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Beach morphodynamics in the lee of a wave farm

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The significant advances in the past years towards the consolidation of wave energy as a major renewable warrant the investigation of the synergies between this novel resource and coastal defence. The aim of this work is to examine the effects of a wave farm operating at different distances from the coastline on the beach morphology. On the one hand, the impacts of the wave farms on the sediment transport are assessed. On the other hand, how the farm affects the modal state of the beach with reference to a baseline (no farm) scenario is examined. For this purpose, a high-resolution nearshore wave propagation model is coupled to a coastal processes model to assess the wave farm impacts on the beach. The wave farm is found to reduce significantly the erosion in the beach. This is a bonus to be added to the primary role of the wave farm – and one which enhances its economic viability by leading to savings in conventional coastal defence measures.
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Beach morphodynamics in the lee of a wave farm
Javier Abanades
#1
, Deborah Greaves
#2
, Gregorio Iglesias
#3
#
School of Marine Science and Engineering, Plymouth University
Marine Building, Drake Circus, Plymouth, PL48NH (UK)
1
javier.abanadestercero@plymouth.ac.uk
2
deborah.greaves@plymouth.ac.uk
3
gregorio.iglesias@plymouth.ac.uk
AbstractThe significant advances in the past years towards the
consolidation of wave energy as a major renewable warrant the
investigation of the synergies between this novel resource and
coastal defence. The aim of this work is to examine the effects of
a wave farm operating at different distances from the coastline
on the beach morphology. On the one hand, the impacts of the
wave farms on the sediment transport are assessed. On the other
hand, how the farm affects the modal state of the beach with
reference to a baseline (no farm) scenario is examined. For this
purpose, a high-resolution nearshore wave propagation model is
coupled to a coastal processes model to assess the wave farm
impacts on the beach. The wave farm is found to reduce
significantly the erosion in the beach. This is a bonus to be added
to the primary role of the wave farm and one which enhances
its economic viability by leading to savings in conventional
coastal defence measures.
Keywords Wave energy, Wave farm, Wave Energy
Converter, Nearshore impact, Beach profile, Erosion
I. INTRODUCTION
A wave farm extracts the energy from the waves through
Wave Energy Converters (WECs). This extraction of energy
implies a reduction in the incident wave height nearshore,
which in turn may modify the patterns of sediment transport
and eventually lead to an attenuation of erosion. This paper is
concerned with the question as to whether wave farms can be
used for coastal protection and in which manner this is
influenced by the farm-to-coast distance.
Previous studies focused on the impact of wave farms on
the wave conditions [1-10] showed a significant reduction in
the wave height in the lee of the wave farm. Abanades, et al.
[11] proved that this extraction resulted in a medium-term
reduction of the erosion exceeding 20% in some sections of
the beach profile (2D). In further studies, Abanades, et al. [12],
[13] considered the 3D response of the beach under storm
conditions in order to establish the applicability of wave farms
to coastal defence. Erosion was found to decrease by more
than 50% in certain areas of the beach. In the wake of these
studies, which evidenced the impact of wave farms on beach
morphology, this paper considers three farm-to-coast
distances: 2 km, 4 km and 6 km from the 10 m water depth
contour [2], to determine the wave farm impacts on the beach
morphology as a function of them.
The objective of this paper is twofold: the analysis of the
wave farm impacts on the sediment transport patterns, and the
quantification of the modal state of the beach with and without
the wave farm during a year. As for the former, the response
of the beach is analysed under frequent storm conditions to
establish the degree of coastal protection offered by the wave
farm as a function of the distance. As for the latter, the
percentages of time in an average year corresponding to each
beach modal state in the baseline scenario, and how these
percentages are altered by a wave farm as a function of its
distance from the coast are quantified.
For this purpose, process-based modelling, analytical
solutions and empirical classifications are applied in a case
study at Perranporth Beach, UK (Fig. 1). To analyse the
response of the beach two process-based models are coupled:
SWAN [14], a wave propagation model used to represent the
wave field-WEC array interaction; and XBeach [15], a coastal
processes model to determine the effects of the farm on the
beach dynamics. For the case of the beach modal state, the
morpohology of the beach is determined by means of an
empirical classification that accounts for breaking wave
conditions, tidal regime and sediment size. To calculate the
breaking wave conditions, the results of the wave propagation
model are coupled to the Kamphuis’ formulae [16].
