Waves

Question 1

What is the energy contained in a wave proportional to?

Answer 1

wave height squared

Question 2

What is the ‘significant’ wave height (H_1/3)?

Answer 2

the average height of the highest third of all waves occurring in a particular time period

Question 3

What is SHM?

Answer 3

When the restoring force is proportional to displacement and in the opposite direction

Question 4

What the fuck is an amphidromic system……

Answer 4

system of tidal action in which the tide wave progresses around a point or centre of little or no tide. Result from the combined effects of ocean basin geometry constraint, non-linear friction and the coriolis force.

Question 5

Amphidromic point….

Answer 5

where the crest of the tidal wave circulates round once a tidal cycle. Have zero tidal amplitude for a tidal constituent. Co-tidal lines
emanate from the amphidromic point and link all the points where the tide is at the same
stage (phase) of its cycle. Co-range lines cut across co-tidal lines approx. at right angles and
join up locations having the same tidal range (or amplitude) Note that amphidromic systems
tend to rotate anticlockwise in the N hemisphere (clockwise in Southern).

Question 6

What is Stokes drift?

Answer 6

The small net forward displacement caused by orbits moving slightly further forward in crests than they do backwards in troughs

Question 7

What defines a shallow wave?

Answer 7

lambda>20*d

Question 8

What defines a deep wave?

Answer 8

lambda<2*d

Question 9

What is g in c=sqrt(gλ/ 2π)

Answer 9

???

Question 10

5 ways of wave energy dissipation

Answer 10

1. White-capping
2. Viscous attenuation
3. Air resistance
4. Non-linear wave-wave interaction
5. Shoaling

Question 11

What is fetch?

Answer 11

The unobstructed distance of sea/ a wave that wind blows

Question 12

In deep water limit how does group speed relate to the phase speed?

Answer 12

group speed is half the phase speed

Question 13

Shallow water limit

Answer 13

Speed dependent on depth but not wavelength

Question 14

Deep water limit

Answer 14

Speed dependent on wavelength but not depth

Question 15

Particle velocity

Answer 15

the velocity of individual particles or parcels of water

Question 16

Group velocity

Answer 16

the velocity of a collection of waves … or the velocity with which the “energy”
of the wave propagates.

Question 17

Phase velocity

Answer 17

the velocity of an individual wave (of given wavelength)

Question 18

Define non-dispersive waves and give an example

Answer 18

For a non-dispersive wave the phase velocity is independent of wavelength, and thus the group
velocity is the same as the phase velocity (e.g. tides).

Question 19

Define dispersive waves and give an example

Answer 19

For dispersive waves the phase velocity
is dependent on wavelength and the group velocity is different to the phase velocity (e.g. wind
waves or tsunamis generated by short wavelength disturbances).

Question 20

provide the relationship between phase and group velocities for waves that are in the deep limit

Answer 20

Towards the deep water limit both slow (with longer wave lengths travelling faster),
with the group velocity converging to half the value of the phase velocity.

Question 21

provide the relationship between phase and group velocities for waves that are in the shallow limit

Answer 21

In the shallow water limit the phase and group velocity reach a maximum with the same value
of √(gH).

Question 22

describe typical particle trajectories in the water column

Answer 22

particle trajectories are near circular near surface, and come more elliptical with depth until the ellipse flattens near the bed, but the extent of the to and fro motion in the horizontal is not reduced with depth.

Question 23

Explain centrifugal force in the context of the Earth-Moon system

Answer 23

The Earth-Moon system rotates about a common centre of mass. This creates a (fictitious)
centrifugal force for every point on Earth. Every point traces the same path and hence this
force is the same for every point on Earth and is parallel to the line connecting the Earth and
Moon centres of mass, and in the opposite direction to the Moon

Question 24

explain the tide generating force and the presence of semi-diurnal tides

Answer 24

Every point on Earth experiences a gravitational attraction towards the moon, with varying magnitudes based on an inverse square law.
Summing these two forces yields the variable tide generating force, the horizontal component
of which is responsible for the tides.
This creates two “bulges”, one under the moon and another on the opposite side of the Earth.
As the Earth rotates over approx a day an observer will find themselves under high water
levels and low water levels twice in that period – hence a semi-diurnal tidal signal.

Question 25

Explain why we observe variations of the tides at approximately daily frequiencies

Answer 25

Since the moon is not above the equator, the bulge(s) are inclined to Earth’s rotation plane,
for an observer at a given latitude it will pass under the two bulges at different points in the bulge or equivalently observe different depths of water. So they would still see a semi-diurnal high, but one would be larger than the other – a diurnal inequality.

Question 26

What causes spring-neap cycle?

fortnightly variation in tide

Answer 26

The Sun leads to another bulge that raises tides and it is the sum of the Moon and Sun bulges that we see as observers on Earth. Over the course of approx a month the moon rotates around the Earth, the relative location of the Sun being approx fixed. Thus at times ( every
two weeks) the Earth-Moon-Sun align and these bulges reinforce one another, and in between they will constructively interfere. In the former we will see higher highs and lower lows (spring tides) and in the latter case they will cancel one another out to some degree (the moon will always win), leading to less high highs and less low lows. This is the spring-neap cycle.

