Download Wave energy converters, sediment transport and coastal erosion

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Wave energy converters, sediment transport and coastal erosion
Arne Vӧgler1, David Christie1, Malcolm Lidster1, James Morrison1
1
University of the Highlands and Islands (UHI) – Lews Castle College
Abstract
As a simplified assumption the north westerly coastline of the Isle of Lewis in Scotland can be taken
as a system in a state of equilibrium. The seasonal removal of sediment from the beaches during
winter storm events is counterbalanced by a natural recovery period during the summer.
The area has one of the highest wave energy resources in Europe, and it is anticipated that large
scale deployments of wave energy converters will occur within the next decade. With a location at
the edge of the Atlantic the area is also affected by the consequences of global warming, namely the
forecasted increase of severe weather events and rising sea levels.
Changes to one parameter in a system in equilibrium will force changes to the wider environment
and this paper investigates if and how the smart siting of wave energy converters can be used to
offset potentially destructive impacts caused by global warming. For example, the devices will
absorb and dissipate wave energy: this could promote landside littoral deposit, augmenting coastal
defences.
Effects of large scale installations of near shore wave energy converters on the coastline are
modelled numerically with experimental validation on micro scale models.
The importance of access to baseline data is described and the continuous research activity monitors
seasonal changes to the sediment patterns of selected locations on the Isle of Lewis with the aim to
support theoretical forecasted and modelled impacts on the system with hard data over the years.
Keywords: Sediment transport, wave energy converters, coastal erosion, Outer Hebrides
Contact author: Arne Vӧgler, University of the Highlands and Islands, Lews Castle College, Stornoway, Isle of
Lewis, Outer Hebrides, Scotland, GB-HS2 0XR, e-mail: [email protected] , tel. +44 (0)1851 770 325
Introduction
It is anticipated that the combined climate change effects of rising sea levels and a forecasted
increased frequency of severe storm events in the north west of Scotland will cause an increased
level of coastal erosion in areas with an exposed shoreline such as can be found in parts of the Outer
Hebrides. Extreme tidal and storm surges increase the risk of coastal flooding with subsequent
destructive effects on sand dunes and beaches, as was strongly evidenced by the 1 in 100 year storm
that affected the north western parts of Scotland in 2005. The amount of damage caused to coastal
public property in the Uists and Benbecula during this storm event, as a result of widespread
flooding and extreme wind loads, was estimated as £15 million [1]. In addition the storm, with
maximum values for wind speed and wave heights for the area to the west of South Uist modelled as
34.6m/s and 14.3m respectively on a 12km grid resolution [2], also resulted in the drowning of five
members of a family that attempted to escape the flooding in their car.
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Coastal erosion is not only a problem during storm events in the Outer Hebrides, it is a continuous
process. Attempts to minimise or prevent damage include the reinforcement of the natural
defences, such as sand dunes, by building fences out of netting or pallets, or transplanting Marram
grass to stabilise the soil and promote deposition of sand[3].
Background Analysis and Overview
To understand the long lasting impact of coastal erosion caused by extreme storm events or as a
consequence of regular seasonal weather patterns, a profound knowledge of the geological
structure of the littoral zone, with a particular view to the foreshore, sub-littoral and coastal zone is
required. Well vegetated and developed dunes or steep cliffs act as a natural protective boundary
which minimises erosion caused by sea winds. Destroyed vegetation on dunes will often result in
sand blown or washed away, which is then replaced by sand eroded upwards from the beach. Other
than sediment that is removed by wind from the sea and carried away landwards, thus lost from the
coastal zone, sand washed down from a dune generally ends up on the beach or in the tidal zone,
where it can act as a replacement for sand that is blown back up onto the dune again.
Waves approaching a shore with an angle of impact other than perpendicular create a longshore
current which, depending on the velocity of this current, removes sediment and thus potentially
reduces the sediment available to form a beach in the affected region. The same is valid for
perpendicular waves in combination with an existing longshore current caused by tidal movements
or larger oceanographic processes such as the North Atlantic drift. In areas that are in equilibrium,
where the sediment removed by coastal processes equates to the amount deposited from areas
upstream, no long term change is measureable. However, seasonal variability can be considerable
where sediment removed from a beach by regular winter storms is mainly deposited in the near
shore region from where it is pushed back up onto the beach by the swells of a longer wavelength
during the summer period [4]. Where in mesoscale areas with a rich supply of sediment, a localised
net loss of sand might be temporary only, due to sufficient resources available for replenishment,
other areas without such a supply will not be able to recover and will face a long term impact.
