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 (???????? ) 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 − ????)(ℎ???? + ????)

????????????

????????

= −???????? +

????????????

????????

+ ???????????????????? − ????????????????????????????

????????=

????

16(???? − 1)√????

√????????????

5/2????????????2????????

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.

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