# Applied Sciences

Coastal Engineering and Modelling – 6110ENG

Assignment 1- Simple Coastal Models Trimester 1, 2020

Due date: 11 PM Wednesday, May 6, 2020, Week 10.

Submission Instructions:

1. Work individually 2. Complete all tasks as instructed with the assignment question sheet 3. Submit both the report and MATLAB script file electronically to the “Submission

Dropbox_Simple Coastal Models Assignment, Due on May 6, 2020” link on

Learning@Griffith – “Assessment”

Question 1: (60 marks)

A submerged pressure sensor can serve as a wave gauge if it is adequately sensitive to detect

the wave induced dynamic pressure. There is a swell wave with the deep-water characteristics

(period T0 and wave height H0 measured by an offshore buoy) perpendicularly propagating

toward a straight shoreline. At the coast near the shoreline, a pressure sensor is installed as

shown in the Figure below. For the progressive swell wave, the minimum and maximum

pressures (Pmin and Pmax at the Sensor are recorded as well. (The density of seawater to be 1026

kg/m3). The wave data of 5 storm events have been included in the Table below. Develop a

model to estimate the swell wave height at the coast using the measured data and estimate the

Shoaling Coefficient for all events. Assume the linear wave theory is valid.

Sensor 1

Deep water buoy record Pressure senor at the Coast

H0 (m) T0 (s) Pmin ( kPa) Pmax ( kPa)

1 1.8 25 82.4 106.7

2 1.3 15 83.2 96.2

3 2.2 18 80.6 106.2

4 1.8 12 82.2 98.2

5 6.2 7 83.6 120.6

Numerical solutions (6 marks)

Develop MATLAB codes to:

(i) Calculate the wave characteristics and generate a table (i.e. wave height, wave length,

wave number, wave celerity) at the coast by solving the Dispersion relation equation

numerically using fzero( ) function in MATLAB with relevant linear wave equations;

(ii) Calculate the Shoaling Coefficient using the linear wave theory and the recorded data

for the 5 events and compare the results for further uncertainty discussion, and generate

a figure to show the relationship between the relative water depth (water depth/wave

length) and the shoaling coefficient;

(iii) Generate figures to show the surface wave elevations offshore and at the coast of Event

1 for 2 wave periods for further discussion, and

(iv) Generate figures to present the time series (t varies from 0 to 2T) of the water particle

horizontal and vertical velocities at the location of the Sensor and at the mean water

level for Event 5 (for the discussion of the relationship between the horizontal and

vertical velocities) and compare the results with the wave height.

Report (54 marks)

Complete a report that address and solves all tasks listed above. It must include:

• Introduction: Introduce the problem and explain your methodology, i.e. problem

formulation including all relevant equations and numerical method used

• Results and discussion: Display the data in a clear and appropriate manner, i.e. all figure

axes and table columns must be properly labelled with the correct units, captions and

brief explanation and discussion are required for all figures, with reference made to

linear wave theory.

• Conclusion: A brief analysis that summarises the data and draws some conclusions.

Question 2: (40 marks)

Consider a 5km stretch of coast oriented in the north-south direction with the ocean to the east. The

predominant wave direction is from the east-south-east. At the southern end the typical breaker height

is 1.4m and the breaker angle is 10. At the northern end, the breaker height is 1.45m and the breaker

angle is 12. The breaker parameter b = 0.8.

The beach profiles along the section are similar with slopes near the break point of 1/40. The sand is

made of quartz (s = 2.63, p = 0.28) with a median grain size of 0.22mm and measureable seasonal

bed level changes are restricted to depths less than 6 metres. The berm height is 3 m AHD.

The average shorenormal sediment transport rates (𝑄𝑥) for 1993-2015 were saved in the data file

“sediment.xls”. There are no sinks and sources for sediment transport in the control domain. The

erosion rate (metres of shoreline retreat rate) can be calculated using (see details in Coastal Process

module lecture notes)

(1 − 𝑝)(ℎ𝑐 + 𝐵) 𝜕𝑥𝑠 𝜕𝑡

= −𝑄𝑥 + 𝜕𝑄𝑦

𝜕𝑦 + 𝑄𝑠𝑖𝑛𝑘 − 𝑄𝑠𝑜𝑢𝑟𝑐𝑒

𝑄𝑦= 𝐾

16(𝑠 − 1)√𝛾 √𝑔𝐻𝑏

5/2𝑠𝑖𝑛2𝜃𝑏

where

South

West

p is the sediment porosity,

xs is the shoreline coordinate

Qsource is a sediment input (e.g. river discharge, beach nourishment)

Qsink is a sediment loss (e.g. dredging)

K ≈0.77 is an empirical coefficient which has a weak dependence on grain size.

s is the specific weight

Hb is the breaker height

is the breaker index

b is the wave crest angle at the break point

all other variables are as defined in the figure

The aerial photographs of the stretch of the coast from 1993 to 2015 indicate the shoreline location, xs

which were saved in the file “shoreline.xls”.

Numerical solutions (6 marks)

Develop a numerical model using MATLAB to calculate the location of the shoreline from 1993 to 2015,

i.e. xs. (assume xs = 0 in 1993) using the provided data and information, and evaluate the accuracy of the

model.

Report (34 marks)

Complete a report that address and solves all tasks listed above. It must include:

• Introduction: Introduce the problem and explain your methodology, i.e. problem

formulation including all relevant equations and numerical method used

• Results and discussion: Display the data in a clear and appropriate manner, i.e. all figure

axes and table columns must be properly labelled with the correct units, captions and

brief explanation and discussion are required for all figures.

• Conclusion: A brief analysis that summarises the data and draws some conclusions.