Activities that force changes to coastal systems in equilibrium, resulting in the localised loss or gain
of sediment, include civil engineering works, such as the construction of offshore breakwaters or
groin structures as described by Dean and Dalrymple [5], or changes to the environmental boundary
conditions, i.e. climate change or severe storm events. The large scale extraction of wave or tidal
energy is another mechanism that is likely to change coastal dynamics, as the energy taken out of
the system to support the generation of electricity will no longer be available for dissipation in the
littoral zone [6].
Recent surveys undertaken by Marine Scotland to the north west of the Outer Hebrides, mainly in an
area with depths between 20-50m between the Butt of Lewis and Loach Roag, have utilised drop
down video technology and still photography to assess the benthic environment and seabed of the
area. Only a limited prevalence of sediment coverage was found as findings of the study have shown
that the seabed in the area consists mainly of “uneven bedrock with patches of boulders and cobbles
on medium-coarse sand” *7]. An area of deeper water to the west of Loch Roag has shown a slightly
higher amount of sand of a fine-medium to medium grain size shaped into ripples and sand waves.
A generally sparse coverage with sediment on the Hebrides Shelf has also been described in a report
commissioned by the Natural Environment Research Council (NERC) in 2006, and is explained by the
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combined effects of wave orbital effects on the open shelves which prevent the accumulation of
large sediment beds, underwater glens that act as sediment sinks, and a general lack of sedimentary
input from the shore [8]. The NERC report refers to Pantin [9] when describing the maximum near
bed wave induced orbital velocities in the outermost region of the Hebrides shelf as of 2.56ms-1 at a
depth of 200 metres and of 4.34ms-1 at 150m depth and highlights that the deposition and
subsequent accumulation of sediment at such extreme velocities is not possible.
The observed general absence of large amounts of sediment on the Hebrides shelf between the
Hebrides slope up to the 20m contour line, which has also been confirmed by local inshore
fishermen [10], is in contrast to the large number of beaches at the west coast of the Outer
Hebrides. Almost the entire Atlantic coastline of South Uist, Benbecula and North Uist is covered
with sediment, and there are numerous beaches along the west coasts of Barra, Harris and Lewis.
In an attempt to classify the UK coastal waters into individual regions where natural boundaries of
major coastal processes act as separators a total of 17 cells were identified by the Joint Nature
Conservation Committee (JNCC) in a study carried out from 1992 onwards. Ten of these regions
were located in the North Sea and English Channel and another seven to cover the west coast and
Isle of Man. The study describes the Outer Hebrides as an area whose exposed western coasts are
subject to severe wave action and a predicted 50 year wave height of 35m some ten kilometres
offshore [11+. The considerable wave potential is also acknowledged in the Scottish Government’s
regional locational guidance for marine energy developments which specifies the wave energy
resource of the Outer Hebrides as up to 42.4KW/m annual mean power output in offshore areas and
this compares with power values of up to 32.8kW/m and 27.9kW/m for Shetland and the Inner
Hebrides respectively [12]. The JNCC report describes the Atlantic coastline of the Outer Hebrides as
a predominantly rocky coast featuring numerous small bays and dunes in the northern parts and
extensive sand dunes and machair southwards of the Atlantic coast of Harris. With the North and
Little Minches acting as a natural boundary to the adjacent cell 16, which extends along the western
Highlands and includes the Inner Hebrides, the Outer Hebrides are classified as cell number 15 [11].
Although the classification of the UK coastline into 17 individual regions might be tolerable on a high
level, to understand localised processes a further breakdown of these regions into additional cells
and sub-cells was suggested by Ramsey and Brampton [13] who have split the Outer Hebrides into
the littoral cells 8 and 9 with an additional ten sub-cells as shown in figure one. Within the identified
sub-cells sediment transport in the littoral zone is restricted to individual bays with no or little
exchange or movement into neighbouring cells. There is negligible inflow of sediment from rivers in
the area and the sediment consists mainly of carbonate, i.e. shells, with small amounts of
terrigenous sands, which are shifted towards the shore by wave generated currents [11,13].
A considerable seasonal variability of sand build up can be observed at Hebridean beaches, with
sediment erosion mainly during storm events in the autumn and winter months and deposition
occurring during the calmer weather in the summer. In some bays, such as Dell beach at north-west
Lewis, it is not unusual to see the beach entirely disappearing during a stormy period, only to be
rebuilt some months, or even years, later. The change of individual bays between featuring sandy
beaches at some times and boulders only at others is a regular occurrence.