Question 27

Explain the differences between the equilibrium and dynamic theories of tides

Answer 27

Equilibrium theory assumes that the Earth can rotate under the bulges “cleanly”, or equivalently
that the bulges can rotate around the Earth to exactly balance the forcing. However,
the (shallow water) wave speed isn’t fast enough to accomplish this (leading to lag), land gets
in the way, and inertia, friction and Coriolis get in the way of the simple equilibrium theory
picture. The dynamic theory seeks to take all of these factors into account and generally relies
on the solution of the equations of motion numerically.

Question 28

explain the tidal dynamics one would expect

within a rectangular basin attached to a larger basin in the Northern hemisphere.

Answer 28

In a rectangular basin, assumed connected to a larger basin and its southern end. During flood
water moves North and is deflected to right by Coriolis raising surface elevation on the Eastern
side of the basin Conversely during ebb, the currents travel south, again deflected to right,
which now raises elevation on western side of basin. Hence, because of constraint of land, the
tidal wave moves around in an anticlockwise manner. This will form an amphidromic system
with a point of near zero tidal amplitude at the centre.

Question 29

What are co-tidal lines?

Answer 29

lines that emanate from the amphidromic point and link all the points where the tide is at the same stage of the cylce

Question 30

What are co-range lines?

Answer 30

cut across co-tidal lines approximately perpendicularly and join up locations having the same tidal range (amplitude)

Question 31

What is equilibrium tide?

Answer 31

When the free surface elevation of an assumed water covered earth’s pressure gradient balances the horizontal tide generating forces, resulting in a steady balanced state.

Question 32

What does the dynamic theory of tides include?

Answer 32

differing ocean depths, coriolis effect, configuration of land…

Question 33

Which way do amphidromic systems tend to rotate in the northern hemisphere?

Answer 33

anticlockwise

(flood tide moving northwards is pushed to right by CF creating higher water level on eastern side, ebb tide moving southwards is pushed to right by CF creating higher water level on the western side)

Question 34

Give estimates for the levels of natural tidal energy dissipation that occur
globally as well as on the North-West European shelf

Answer 34

In coastal regions the interaction with shallow water waves (horizontal motion
extending down to the sea bed) dissipates energy through friction/drag effects. Globally this
account for approx 2.5-3TW of energy dissipation. On the NW European shelf approx 250GW
is dissipated.

Question 35

What is tidal streaming?

Answer 35

physical response to maintenance of the continuity equation. When deep
ocean tidal currents reach the shallower continental shelf they accelerate. Further, when a
current is forced through a constriction, the flow must accelerate, (e.g. Strangford Lough
narrows)

Question 36

What is a hydraulic current?

Answer 36

If two adjoining bodies of water are out of phase, or have different tidal ranges, a hydraulic current is set-up in response to the pressure gradient created by the difference in water levels (e.g. Pentland Firth).

Question 37

What is a resonant system?

Answer 37

Occur as a consequence of a standing wave being established. These occur when the incoming tidal wave and a reflected tidal wave constructively interfere
(e.g. Severn estuary or the Bay of Fundy).

Question 38

Discuss some of the issues that need to be considered in a tidal stream power resource assessment

Answer 38

Assessing resource: location and magnitudes of currents; difference between flood and ebb
(magnitudes and direction); water depth in relation to turbine size, top and bottom clearance
etc; device spacing and number of turbines that can be supported; bathymetry; phased deployment
constraints; Potential exclusion constraints: protected sites (e.g. habitats, cultural
significance, archaeological, etc); other renewable developments; MoD exercise sites; pipelines
and cables; dredging areas; oil and gas sub-surface installations; other renewable developments
in area.

Question 39

Discuss some of the issues that need to be considered in an environmental impact assessment.

Answer 39

Environmental impact: coastal and sedimentary processes; marine ecology, including intertidal
and benthic ecology, marine mammals; fish resources and fisheries; marine navigation; cultural
heritage. Other environmental parameters that should be assessed include: ornithology; terrestrial
ecology; landscape and visual impact; road traffic and access; tourism & recreation;
water, sediment and soil quality; noise and air quality; socio-economy. Decommissioning phase
and cumulative impact of other existing and planned offshore projects in area

Question 40

Discuss the pros and cons of tidal barrages

Answer 40

Pros: lots of local power, storage potential, control water depths behind barrier, possibility
for flood and/or ebb generation, pumping to increase head
Cons: large costs, potentially large
impacts such as sediment build up, water quality as reduced estuary flushing

Question 41

Discuss the pros and cons of tidal lagoons

Answer 41

Lagoon: many of the advantages of barrages, but smaller scale, potentially the need to build
a wall all the way around, less environmental impacts.

Question 42

Discuss the pros and cons of TECs (Tidal energy converters)

Answer 42

Stream (arrays): more diffuse power, also only limited locations, inhospitable environment
leading to survivability issues for turbines, over-installation can lead to blockage which redirects
flow, not damming off a whole region so lower impacts, potential for turbines of different sizes
to extract energy in shallower regions, and for floating devices in deeper water.

Question 43

Contrast tides with some some other sources of renewable energy.

Answer 43

Big advantage of tidal is that it is completely predictable and we will get power twice per day
for extended periods (cf. solar and wind - not predictable and could not generate anything for
long periods). But also periods of slack, and changes in currents/range over e.g. spring-neap
cycle leads to large variations in peak power. Tidal stream out of sight, barrages/lagoons
could be dual use, e.g. roads, flood defence, recreational activities – not the case with other
renewable sources.