1400 word Report

Question 1:

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.

Numerical solutions (24 marks) Develop MATLAB codes to: (i) Calculate the wave characteristics (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 and the shoaling coefficient; (iii) Generate figures to show the surface wave elevations offshore and at the coast of Event 5 for 2 wave periods, 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 for Event 1 (for the discussion of the relationship between the horizontal and vertical velocities). Report (36 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.

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.xlsm”. 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)