Considering the concept of individual coastal sub-cells in which there is little interchange or cross
border transport of sediment, and the observation that no large amounts of sediment are evident in
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the coastal zone at depths of more than 20m, it is likely that most of the sediment eroded from a
beach is deposited near shore within the same cell and is not transported away from the area. This
is further backed by statements in literature that “sediment is removed from the beach during
winter and transported seawards, where it may build a longshore bar” *14]. These longshore bars,
which are caused by beach erosion through the impact of steep storm waves in the winter, are
shifted towards the shore in summer by the longer swell dominated waves of a lower frequency.
An experimental analysis of wave induced sediment shift carried out at Lews Castle College has also
observed this effect and is described later in this paper.
Figure 1 – cells and sub-cells in region 15: Outer Hebrides, (adapted from [11], p.37)
A higher frequency of storm events and wind speeds as a result of climate change will not only
increase the amount of sediment eroded from the beach into deeper water, but will also reduce the
amount of time with favourable conditions for the re-deposition of sand in the shallow water region.
This shift of the ratio between beach erosion and recovery will change the present quasi equilibrium
of seasonal variability of sediment presence at the shore, with the effect that more sand will be
removed than is deposited over an annual cycle. This could potentially lead to a complete removal
of sediment from the beaches in the Outer Hebrides over time. Further contributing to a reduction
of beach sediment are the removal of sand from the beaches in the Outer Hebrides to grit roads in
the winter, as during the winter 2010/2011, or the use of sand as construction material to build
roads, etc. As indications are that the sediment in the area is a very limited resource and a removal
of scale could lead to long term changes of the environment, the industrial removal of sand should
be avoided, unless a full assessment has been carried out on the sustainability of such a practise.
The Outer Hebrides are a key area in Europe for the development of wave energy sites, and ongoing
research at Lews Castle College investigates the feasibility of utilising wave energy converters (WECs)
to offset wind wave forced erosion by conditioning the wave spectra to promote shore deposition of
sediment.
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At present there is only limited data available on the littoral processes in the area, and without
having adequate baseline data to provide a snapshot of the present state and dynamics of the
coastal system, an assessment of change within this system, induced by climate change scenarios or
also industrial developments, will be difficult to make.
Sediment samples of Lewis and Harris
An assessment of the sediment was conducted on 11 different sites on the west coast between
Horgabost in Harris and Shawbost in Lewis. Samples were taken over a seven day period from below
the high tide mark and a visual comparison was carried out using a microscope with a magnification
factor of 1:200. It was found that all samples consisted almost entirely of carbonate in the form of
shells broken down into pieces of 0.2mm to 2mm with a small amount of terrigenous particles of
medium size on the Wentworth scale (0.25-0.5mm). Notable was an apparent higher content of
quartz particles in the samples taken from Mangersta, Cliff and Dalmore, as this contrasted with the
higher shell content of the other samples. Figure 2 shows the sample sites numbered according to
size and table one gives an overview of the predominant grain sizes. The images in figure three give
samples from four of the test sites for comparison. The findings of a very high shell content in the
sediment are consistent with reports in literature, where a beach sediment shell content in the
range of 80%-95% in the north of Scotland are reported [4, 15].
Figure 2 – Sites sorted by predominant size of sediment samples
1
2
3
4
5
6
7
8
9
10
11
Site
Predominant size [mm]
Bosta (mainly shells)
0.2 – 0.5
Shawbost (mainly shells, some terrigenous particles)
0.2 – 0.6
ArdroilUig (mainly shells)
0.2 – 0.6
Reef (mainly shell fragments)
0.3 – 0.5
Hushnish (shells only)
0.4 – 0.8
Mangersta (shells and terrigenous particles)
0.4 – 0.8
Dalbeg (shells and terrigenous particles)
0.5 – 0.8
Mealasta (shells and terrigenous particles)
0.6 – 0.9
Cliff (shells and terrigenous particles)
0.6 – 1.0
Dalmore (shells and terrigenous particles)
0.6 – 1.0
Horgabost (shells only)
1.0 – 2.0
Table 1 – Sample sites sorted by size
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Figure 3 – Images of sediment from four test sites
Wave Energy Converters, Waves and Beach profiles
Arrays of wave energy converters have the potential to influence the local wave climate and
consequently affect sediment dynamics. It has recently been hypothesised that wave height
reduction in the lee of WECs, particularly nearshore, could benefit coastal protection by promoting
deposition of sediment [16]. The morphology of a coastline is closely bound up with the wave
climate, and the requirement for accurate models of the effects of WEC installations has been
identified [16]. A change in the longshore littoral transport processes can have implications further
along a coastline, as well as in the vicinity of a WEC.
