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The Simulation of Nearshore Wave Energy
Converters and their Associated Impacts around the
Outer Hebrides
Charles E. Greenwood#1, David Christie#2, Vengatesan Venugopal*3
#Lews Castle College, University of the Highlands and Islands
Stornoway, Isle of Lewis, Scotland
1charles.greenwood@uhi.ac.uk
2david.christie@uhi.ac.uk
*University of Edinburgh
School of Engineering, The University of Edinburgh, Edinburgh, Scotland
3v.venugopal@ed.ac.uk
Abstract— The results of a numerical wave modelling study
carried out to assess the nearshore effects of wave energy
extraction on the local wave climate by an array of hypothetical
wave energy converters (WECs) are presented in this paper. This
study uses the Danish Hydraulic Institute’s (DHI) MIKE 21
Spectral Wave model to identify and test three different
techniques of simulating hypothetical WECs on a regional scale.
The results suggest the more complex approach of simulating
absorption using directional and frequency absorption spectra in
addition to the effects of wave reflections yields a more realistic
simulation. This technique was further applied to a potential
wave energy deployment site consisting of an array of 30 WEC
devices identified by the Crown Estate in the Outer Hebrides in
the United Kingdom. The boundary input used seasonal
averaged data to represent winter, summer and a complete
year’s wave spectra. The results suggest there is an average
shoreline reduction in wave power behind the array of 5% with a
peak value of 9.5%. The inclusion of wave reflection in to the
model leads to a larger average percentage change in wave power
of 7.5% 300m from the devices. While the results of this study
also provide an insight into the distribution of wave energy
around a nearshore array, this study focuses on developing
advanced technique for the simulation of WECs.
Keywords— Wave Energy, Mike 21 Spectral Wave model, Wave
farm, Wave modelling, Nearshore impacts.
I. INTRODUCTION
As global energy demand increases renewable energy
offers a clean solution to help mitigate anthropogenic climate
change. In recent years alternative technologies have been
explored with the intention of up scaling them to help provide
a broad energy mix. As these technologies evolve,
governmental support and legislation is being implemented to
ensure the generation of clean energy. The Scottish
government has led the way by setting a target of producing
100% of its electrical energy demand by 2020 from clean
renewable sources [1]. However international legislation
states that any large scale developments of this kind require an
Environmental Impact Assessment (EIA). This assessment
reviews the possible impacts a proposed development may
have on the existing environment. This process has been
applied to existing renewable energy projects highlighting the
potential environmental implications of the installation,
operational and decommissioning stages of a project [2, 3].
With ocean waves containing vast amounts of energy a niche
was created for developing devices to withstand and extract
this energy in a cost efficient manner. With the imminent
transition from single Wave Energy Converter (WEC)
deployments to large arrays, the potential environmental
effects caused by alterations in the wave climate are unknown.
As no large scale arrays have been deployed the quantification
of the change in wave climate has been conducted using
laboratory experiments and computational models.
The west coast of the Isle of Lewis (Outer Hebrides) has
been highlighted as an area of high wave resource. This has
lead to the interest of several device developers. Aquamarine
Power have successfully gained two lease sites on Lewis with
the potential of extracting up to 40MW [4], Pelamis Wave
Power have acquired a lease allowing up to 10MW
development [5] and Voith Hydro Wavegen were granted a
lease to construct a 30MW breakwater. However the
development proposed by Voith Hydro Wavegen has been
suspended [6]. This would have allowed the cumulative
extraction of up to 80MW along the north-west coast of Lewis.
The original planned development areas can be seen in Fig. 1.
The large existing resource provides a lucrative opportunity
for any successful device developer. With the interest of
several developers, the spatial distribution of the resources
and the resultant wave-device interactions require an in-depth
study, the results of which are of great importance to current
and future research, both on Lewis and other potential WEC
array sites.
This study uses Mike 21 SW (Spectral Wave) model
produced by DHI (Danish Hydraulic Institute) [7] to simulate
the transformation of waves in the nearshore region. Existing
wave resource maps and climate data for the area are
inadequate for detailed deployment planning, consisting of
national maps with low resolution only [8, 9]. These, however,
show the highest wave resource of the UK offshore off the
Outer Hebrides. While these maps show a general distribution
of wave energy, their low resolution and lack of addition
information makes them unsuitable for assessing an area for a
WEC development.
Over recent years the planned proposals for large scale
arrays and the legal obligation to perform EIA has lead to
several detailed studies predicting wave-array interactions.
One such study uses a SWAN based model to simulate the
shoreline change as a result of the installation of a wave farm
[10]. This model was driven by frequency spectra generated
from a JONSWAP spectrum. The WEC array was treated as a
single permeable block and the simulation repeated for several
transmission coefficients. The results show a reduction in the
downstream wave height dependant on the transmission
coefficient, with a larger energy transmission showing a
smaller change in the shoreline wave height.
Venugopal and Smith [11] shows the wave–array
interactions and the effects of a varying array layout using
DHI Mike 21 SW to model the existing wave resource for
Orkney Islands before applying the data to Mike 21 BW
(Boussinesq Wave) model to simulate the presence of WEC
arrays. The arrays are considered as porous structures with
known wave energy absorption and the simulation was run for
various porosities and layouts. This study shows both the up
and downstream wave-device interactions, where wave device
reflections can be seen. The results demonstrate that spatial
distribution in wave height depends on array layout, and
confirm that the change in wave height reduces as porosity is
increased and more energy is transmitted.
The previous studies [10, 11] both show a general method
of representing WEC arrays as large blocks with frequency
independent energy absorptions. More recent research looking
at an array of horizontal overtopping devices uses scaled
prototype models in a wave tank to obtain a device energy
transmission coefficient, which is then applied within a
SWAN based model [12]. The model was driven using
locational wave climate parameters after a JONSWAP
spectrum was applied. The transmission coefficients were then
applied to each individual device. A revised version of [10]
applies a PTF (Power Transfer Function) based on a damped
linear oscillator [13] following previous research from [14].
The PTF is a basic representation of a frequency specific
absorption that removes a given amount of energy depending
on the device characteristics based on frequency absorption
widths. Additional changes see the break-up of the solid array
structure into smaller sub-sections. The results of [12, 13]
provide the most up to date method of simulating device
arrays and show the downstream spatial distribution of the
change in resource. However both studies neglect the change
in resource from reflective effects and device directionality.
Additional work simulating downstream wake effects of
multiple Wave Dragon devices demonstrates the use of the
mild slope equations for simulation of large devices [14].
While [14] focuses on sea state and array lay out the purpose
of this study demonstrates new methods of simulating devices
within existing commercially used software.
The present study uses Mike 21 SW as it has been shown
that the software provides a good application for modelling
wave propagation in the nearshore region. Mike 21 SW
simulates the build-up and transformation of wind and swell
waves in the offshore and nearshore environments. This study
applies the fully spectral formulation, based on the wave
action conservation equation, to simulate the propagation of
directional frequency spectra. This allows the model to
account for bathymetric refraction and shoaling, wave induced
currents, and tidal variations, while wind forcing, nonlinear
wave interactions, white capping, bottom friction and depth
induced breaking are included as source terms. Diffraction
within the model uses a phase-decoupled refraction diffraction
approximation; this is based on the mild slope formulation for
diffraction and refraction. When a time varying quasi-
stationary model is considered the inclusion of diffraction may
prevent time step convergence. To prevent this, the software
allows the diffraction term to be either smoothed or modelled
using a predefined value irrespective of the incident wave
climate. By using a cell-centred finite–volume technique the
model applies an unstructured mesh grid to propagate the
wave action through the model domain using phase averaged
equations. Further details on the SW model can be found in
the user manual [7]. The application the Mike 21 SW software
to simulate the effects of operational WECs are assessed.
These results are then applied to bathymetry from the west
coast of Lewis, where the effects of a large nearshore WEC
array will be presented.
II. MODELLING HYPOTHETICAL WECS
A. Device type and Mike 21 SW
With the large scale proposed developments for the north-
west coast of Lewis this study focuses on a large scale
Fig. 1 WEC development sites (West to East: Pelamis Wave Power,
Aquamarine Power 1, Voith Hydro Wavegen, and Aquamarine Power 2) and
wave data sensors locations.
nearshore wave surge oscillator farm. This array is located in
the proposed development area for Aquamarine Power [16]
where Hebridean Marine Energy Futures has deployed an
Acoustic Wave and Current profiler (AWAC). The notional
devices are located in the very nearshore waters that follow
the 10 m depth contour. As an array of this scale does not
currently exist, the changes to the surrounding wave climate
are simulated in MIKE 21 SW. Also as the SW model has no
specific facility for simulating WECs, this study explores
three possible methods of removing energy from the model
domain as described below.
Technique -1 WEC as a Source Term: This method uses a
spectral wave based tool that applies a source term to a
location to simulate the presence of a structure. The source
term approach removes energy using a decay term. For
energy density E(σ, θ), group wave speed cg, mesh element
area A and reflection coefficient c, the source term, s is given
by
(1)
The size and shape of the structure can be altered to suit a
specific device and this study used the default circular pier
with a diameter of 20m.
Technique -2 WEC as an Artificial Island: This method of
applying a WEC in Mike 21 SW employs a user defined
polygon structure. The location, size and shape of the
structure are included when the mesh is created. As this study
is focusing on an array of nearshore wave surge oscillators
dimensions of the structure are 20m x 3m. Polygon structures
within Mike 21 SW are interpreted as islands and therefore
allow a 0% energy transmission.
Technique -3 WEC as a Reactive Polygon: This method is
similar to the artificial island polygon but the up- and
downstream device boundaries conditions are modified to
produce driving boundaries, where a given wave spectrum
maybe emitted. The absorbed spectra are transformed
according to the directional frequency relation and reemitted
downstream, while the upstream boundary comprises device
reflections. The reactive polygons structures used within this
study have device dimensions of 20m x 3m.
B. Directional Absorption
When the wave-device interactions for the Reactive
Polygon boundaries are considered the energy propagation up
and downstream can be effectively controlled. As most wave
surge oscillators are directional, only a certain proportion of
the directional wave spectra can be absorbed. A formula for
the directional absorption coefficient was outlined in [17] and
is shown as
(2)
where (θdevice - θwave) is the angle between the device and the
incident wave direction. This formula produces a curve with a
maximum of 1 for the device when device angle and wave
direction are equal. As the incident wave angle diverges from
the device angle the absorption coefficient is reduced. This
assumption assumes 80% of the wave energy travelling at 90°
to the device is absorbed. As this is not the case for a wave
surge oscillator this formulation was modified to
(3)
where n is the absorption width and ℝ implies taking the real
part of the square root (thus ensuring that no energy is
absorbed above 90°). If this equation is plotted the effects of
n can be seen (shown in Fig. 2). As n increases the curve
becomes narrower but the peak remains at 1. This provides a
uni-lateral directional abortion coefficient, where energy is
only absorbed when it propagates one direction across the
device. This expression shows that as a device gets more
directionally sensitive the amount of total absorbed energy
reduces as the area under the graph reduces.
Fig. 2 Modified directional absorption coefficient
When the modified directional absorption is applied to the
incident wave spectra at the device location the energy
propagating within ±90° will be absorbed dependant on the
device relative direction. This study will use an n value of 2 as
it shows a relatively large absorption width associated with a
well designed device.
C. Frequency Absorption
As modern devices are designed to actively resonate with their
local wave climate the notion of extracting the same
proportion of energy from all frequencies produces an
unrealistic Power Transfer Function (PTF). The PTF of
devices varies considerably and is dependent on the device
and incident wave climate. Currently the energy absorption of
a device relative to the incident wave spectra is unavailable.
This has led to the development of an approximation that uses
a Gaussian curve to simulate energy absorption based on
adjustable values from [15] and more recently applied in [13].
This assumption is used to demonstrate the application of PTF
and can be shown as
(4)
Here, fc is the peak energy frequency, α is an adjustable
absorption coefficient and σ is the curve bandwidth. For this
Fig. 3 PTF with varying σ values
purpose α is set to 40 as this produces an absorption
coefficient of 1 when the width is set to 0.01. Fig. 3 shows
how the level of distribution and peak magnitude are altered
as σ is changed. As this is a Gaussian formula the amount of
energy absorbed remains constant, allowing similar power
rated devices to extract different amount of energy according
to device design. This study uses a σ value of 0.01 as this
represents a well tuned device with maximum absorption and
this provides a realistic high absorption rate.
D. Directional Frequency Absorption
To simulate the device energy absorption from a directional
frequency spectrum both the direction and frequency
absorption coefficients should be applied. The absorption
spectra (Sabs) can be shown as
(5)
where S is the directional frequency spectrum at the WEC
location. The absorption spectra consists of the transmitted
wave energy as the directional and frequency dependent
energies have been removed.
E. Device Reflection
As waves propagate across a device the energy is absorbed
from the incident wave spectra. However, a proportion of the
remaining energy will also be reflected by the device. The
amount of reflected energy depends on multiple factors; this
study uses a simplification based on work by [18]. This briefly
states that a well tuned wave surge oscillator in a 2-directional
field shows an approximate 50% reduction of the incident
wave energy, 25% is transmitted in the direction of wave
propagation and 25% is reflected. This suggests that
approximately 50% is absorbed then 50% of the remaining
absorption spectra should be reflected from the upstream
device boundary. When the incident absorbed and reflected
wave energy are shown in the frequency distribution for an
example sea state, the magnitude of the reflected and absorbed
wave spectra can be seen (see Fig. 4).
F. Theoretical Single Device Modelling
To determine the best possible method for modelling WEC
performance in Mike 21 SW each technique was tested using
a theoretical domain. The model domain extends from a 100
m depth with a mesh resolution of approximately 30 m2 that
reduces around the devices to 6 m2. The simulation was run
using a JONSWAP wave spectrum with a peak enhancement
factor of (γ) equal to 3.3, resulting in the production of wave
parameters Hm0 = 2 m, Tp = 10 seconds, mean wave direction=
270° and a directional standard deviation = 5°.
G. Theoretical Single Device
Fig. 5 shows the spatial distribution of wave power for each
hypothetical WEC. The Source Term modelling technique
depicted in (a) shows a wave shadow with a small reduction in
wave power behind the WEC device that is extended far
downstream. The Artificial Island structure modelling labelled
as (b) shows a large reduction in wave power behind the
hypothetical device with no alteration to upstream wave field.
The Reactive Polygon structure technique (c) shows a similar
downstream wave shadow however there is a significant
reduction of the absorbed wave energy resulting in a smaller
reduction in wave power downstream of the device. The
upstream wave field in (c) shows a significant increase in
power by reflected waves that reduces as the distance
upstream of the device increases.
To better quantify the change in the spatial wave power
distribution as a result of varying device modelling techniques
several transects are reviewed. In Fig. 6 a device
perpendicular transect is considered, that extends from 150m
upstream of the device to 750m downstream. The Source
Fig. 4 Wave-device interactions and the frequency energy distribution of an
example sea state.
Fig. 6 Change in wave power along the perpendicular transect where y =
500 for each method of modelling a device presented in Fig.5.
Term technique shows a small peak reduction in wave energy
of 2 kW/m a few metres leeward of the device. As the
distance increases downstream the wave power shows a small
increase with a slow regeneration rate. The Artificial Island
technique shows a large peak reduction in wave power of over
14 kW/m leeward of the device. As the distance downstream
increases the change in wave power is reduced. The rate of
regeneration shows an inverse exponential relationship that
becomes less than that of the Source Term method at 450m
downstream of the device. The Reactive Polygon technique
shows an initial wave power reduction of approximately 5.5
kW/m a few metres behind the device with a similar inverse
exponential rate of regeneration as the downstream distance
increases. The rate of wave power regeneration of the
Reactive Polygon method is almost equal to the incident wave
energy at 700m behind the device. The upstream wave
interactions show a slight reduction in wave power for the
Source Term and the Artificial Island methods. The Reactive
Polygon method shows a small increase of 2 kW/m in front of
the device that reduces as the distance from the device
increases.
When the cross device wave power distribution is plotted at
100m, 300m and 600m behind each device then the evolution
of the propagation of the change in wave power can be seen.
Fig. 7 shows the wave absorption behind the device where the
device is located in the centre of the plot at 500m. The
transects were taken 100m, 300m and 600m behind the device,
and the results show as the distance increases downstream the
change in wave power is reduced. The 100m transect shows
the Artificial Island method having the maximum absorption
of 3.5 kW/m, the Reactive Polygon and the Source Term
methods shows a significantly smaller reduction of 2kW/m.
For the closest transect all experimental techniques show a
narrow absorption bandwidth. With increasing distance
downstream, the magnitude of the change in power decreases.
600m behind the device the Artificial Island and the Reactive
Polygon methods show a small reduction in wave power when
compared to the incident wave power. The Source Term
method shows a small reduction as the distance increases from
100m to 600m, this results in the eventual overtaking of the
Source Term method by the Artificial Island. Analysis of the
spread of the absorption bandwidth shows that the spread
increases for the Artificial Island and the Reactive Polygon
devices as distance increases. For the Source Term device
there is little alteration from the 100m to the 600m transect.
Only the Reactive Polygon device shows upstream wave-
Fig. 5 Wave-device interaction for (a) Technique-1 as Source Term, (b) Technique-2 as Artificial Island (c) Technique-3 as Reactive Polygon structure for the
reference sea state in UTM coordinates.
Fig. 7 Change in downstream wave power for device parallel transect downstream of a single device where (left) x = 300m (middle) x = 500m and (right) x =
700m behind the device. Corresponding to 100m, 300m and 500m behind the device.
x [m]
y [m]
Fig. 8 Change in wave power from a device parallel transect across the y-
axis.
Fig. 9 Wave power distribution around multiple Reactive Polygon devices
for the reference sea state.
device interactions. When a device parallel transect is taken
50m upstream of the device the change in wave power from
reflective processes can be seen in Fig. 8. The Reactive
Polygon device shows an increase in wave power of 1kW/m,
whereas the other method of simulating devices shows no
alteration in the upstream wave power.
When the downstream wave shadow transects of each
hypothetical device are compared with existing literature, the
profile shape of the parallel transect of the Artificial Island
and Reactive Polygon devices show similarities to that of the
work from [12]. However as the diffraction smoothing was
not calibrated this comparison is somewhat limited. This may
result in the propagation of the wave shadow that only
provides an insight into the reduction of wave power behind a
device and may not provide realistic solution. As the proposed
WEC array is located nearshore, the observed large rate of
diffraction shown in this study becomes less significant as the
distance to the shore is limited.
The energy transmission coefficient was calculated for each
absorption technique. The results show a similar pattern to the
wave power transects where techniques 1, 2 and 3 have an
energy transmission coefficient of 0.88, 0.0 and 0.50
respectively. This indicates that immediately behind the
device the Source Term allows the majority of the wave
energy to pass, the Artificial Island allows no energy to
propagate across the device and the Reactive Polygon allows
half the energy to pass though a device. While techniques 1
and 2 do not account for wave device reflections the Reactive
polygon technique has a reflective coefficient of 10.60%. For
the purpose of this study the energy transmission coefficient
its self is less of a lesser significance as the value of the
coefficient is dependent on the incident wave directional
standard deviation and the directional frequency absorption
parameters applied to the Reactive Polygon.
The single device interactions show that while the Source
Term technique is quick to apply within the SW model,
further application of the structure is limited due to the limited
control over energy transmission. The Artificial Island
technique provides a representation of a solid structure with
100% wave power absorption. The shape of the structure can
be varied but the inability to select absorption below 100% is
a severe limitation. The Reactive Polygon technique allows
the use of a more realistic energy transmission where wave
absorption is dependent on the incident direction frequency
spectra. In addition the upstream boundary of the device
allows the propagation of a reflected wave that is dependent
on the device absorption. The adaptability of the Reactive
Polygon method provides the most realistic device simulation
for modelling the potential impacts of an array in this study.
The following section will briefly review the effects of
multiple Reactive Polygon structures in close proximity in a
theoretical domain.
H. Theoretical Array Modelling
For a multiple device test domain, extra polygon structures
were added to the north and south of the previous single
device mesh. In total, three devices were simulated, allowing
for downstream wake interaction without incurring additional
complexities. This simulation uses identical model parameters
as in the single device tests with the same reference sea state.
Fig. 9 shows the spatial wave-device interaction for 3
hypothetical devices. The results show a large downstream
reduction in waver power behind each device. As the
downstream distance increases the individual effects of each
Fig.10 Change in wave power along a device perpendicular transect that
bisects the central WEC and spanning the x-axis.
Fig. 11 Change in wave power in lee of the device array plotted in
distance across the y axis.
Fig. 12 Upstream change in wave power for a series of transects on the y-
axis.
device lessen and merge into a general reduction in wave
power. The upstream results show a similar pattern, where
individual device reflections propagate and decay into a
general increase in wave power as the distance increases.
When the change in wave power is considered as device
parallel transect for the central device in the array, Fig. 10
shows the downstream wave climate with a greater reduction
in wave power. The rate of wave power regeneration shows a
significant change approximately 40 m behind the device. The
upstream wave climate shows an increase in wave power that
diminishes as the distance upstream increases. The maximum
increase and decrease in the observed wave power for the
multiple device test shows a larger reduction than experienced
for a single Reactive Polygon WEC. This indicates the
presence of cumulative device effects even at close
proximities to the individual devices. When the device
perpendicular transects are considered for 20m, 40m , 60m,
100m, 300m, 600m behind the array the evolution of the
absorbed wave is shown in Fig. 11. The 20m transect shows 3
clear peak reductions at 440m, 500m and 560m, indicating the
presence of the individual devices. As the distance behind the
device increases the definition of these peaks are reduced. At
100m downstream there is little sign of individual devices. As
the distance increases further, the flat troughed profile
broadens resulting in a curved profile with the peak absorption
located at the centre of the array. The upstream absorption
shows a similar profile for the near device transects. When the
20m upstream transect is plotted (see Fig. 12), the individual
device reflections can be seen. As the distance increases, the
50m transect shows a reduction in the magnitude of increased
wave power with less defined peaks for the individual device
reflections. At 100m behind the device the reduction in wave
power is less severe. The individual device reflections have
reduced and merged into a single peak with the largest
increase in wave power at the centre of the devices. The
results of the theoretical model show a significant increase in
the change in wave power around the devices when compared
to the individual device results, where the highest change can
be seen towards the centre of the array. The larger change in
wave power observed in the array test will result in a greater
propagation distance of wave-device interactions. This gives a
larger wave shadow downstream and a larger reflective effect
upstream. By including individual devices the downstream
device interactions can be monitored as distance from the
devices increases. The results show that the individual device
reductions in wave power can be measured up to 300m behind
the device. The upstream results show a smaller absolute
change in wave power, where the observed individual device
reflections do not exceed 100m upstream of the array. This
suggests that when modelling the long distance propagation of
the wave-array interactions, blocks of WECs may be used.
However as the propagation of the wave shadow depends on
the incident wave directional spreading, the distances shown
within the theoretical tests will vary as the incident wave field
changes. As this study considers effects of nearshore WEC
arrays, the short distance from device to shoreline will require
the use of individual devices to be included within the model.
III. APPLICATION TO WEC ARRAY
A. Model Setup
The method shown to simulate hypothetical devices was
applied to a simulation containing bathymetry and wave data
from the west coast of Lewis. The domain construction used
multiple sources of bathymetry data with a varying resolution.
For the offshore regions the coarse 30 arc second GEBCO 08
data was used. For large proportions of the nearshore and
intermediate water depths the domain was covered by Marine
Scotland bathymetry data, the resolution of which was
reduced for this study to 20m2. For shallow water regions near
to the proposed WEC array data provided by Aquamarine
Power provides an extremely high resolution data, however
this data was also reduced to a 20m2 resolution for
computation requirements. The combined data was used to
create two meshes. The first was a simple mesh with no WEC
devices. The second mesh was based on the first mesh with 30
Reactive Polygon structures positioned at the south end of the
Aquamarine Power 2 site with a reduction in mesh element
size surrounding the hypothetical devices .
The driving boundary data was taken from directional wave
measurements from a Datawell Waverider MkIII buoy
positioned on the domain’s north-western boundary. This data
was converted into representative directional frequency
spectra using a Gaussian directional distribution at a 30minute
time step. The data used in this study covers a one year period
from December 2011 to December 2012 and was simulated
within the model at an hourly time step. The change in water
level from tidal constituents was included by applying a
varying water level across the domain at a 30 minute temporal
resolution. The tidal variation time series was generated with
DHI’s global tidal model for the location of the array. This
data was validated using measured data from the AWAC in a
previous study [19]. All additional model parameters remain
the same as the previous tests.
B. Pre-device Model Calibration and Validation and Device
Setup
The pre-array domain was calibrated by varying white
capping, bottom friction and wave breaking parameters within
the spectral wave model. The pre-device model was run for a
one year period at an hourly time step to ensure a year round
accurate simulation. The results of this base model were
compared with measured data from the AWAC over the same
time period. Further details on the calibration processed are
outlined in [19]. The results show the modelled wave climate
at the AWAC location have an 87% correlation for the
significant wave height and 85% for the average wave period.
This provides accurate incident wave spectra for each device
location, where the absorption and reflection can be calculated.
The individual device locations are situated along the 10m
depth contour with an approximate spacing of 60m between
devices. The devices were aligned with the 10m depth contour.
The addition of the devices provided more node points during
the creation of the mesh, resulting in an increased detail of
20m2 around the devices.
C. Results and Discussion
The WEC array domain was run for the same time period
as the base model. This study reviews the potential changes in
spatial wave power for the winter (Dec 2011 - Jan 2012),
summer (Jun 2012 – Jul 2012) and yearly average conditions
(Dec 2011 – Nov 2012). To provide a detailed comparison the
percentage change for each node is calculated. As the number
of mesh nodes between the different domains varies, the base
model data was interpolated to match the WEC mesh.
Fig. 13 shows the percentage change in the wave power
around the devices for each representative spectrum. The
location of each device is indicated by a large reduction in
power leeward of the device accompanied by a large increase
of power in front of the device as seen in the theoretical tests.
As there is a large variation in seasonal wave spectra to allow
comparison the percentage change in wave power is
considered. The distribution of the change in wave power
shows the southernmost devices within the array causing a
larger impact on the existing wave climate. Further
Fig. 13 Percentage change in wave power behind multiple Reactive Polygon structures in UTM-29 coordinates. Top left: winter average, bottom right:
summer average and right: yearly average.
Fig. 14 Change in wave power along the central device perpendicular transect
for each seasonal average.
Fig. 16 Change in wave power 300m in front the array for a device parallel
transect.
observations show groups of reduced wave power located at
the southern and northern end behind the array. The winter
average shows a high level of reduced wave power
downstream of the devices with a high increase in upstream
wave power. The summer results show a lower change in the
percentage wave power behind the devices, with a significant
change to the very nearshore location. The annual average
shows a similar distribution of the change in wave power in
lee of array compared to the winter period, however large
areas of significant changes in wave power up and
downstream of the array are present. Fig. 14 shows a
perpendicular transect that bisects the central device. The
results show a large reduction in wave power behind all
devices with the largest reduction of -15% for the winter and
full year averages. The summer seasonal average produces
peak values for the change in wave power of -11%. As the
distance downstream increases the change wave power
reduces and retunes to the pre-device level at approximately
320m behind the device, this value continues increasing and
peaks at 420m behind the device with an increase of 2.5 for
the winter and yearly results and 1.8 for the summer average.
As the distance further increases a second reduction in wave
power occurs. This second reduction in wave power occurs in
very shallow water, as Mike 21 SW model may not provide
accurate convergence for regions of very shallow and/or
complex areas these results may be unreliable and should be
ignored. The upstream results show a peak change in wave
power of above 15% for all representative sea sates. As the
distance upstream increases the change in wave power shows
a slow decay that propagates beyond 3km. This shows while
the reflection contains a small proportion of the incident wave
energy the combined upstream propagation causes a
significant change to the surrounding wave climate. A
downstream transect was taken parallel to, and approximately
350m behind, the central device, extending beyond the width
of the array (see Fig. 15). The results show no sign of
individual device absorption at the location of the transect.
The distribution in the change in power shows the cumulative
effects of the wave shadow for all time averaged results. The
winter and year averaged results show two regions with
increased reductions in wave power. These regions have a
peak reduction of 8% and 9.5%. The summer results show a
similar variation as the winter and yearly average, however,
the central reduction in wave power is much broader with the
northern end of the array showing a reduction in variation for
the most part. As the transect extends beyond the area directly
behind the array the results show an increase in wave power
either side of the array for the winter and year averaged results.
These results show that the more energetic winter wave
conditions cause a larger change in wave power. A further
transect is taken approximately 300m upstream of the central
array device, and the results are shown in Fig. 16. All results
show an increase in wave power, with the largest increase
located at the southern end of the array with an increase in
power of 12.7% for the winter and year results. For all test
conditions the change in wave power at the end of the array
tails off. The summer results show a more even distribution of
increased power across the upstream transect when compared
with the winter and year averaged results. At the northern end
of the array a large difference between the winter, annual and
summer results can be seen. This difference is likely to be
caused by a significant change in the incident wave climate.
The winter and year results show a very similar distribution,
however the summer average has a general lower magnitude
of percentage change. This observed alteration in the
distribution of the percentage change may be caused from a
seasonal directionally varying wave climate. This change in
incident wave climate will cause a significant difference for
the absorption and therefore reflective spectra for each device.
The application of the Reactive Polygon technique to the
regional bathymetry around the north-west coast of Lewis
shows potential for significant nearshore changes to the wave
resource. The spatial results show a varying absorption of
individual WEC devices that resulting in a cumulative
reduction in wave power behind the array. This method also
includes the upstream wave-device interaction that shows a
large increase in the upstream wave power. By using transects
to review the data it can be seen that the incident wave
spectrum plays a significant role when assessing the effects of
an array on the surrounding wave climate. While seasonal
average provides a good approximation to the spatial change
in power they exclude the temporal variation containing the
extreme results. These excluded periods may contain data
important to environmental impacts.
Fig. 15 Change in wave power 300m behind the array for a device parallel
transect.
IV. CONCLUSION
In assessing the potential impacts of WEC on the
surrounding wave climate a highly detailed method of
simulating a nearshore WEC array has been demonstrated.
The theoretical experimentation outlines three possible
techniques for modelling WECs and reviews their
performance in single and multiple device configurations.
Among the three techniques chosen for WEC modelling, the
Reactive Polygon technique was found to be the most realistic
method., and hence this method was applied to north coast of
Lewis at the location of a planned multi-megawatt WEC
development. While the methods shown in this study uses
hypothetical device characteristics, the flexibility of these
technique allows its application to suit a range of WEC
technologies and locations.
The result show the more complex Reactive Polygon
method provides the most realistic simulation as it accounts
for device specific directional and frequency factors. When
the Reactive Polygon technique was applied to the average
winter, summer and one year wave conditions for a proposed
WEC array consisting of 30 devices, the changes to the wave
climate were observed. The results indicate the average yearly
reduction in nearshore wave power is 5%, this value increases
to a peak value of 9.5% during the winter average at the
nearshore location. The upstream results show an increase in
percentage change, where the yearly average shows an
increase of approximately 7.5% that extends as high as 12.7%
at the southernmost end of the array. The results show that the
spatial distribution in wave power is strongly based on the
device-incident wave climate and the device absorption
parameters. This study shows that the inclusion of the
reflective wave field provides important information not only
for environmental effect but for regions with multiple WEC
developments, where reflective waves may alter the existing
resource at neighbouring development size. While the
methods shown within this study were applied to the current
environment conditions, the absorption values used were not
intended to represent a particular device performance, and
power takeoff behaviour can vary significantly between
device types and models.
The further development of the processes to quantify the
change in wave climate due to WEC arrays has provided a
new technique for simulating WECs on a regional scale.
While the predicted changes to the surrounding wave climate
provide an insight into the potential effects an array may have
on this location, further work looks at a temporally varying
simulation that includes storm events to determine additional
changes in wave power in specific conditions. Additional
work should focus on including a realistic diffraction term that
allows for a more appropriate regeneration of wave energy
behind a device within Mike 21 SW.
ACKNOWLEDGMENT
The authors wish to acknowledge the funding received
from the European Regional Development Fund and the
primarily SFC funded Hebridean Marine Energy Futures
Project. Furthermore the author is grateful for the data and
support from the Hebridean Marine Energy Futures project
partners Aquamarine Power and Lews Castle College.
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