UNIVERSITY OF EAST ANGLIA
School of Environmental Sciences
Main Series Postgraduate Examination 2012-2013
WAVES, TIDES AND SHALLOW WATER PROCESSES
ENV-MA40
Time allowed: 2 hours
Answer TWO questions from SECTION A and ONE question from SECTION B.
Write EACH answer in a SEPARATE answer book.
Both sections carry equal marks.
Acceleration due to gravity, g = 9.81 ms-2
Typical density of seawater, ρ = 1025 Kg m-3
Angular rotation rate of the Earth, Ω = 7.29 x 10-5 (rad) s-1
Principle lunar semi-diurnal tide (M2) period = 12.42 hours
Scientific calculators are permitted.
Notes are not permitted in this examination.
Do not turn over until you are told to do so by the Invigilator
ENV-MA40
Copyright of the University of East Anglia
Module Contact: Dr Rob Hall, ENV
Version 2
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SECTION A
1. a) Explain why the Moon typically causes two high tides per day and not one.
Include a diagram of the gravitational, centrifugal, and tide generating forces
acting on the Earth.
[40%]
b) Why is the lunar semi-diurnal (M2) tidal constituent period longer than the
solar semi-diurnal (S2) tidal constituent period?
[10%]
c) Draw a diagram to show how the M2 and S2 tidal constituents interact to cause
the spring-neap cycle.
[20%]
d) How long in days must an observational timeseries be to well resolve the M2
and S2 tidal constituents separately? The S2 tidal period is 12.00 hours. [10%]
e) Explain how the location of a tidal mixing front may be adjusted by the springneap cycle.
[20%]
2. a) Explain the difference between short (deep-water) waves and long (shallowwater) waves.
[25%]
b) Tides are always shallow-water waves. Calculate the phase speed,
wavelength, and energy flux of the M2 tide in the deep ocean. Assume the water
depth to be 2000 m and, the elevation amplitude to be 50 cm.
[20%]
c) When the tide crosses the shelf edge, the water depth decreases to 150 m.
What are the new phase speed, wavelength, and elevation amplitude of the tide?
What must remain constant for these calculations to be valid?
[20%]
d) The equation for co-oscillation in a semi-enclosed bay is
where Asw is the elevation amplitude of the standing wave, A0 is the elevation
amplitude at the mouth of the bay, L is the length of the bay, and λ is the
wavelength.
The tide enters a semi-enclosed bay that is 400 km long. The water depth
remains 150 m. What is the tidal elevation amplitude at the head of the bay?
Why would tidal elevation amplitude not reach this maximum in the real world?
[15%]
e) Explain the effects of rotation and friction on the propagation of tides around
semi-enclosed seas.
[20%]
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3. a) Explain why some shelf sea regions become stratified during summer while
other regions remain vertically mixed all year.
[35%]
b) Explain why chlorophyll concentration is often greatest at the base of the
pycnocline in stratified regions during summer.
[15%]
c) Write down the Osborn relation and use it to calculate the vertical eddy
diffusivity through the pycnocline. Assume turbulent kinetic energy eddy
diffusivity is 10-6 m2 s-1 and the buoyancy frequency is 0.005 s-1.
[15%]
d) Microstructure profilers are used to estimate the turbulent kinetic energy
dissipation rate in the ocean. What to they actually measure in order to infer the
rate of energy dissipation and why is it important that they are streamlined and
“free-falling”?
[15%]
e) If you do not have access to a microstructure profiler you can estimate
turbulent mixing using Thorpe scale analysis. Outline the Thorpe scale method
and explain its limitations.
[20%]
4. a) Compare and contrast the two ways that marine renewable energy may be
harnessed. Explain briefly how each distinct type works (using annotated
sketches where appropriate) and discuss predictability and maintenance issues.
[60%]
b) A tidal stream turbine is to be chosen to provide power for a small coastal
community of 100 households. A survey of the tidal conditions has indicated that
at peak neap tides the velocity at the site is 3.2 ms-1 in water 11 m deep.
Calculate a suitable turbine diameter that will provide for the communities
average power consumption. State the reasonable assumptions you make for
any unknown quantities
[40%]
You are reminded that
1
AU 3
2
where the symbols have their usual meaning.
Power  C P
PLEASE TURN OVER
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SECTION B
5. Describe and explain, with the aid of diagrams, how water movement and
sediment movement in estuaries are related.
6. a) The diagram below shows a model representation of the average number
of days that the water column is stratified each year. Describe the mixing
regimes in areas A, B, C.
[30%]
b) The likelihood that a shelf sea location of a particular depth will stratify can be
simply described as a balance between which two processes? Which of these
processes is more likely to be affected by climate change and, why?
[30%]
c) What gives rise to ‘extreme sea level’ around the coasts of the UK? Relative
sea-level rise is one climate-driven factor that can change extreme sea level at
the UK coast. Explain the term ‘relative sea-level rise’. What changes in
atmospheric storms could also change extreme sea level at the coast? Give
three examples of coastal adaption to limit the impact of changes in extreme sea
level.
[40%]
END OF PAPER
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