Producing theoretical predictions of equilibrium beach profiles from first principles presents a
considerable challenge. The interplay of long- and cross-shore transport, the various hydrodynamic
regimes encountered between the deepwater limit and the surf zone, and the multiplicity of
different length scales, from the individual grain of sediment, through the scale of bathymetric
features, up to the overall size of the littoral cell, add to the complexity of the task [5]. The process
will also depend on the nature of the sediment itself. This will not be homogeneous, and the
composition can vary greatly over relatively small regions.
One classic treatment [17] involves deriving functional form for the beach profile from the
assumption of constant energy dissipation per unit volume in the surfzone. This produces results in
good agreement with observation, but involves free parameters and neglects the influence of the
wave climate. An adapted version of the analysis introduces some wave height dependence, but still
includes a parameter that must be derived from external data [18]. Considerable recent activity has
given rise to a number of promising new theoretical models for beach profiles, though they often
require calibration with measured, empirical or historical data, and few account explicitly for the
effects of the wave climate [19-21].
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A validated, fully predictive set of equations to link beach profile to wave climate is yet to emerge
[18]. Until measurements are available from future commercial scale wave energy farms,
researchers hoping to calculate the possible effects of arrays of WECs on the wave climate and
sediment dynamics must resort to scale modelling and numerical simulation.
Ruol et al [22] experimentally measure wave transmission indices for a class of hinged WEC and use
the CERC formula to evaluate possible consequences for longshore sediment transport. Alexandre
et al [23] used a combination of computer modelling with SWAN and experimental work to predict
how a row of frequency-dependent point absorbers would alter the local wave spectrum and wavebreaking processes. Venugopal and Smith [24] model the change in wave climate behind an array of
devices, which are treated as porous barriers, in the waters near Orkney. They use the DHI MIKE21
suite[25]: the wave parameters near the devices are obtained from the offshore climate with the
spectral wave model, and are then used as input for a local-scale Boussinesq wave model. Palha et
al [26] use the REFDIF model to calculate the change in wave height of monochromatic waves due to
various arrangements of Pelamis wave energy devices. They take mean wave heights for four
different months and model the WECs by including additional energy dissipation factors equal to the
Pelamis rated powers. Miller et al [27] use a year's worth of sea-state data, and the bathymetry of
the Cornish coast to model the alteration of the directional wave spectrum behind an array of
obstacles with various degrees of transmission, which represent WECs. Zettler-Mann [28] treats
WECs as land masses of the same size as the device and calculates the evolution of wave energy by
numerical integration over a gradually varying domain. Many of these studies are motivated at least
in part by sediment and coastal process considerations, but few include explicit treatment of these
effects.
Over the next three years, the Hebridean Marine Energy Futures project will computationally
generate a repository of high resolution wave climate data for the west coast of Lewis, which will be
validated by using several directional wave buoys and acoustic depth current profilers. Coupled with
ongoing site surveying activities, this will also yield detailed, validated quantitative numerical models
for the sediment dynamics in the area. An extended programme of wave tank experimentation will
be undertaken, and these complementary approaches should yield an improved understanding of
the potential impacts of various arrangements of wave energy farms.
The next sections include initial results from the preliminary experimental and numerical
investigations.
Wave induced sediment dynamics – experimental analysis
Experimental testing for the wave induced sediment transport was carried out, with the
experimental setup consisting of the following arrangement.
The wave tank used was a glass tank measuring 1830 x 305 x 457mm externally. This was
partitioned to provide a useful width of front section (150mm), where the testing was done, and a
back section which was closed off, but contained water to equalise the load on the partition. The
water depth was kept at around 160mm to simulate a 20m depth at the coast.
The wave-generator consisted of a crank-slider mechanism, having a horizontal rotating shaft with
hub rotor which carried an adjustment slot, to allow the choice of a range of eccentricities giving
various strokes to the paddle. The horizontal shaft was the output shaft of a spur gearbox
integrated to a 12 volt DC motor. The speed of the 12 volt motor was controlled by setting the
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voltage on a power supply unit, a TTI #PL320. The motor-gearbox unit was mounted on a fabricated
sheet metal stand, which was fastened to a SMART Optical Table, #M-ST-48-8, together with the
glass tank. The paddle assembly was mounted to the glass tank using a sheet metal clamping
baseplate. This baseplate held a UHMW linear bearing, made to accept a slider of angle section,
which guided a fabricated aluminium paddle operating in a vertical direction. The choice of rotor
eccentricity generally determined the wave height developed (although this was also speed
dependent), and the shaft speed determined the generated wave period.
