height, Hs =6.434 m
Peak wave period, T p=15.22 s
For:
Break criteria, γb=0.9
Water depth breakwater,hb =9.8 m
Slope, tanα
Density of BW, ρs=2650 kg /m3
The density of waterρw =1026 kg/m3
Find H10 %
For finding this, we need Hrmsvalue:
We can find it on the Raleigh distribution chart given below: