Waves Flashcards
What is the energy contained in a wave proportional to?
wave height squared
What is the ‘significant’ wave height (H_1/3)?
the average height of the highest third of all waves occurring in a particular time period
What is SHM?
When the restoring force is proportional to displacement and in the opposite direction
What the fuck is an amphidromic system……
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.
Amphidromic point….
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).
What is Stokes drift?
The small net forward displacement caused by orbits moving slightly further forward in crests than they do backwards in troughs
What defines a shallow wave?
lambda>20*d
What defines a deep wave?
lambda<2*d
What is g in c=sqrt(gλ/ 2π)
???
5 ways of wave energy dissipation
- White-capping
- Viscous attenuation
- Air resistance
- Non-linear wave-wave interaction
- Shoaling
What is fetch?
The unobstructed distance of sea/ a wave that wind blows
In deep water limit how does group speed relate to the phase speed?
group speed is half the phase speed
Shallow water limit
Speed dependent on depth but not wavelength
Deep water limit
Speed dependent on wavelength but not depth
Particle velocity
the velocity of individual particles or parcels of water
Group velocity
the velocity of a collection of waves … or the velocity with which the “energy”
of the wave propagates.
Phase velocity
the velocity of an individual wave (of given wavelength)
Define non-dispersive waves and give an example
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).
Define dispersive waves and give an example
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).
provide the relationship between phase and group velocities for waves that are in the deep limit
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.
provide the relationship between phase and group velocities for waves that are in the shallow limit
In the shallow water limit the phase and group velocity reach a maximum with the same value
of √(gH).
describe typical particle trajectories in the water column
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.
Explain centrifugal force in the context of the Earth-Moon system
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
explain the tide generating force and the presence of semi-diurnal tides
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.
Explain why we observe variations of the tides at approximately daily frequiencies
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.
What causes spring-neap cycle?
fortnightly variation in tide
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.
Explain the differences between the equilibrium and dynamic theories of tides
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.
explain the tidal dynamics one would expect
within a rectangular basin attached to a larger basin in the Northern hemisphere.
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.
What are co-tidal lines?
lines that emanate from the amphidromic point and link all the points where the tide is at the same stage of the cylce
What are co-range lines?
cut across co-tidal lines approximately perpendicularly and join up locations having the same tidal range (amplitude)
What is equilibrium tide?
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.
What does the dynamic theory of tides include?
differing ocean depths, coriolis effect, configuration of land…
Which way do amphidromic systems tend to rotate in the northern hemisphere?
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)
Give estimates for the levels of natural tidal energy dissipation that occur
globally as well as on the North-West European shelf
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.
What is tidal streaming?
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)
What is a hydraulic current?
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).
What is a resonant system?
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).
Discuss some of the issues that need to be considered in a tidal stream power resource assessment
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.
Discuss some of the issues that need to be considered in an environmental impact assessment.
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
Discuss the pros and cons of tidal barrages
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
Discuss the pros and cons of tidal lagoons
Lagoon: many of the advantages of barrages, but smaller scale, potentially the need to build
a wall all the way around, less environmental impacts.
Discuss the pros and cons of TECs (Tidal energy converters)
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.
Contrast tides with some some other sources of renewable energy.
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.