A model of a WEC device was sometimes added to the test tank to assess the effect of the device on
the erosion rate of deposited sediment for specific wave conditions. The WEC device assembly
consisted of a tube of diameter 29mm, and length 143mm, ballasted for both buoyancy and inertial
mass, which was connected to a mooring base by ties.
Images were recorded using a webcam controlled by PC to record time lapse frames at intervals of
15 seconds. At suitable times during the testing, (such as before making a change to the settings, or
when it was thought equilibrium had been achieved), the sediment profile was recorded using
marker pens directly on the glass tank. Small changes and cyclic events were made obvious by doing
so.
The sand sample was taken from a Lewis beach on the west coast. The sediment particles measure
from 0.5 to 0.8mm, and consist of sea shells mainly, with stone and some magnetite. The variation
of sediment constituents showed sorting effects during the testing between the materials of
differing densities.
Figure 4 – Test Tank Arrangement (alternative WEC shown)
The wave-generator is positioned at the left hand end of the tank, so the sand sample was heaped
up into a mound at the right hand end of the tank. When the wave generator was started for the
first time, the sand mound was quickly reduced to a beach profile with a sloping upper beach,
horizontal plateau and ramp leading to deeper water. Various wave types were generated, allowed
to interact with the sediment for some time, and their effects on the sediment were noted. Tests
were repeated several times until confidence was gained in the prediction of the resulting beach.
This was done to verify if a particular wave type always interacted with sediment in a predictable
way and always gave the same final result. Often the tests were left to run for several days to
ensure stability had been reached.
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Figure 5– Beach Profile after a Deposition run showing marked stages in build-up
Figure 6 – Beach Profile during an Erosion run showing marked stages in erosion.
Figure 7 – Stable Beach Profile after a run showing marked start profile
Figure 8 – Sediment in motion near centre of image during a run
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From the current literature, seasonal differences are described [4] where in summer long swell
waves move sediment inland up beaches to build swash bars and plateaus, whereas in winter short
steep waves remove sediment from beaches moving it seaward to form longshore bars. Tests were
carried out to replicate the building of beach features with long waves and the destruction of these
summer features by generating short steeper waves typical of winter weather. Following these
beach building and beach eroding events, further testing was done to establish whether there was a
threshold wave value, where waves of a similar wavelength could be responsible for both deposition
and erosion, while acting under different environmental conditions. Different environmental
conditions which may influence the action of the threshold wave could be the presence of a WEC. A
threshold value of wave was found, and more testing was done with and without a WEC, and the
effects were noted.
Froude Scaling
The experimental test model could be scaled with three types of similarity - geometric, kinematic
and dynamic. Geometric similarity is desirable, so that the model is a True model and not a
Distorted one. Kinematic similarity will be met between the model and prototype if the ratio of the
velocities is equal and the paths of motion are geometrically similar. Dynamic similarity is needed to
model for correct forces.
Dynamic similarity, relates geometric similarity with similarity of forces, where the full size forces are
in the same ratio at model scale. Forces acting can be of several types: inertia, gravity, pressure,
viscous, elastic, surface tension.
In situations where there is a free water surface, the gravity, inertia and pressure forces are the
significant controlling forces. For dynamic similarity, the magnitude ratio of the inertia to the gravity
forces must be the same.
The Froude number describes the ratio between the inertia and gravity forces. The inertia and
gravity forces Fi and Fg are proportionally related to the expressions (ρ.v².l²) and (ρ.g.l³) respectively,
where ρ is density, v is fluid velocity and l describes the model length.
The Froude number is given by Fn = v(g.L)-0.5
Gravity forces are scaled correctly when the Froude number is equal at both model and full scale.
With a scaling factor (or multiplication factor) of x, the full size arrangement is x times the model.
Linear dimensions are x times the model, mass and force are x³ times the ratio of the densities of the
full size and model, pressure is x times the ratio of the densities of the full size and model,
acceleration is equal between model and full size, and the full size time period is sqrt(x) times the
model time period. The full size velocity is also the sqrt(x) times the model velocity.
Table 2 shows the relation between test tank waves to a water depth of 20m using Froude similarity.
Model
Full scale
Wavelength
1.325m
165m
Period Amplitude
Wavelength Period
1.157s
0.017m
0.8m
0.778m
12.9s
2.1m
100m
8.7s
Table 2 –Waves and Froude Scaling for 20m depth
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Amplitude
0.017m
2.1m
The most significant force tending to move sediment is that force due to the impact of the orbital
water motion imparted by the moving wave. As in the case of full size velocity, this force will be
scaled in the ratio of the sqrt(x) times the model velocity, as noted above. The wave power density
of the full size wave scales in the ratio x2.5 times that of the model waves in the test tank. The full
size sediment particle size will be scaled in the ratio of x times the model sediment. This ranged
from 0.5mm to 0.8mm which would give a full size particle of 62mm to 100mm. The mass of the full
size particle will be x³ times that of the model particle mass.
The grain size of our sand sample was exactly the size of local beach sand, so the geometric scaling
cannot be applied to the sediment. For these initial trials no effort was made to correlate our test
sediment with the full size sediment, but the qualitative relationship between wavelength and
deposition / erosion was explored.
While the scaling is not completely exact between full size and model, the behaviour of the sediment
in the test tank will give an indication of the general trend of different waves, but the results cannot
be used to predict accurately in detail the behaviour of the full size events. This suggests there is
scope for future work to investigate what changes can be made in testing and analysis to make the
testing more relevant to the full size events.
The WEC used in the tank testing was equivalent to a cylinder of diameter 3.6m, which is similar to
the sizes of some WECs. One problem encountered was the difficulty of accurately measuring the
wave amplitude downwave of the WEC. The method of wave amplitude measurement was to blank
off the wave and progressively uncover it until the peak, or the trough, became visible. Both
positions were marked individually, and the amplitude was measured directly from them.
The images of the test tank and sediment were processed for contrast and the beach profile was
picked manually in GIMP with at least 450 readings over the length of the image. The x-coordinate
was taken at equal intervals, and was recorded with the corresponding y-coordinate. These
coordinates were entered into a MS Excel spreadsheet as a pair of values and a graph was produced
to represent the beach profile.
For the results shown here, a wave of 17mm amplitude was used in all cases. The wave period and
wavelength were varied by adjusting the applied voltage to the motor, and the eccentricity at the
rotor. Results are shown below for various waves and conditions. In summary, these are:A – Well developed beach profile after deposition
B – Eroded beach profile
C – Rebuilt beach after erosion followed by deposition
D – Deposition with WEC
E – Erosion without WEC
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Wavelength = 1.325m
Period
= 1.157s
Amplitude = 17mm
Well Developed Beach Profile A
Figure 9 – Well developed beach profile, wavelength = 1.325m, period = 1.157s
Wavelength = 0.800m
Period
= 0.778s
Amplitude = 17mm
Eroded Beach Profile B
Figure 10 – Eroded beach profile, wavelength = 0.800m, period= 0.778s
Wavelengths = 1.325m & 0.800m
Period s
= 1.157s & 0.778s
Amplitudes = 17mm
Beach Profiles A and B
Figure 11 – This image shows the previous two results for direct comparison.
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Wavelength = 1.325m
Period
= 1.157s
Amplitude = 17mm
Rebuilt Beach Profile C
Figure 12 – Rebuilt beach after erosion followed by deposition
Wavelength = 0.800m
Period
= 0.778s
Amplitude = 17mm
Deposition with WEC Beach Profile D
Figure 13 – Deposition with WEC
Wavelength = 0.800m
Period
= 0.778s
Amplitude = 17mm
Erosion without WEC Beach Profile E
Figure 14 – Erosion without WEC
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Wavelength = 0.800m
Period
= 0.778s
Amplitude = 17mm
Upper Beach Profiles with and without WEC
Delta 4x
Depositing
Eroding
Figure 15 – This plot shows the previous two results (D and E) for direct comparison.
Beach Profile A (well developed beach) shows the result of running the wave-generator at a beach
building setting to produce a longer wave, which was discovered by previous testing. Wave action
moves sediment to the top areas of the upper beach to form a ridge. Eventually, equilibrium is
reached, the sediment transfer stops, the upper beach is at maximum thickness over its length and
tends to form a long ramp.
Beach Profile B (eroded beach) shows the effect of a shorter wave acting on the fully developed
beach. Immediately material is removed from the upper beach and a bar begins to form. Sediment
transfer continues with material moved to the deeper water. Again, the sediment transfer stops
when equilibrium is reached. Some small scale re-cycling may occur in areas of the surf zone when
the profile alternates between two closely related positions.
Beach Profiles A and B compared (well developed beach and eroded beach), shows a large volume of
sediment is removed from the highest part of the developed beach. A smaller quantity of sediment
is removed in the surf zone and all this material is deposited in deeper water forming a bar.
Beach Profile C (rebuilt beach) shows the result of running the wave-generator at the previous beach
building setting A to produce a longer wave. This image represents the effect of returning to a beach
building setting, where an eroded beach is restored exactly to the previous well developed profile.
This was noted many times and the exercise was repeated over a range of settings which resulted in
beaches being restored. This also gave confidence to the idea of predicting the effects of waves on
sediment transport.
Beach Profile D (deposition with WEC) shows the beach profile achieved when running the wavegenerator at a setting close to the threshold value where beach building changes to beach erosion,
with a WEC model in front of the beach.
Beach Profile E (erosion without WEC) shows the beach profile produced when running the wavegenerator at the previous setting in D, without a WEC model in front of the beach. The images look
very similar but differences can be seen in the comparison image which has been cropped to show
the upper beaches only.
Beach Profiles D and E compared (deposition and erosion with and without WEC) in figure 15 shows
the effect on the upper beach. The comparison image has been cropped to show the upper beaches
only. An extra data plot is included to represent the profile difference which has been given a scale
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increase of 4x, to make the result more visible in the area plot. This area plot gives an impression of
the sediment volumes removed from the beach and volumes deposited in deeper water.
Interim Conclusion
From the experimental testing, it has been found that:
1) Wave types are predictable in their effect on sediment transport, erosion and deposition
2) The deposition and erosion processes are predictable in a precise way for a given wave, so
that beach profiles can be reformed with accuracy
3) A wavelength threshold value exists, where a wave acting on sediment can switch from
erosion to deposition, and vice versa, given a small change in wavelength
4) Also, an eroding wave acting on sediment can change to a depositing wave with the addition
of a model WEC
5) WECs can influence waves and the environment
Simulation of Sediment Processes
Figure 16 – Area west of Uist modelled. The larger area was the domain for the MIKE 21 spectral
wave (SW) model. Devices are positioned along the -7.5° line. The area in the red rectangle was
then modelled in the combined SW, hydrodynamic and sediment transport package, in the presence
and absence of WECs.
Page 15 of 22
A qualitative estimation of the possible effects of a group of nearshore wave energy converters on
the coastal environment was obtained using the DHI MIKE 21’s suite of wave modelling tools [25].
The devices were assumed to be positioned in a straight line, approximately parallel to the coast. A
combined hydrodynamic (HD), spectral wave (SW) and non-cohesive sediment transport (ST) model
was run, for a year's worth of wave data, for the region between the devices and the coastline
A region west of Uist, shown in Figure 16, was selected for this demonstration. The high energy
waves predominantly approach from the west, so that the bays can be considered as individual
units, and cross-shore dominates longshore as the primary sediment transport mechanism [13]. The
long sandy coastlines are susceptible to erosion. Following the 2005 storm, a directional wave buoy
was deployed in approximately the mid-point of the westerly boundary of the area, and has so far
provided almost two years of continuous wave data [29]. This takes the form of half-hourly values
for significant wave height, peak wave period, and wave direction and standard deviations. The data
was converted to 12 monthly averages. For each month, the MIKE 21 spectral wave model was run
in quasi-stationary mode, using the averaged buoy data for the westerly boundary condition. This
yielded wave parameters for 24 equidistant points along the line from 57.2°N 007.5°W to 57.4°N
007.5°W (being the westerly boundary of the smaller nearshore region of interest) for each of the 12
months under consideration.
The MIKE21 combined HD, SW and ST model [25] was then set to run for a year in the smaller,
nearshore region (22.25km x 6km). The HD component provides solutions to the Reynolds-averaged
Navier-Stokes equations, while the SW part numerically solves the wave action conservation
equation in the spectral domain for gradually varying bathymetries, incorporating processes such as
whitecapping and wave-wave interactions through source terms. The ST module uses DHI's
deterministic intra-wave sediment transport model STP to calculate the movement of non-cohesive
sediment under combined wave and current forcing. The modules run simultaneously: waveinduced changes in the bed level are fed back to alter the hydrodynamics, and the refraction and
shoaling behaviour of the waves. The bathymetry at the start of the modelling period is shown in
Figure 17.
For the baseline case, without wave devices, the monthly wave data along the westerly boundary,
produced by the spectral wave model of the larger area, was used to drive the model.
The analysis was then repeated to simulate a row of WECs positioned along the 7.5°W boundary
line, at the manufacturer’s suggested minimum spacing. A nearshore WEC developer provided
indicative power ratings for a range of wave periods and heights. The power outputs were used to
estimate the change in wave height at each data point, which was used to drive the combined
model, as described in the next sections.
Page 16 of 22
Figure 17 – Initial bathymetry shoreward of the devices. The axes are degrees longitude and latitude.
Change in wave climate behind the devices
The large scale spectral wave model produced, for each month, wave heights and energy-averaged
wave periods, as well as water depths, at 24 points along the western boundary of the smaller
sediment model. At each point, the wave number was obtained from the period and water
depth
by numerically solving the dispersion relation
The group velocity
can be written
[
where
.
]
The energy flux per unit wavefront length is related to the significant wave height Hs by [30]
, where
. If the power removed by the devices per metre
wavefront is , then the reduced significant wave height
can thus be related to the original
wave height
with
[
]
Page 17 of 22
The rated device power for various regimes being the only information available, the spectral
parameters, apart from , were left unchanged. This approximate treatment also assumed the
amount of power removed from the wave to be equal to the rated electrical power output. This is
likely to underestimate the change in wave height directly behind the devices. The adoption of the
densest advisable arrangement of WECs is intended to go some way towards compensating for this.
The analysis also ignores scattering, reflection and diffraction from the devices, which are treated as
a homogeneous line absorber, rather than discrete entities.
Figure 18 – The shape of the seabed after a year, in the absence (left) and presence (right hand side)
of wave energy converters. We use the same colour scale as Figure 17 for the initial bathymetry.
Numerical Model Outputs
The shape of the seabed after a year’s wave action is shown in Figure 18 above. Overall, the
presence of WECs appears to moderate any morphology change caused by wave action, so that the
plot on the right of the figure (with WECs) is closer to the original bathymetry than the plot on the
left. Between about 57.32°N and 57.34°N, sediment is moved away from the shoreline by the wave
action: this behaviour is more moderate when WECs are present. This can be illustrated by the bed
level plot for cross-section at 57.328°N, shown in Figure 19. Without the WECs, the bar is seen to
move offshore, while the bed level in the presence of WECs barely changes from its initial state. The
offshore movement of sediment under wave action is also seen below the outcrop of land in Figure
Page 18 of 22
18, at about 57.24°N. In the absence of WECs, a darker blue region shows loss of sediment
nearshore, where the increased size of the green area indicates that it is being deposited further
offshore. This can be seen more clearly in Figure 20, for the 57.239°N cross-section. Again, the
movement offshore is barely present when the WECs reduce the wave height. Future research will
yield fully validated and calibrated results to quantify the behaviour indicated by this preliminary
demonstration. An important refinement will incorporate a description, based on field
measurements, of the heterogeneous composition of the sediment. For example, the offshore bar
regions are thought to contain a higher concentration of shingle than currently modelled [31].
Figure 19 – Bed level along a line of 57.328°N. The shoreline is at approximately 007.4°W longitude.
Figure 20 – Bed levels along a line of 57.328°N. The shoreline is at approximately 007.4°W longitude.
Page 19 of 22
Conclusion
Samples of sediment that were collected below the high tide mark from a number of beaches on
Lewis and Harris have shown differences in grain sizes and composition and this indicates the
existence of a natural grading process within the sediment transportation regime along the western
shoreline of the Outer Hebrides. This finding also indicates the existence of individual coastal cells
without interaction, as the sediment from certain beaches appears not to be mixed with that from
neighbouring beaches. All samples taken have shown a very high shell content with very little or no
terrigenous components. More intense observations of sediment properties are required to validate
these findings.
Experiments in the lab facilities of Lews Castle College were carried out on a microscale in a small
tank. Although the experiments were carried out using Froude scaling, not considering sediment
size, initial results have shown good similarity with reports from literature. This is particularly valid
for the observed formation of a longshore bar as a result of beach erosion caused by steep wind
waves, and for the deposition of sediment at the beach during swell waves of a longer period. By
working with a wave regime close to the threshold setting between deposition and erosion, it was
observed that the introduction of a model wave energy converter into the system can change the
dynamical processes from erosion to deposition and this indicates that farms of WECs might be able
to act as coastal protection devices.
The effects of WECs on longshore bar dynamics were also observed in the MIKE21 simulation.
Waves approaching normal to the shoreline, over the course of a year, were seen to cause a nascent
offshore bar to increase in size. The power matrix of a nearshore WEC was used to estimate the
reduction in energy flux and hence wave height when a line of devices was placed parallel to the
shore. Erosion and bar formation appeared less pronounced following energy absorption by the
WECs.
With an increased number of wave data acquisition devices and surveying activities at the Atlantic
coast of the Western Isles under the Hebridean Marine Energy Futures project, these initial findings
will be explored further and calibrated against real world data before and following the imminent
installation of farms of wave energy converters by multiple developers in the coming years.
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