Fig. 1 Bathymetry of SW England [water depths in m] including the location
of Perranporth Beach, the WaveHub Project and an aerial photo of
Perranporth Beach [source: Coastal Channel Observatory].
II. MATERIALS AND METHODS
A. Case study: Perranporth Beach
For the present paper Perranporth Beach, located in the
Cornwall Coast (SouthWest England), was selected as a case
study to analyse the impacts of wave farms. This coast is one
of the areas with greatest potential for wave energy since it
was selected to house the Wave Hub project a grid-
connected offshore facility for sea tests of WECs. Perranporth
Beach is a 3.6 km beach composed of medium quartz sand,
D
50
= 0.27 0.29 mm [17] and a relatively flat intertidal area,
tan β = 0.015 0.025. The bathymetry data obtained through
field survey by the Coastal Channel Observatory were used.
Perranporth faces directly toward the North Atlantic Ocean
and it has experienced an increase in flooding and erosion
risks from rising sea levels and increased storminess [18], as
was shown during the energetic storms in 2014. Therefore,
Perranporth constitutes a prospective location for using such
wave farms for coastal defence. During the year studied to
establish the modal state of the beach (November 2007 to
October 2008), the average values of the significant wave
height (H
s
), peak period (T
p
) and direction (θ) were 1.60 m,
10.37 s and 282.59 °, respectively. In the case of the short-
term analysis for determining the impacts of wave farms on
the sediment transport patterns, two wave conditions
representative of the offshore wave climate in the area [19]
were chosen (Table 1).
Case study
H
s
(m)
T
p
(s)
θ (°)
CS1
3
12
315 (NW)
CS2
3.5
11
315 (NW)
Table 1: Offshore wave conditions: significant wave height (Hs), peak period
(Tp) and mean direction (θ) for the different case studies.
B. Process-based modelling: coupling SWAN-XBeach
The wave propagation was carried out using SWAN, a
third-generation phase-averaged wave model for the
simulation of waves in waters of deep, intermediate and
shallow depth. SWAN computes the evolution of the wave
spectrum based on the spectral wave action balance equation.
Fig. 2: Computational grids of the wave propagation and the coastal processes
model
A high-resolution grid was essential in this work in order to:
(i) implement the WECs that formed the wave farm in their
exact position, (ii) represent accurately the impact of the wave
farm on the wave conditions in its lee, and (iii) couple the
results to the coastal processes model and the Kamphuis’
formulae. On this basis, two computational grids are defined
(Fig. 2): (i) an offshore grid covering approx. 100 km × 50 km
with a grid size of 400 × 200 m, and (ii) a high-resolution
nearshore (nested) grid covering the study area, with
dimensions of approx. 8 km × 6 km and a grid size of 16 m ×
12 m.
The wave farm consisted of 11 WaveCat WECs arranged in
two rows, with a spacing between devices equal to 2.2D,
where D = 90 m is the distance between the twin bows of a
single WaveCat WEC and corresponds to the capture width of
the device. The farm was located at distances of 2 km, 4 km,
and 6 km (Fig. 3) from a reference contour (10 m water
depth), which corresponded to water depths of approx. 25 m,
30 m and 35 m, respectively [2, 10]. The WEC-wave field
interaction was modelled by means of the results obtained for
the wave transmission coefficient in the lee of the device in
the laboratory tests carried out by Fernandez, et al. [20].
Fig. 3: Wave farm located at different distances: 2 km, 4 km and 6 km to the
10 m water depth contour at Perranporth Beach [water depth in m].
Based on the results of the wave propagation model, the
coastal processes model, XBeach, was used to compute the
impact of the wave farm on beach morpholology. XBeach is a
2DH (two-dimensional horizontal) time-dependent model that
solves coupled cross-shore and alongshore equations for wave
propagation, flow, sediment transport and bottom changes.
The full description of the model can be found in Roelvink, et
al. [15].
XBeach has been widely validated to determine the impact
of storms on sandy [21-23] and gravel beaches [24-27] at
different locations. In this case, the impact of the wave farm
on the beach morphology (3D) was compared to the baseline
scenario at Perranporth Beach following the model set up
applied by Abanades, et al. [11] at the same location. The
high-resolution grid implemented on XBeach covered an area
of 1.4 km cross-shore and 3.0 km alongshore at Perranporth
Beach with a resolution of 6 m and 12.5 m, respectively. The
bathymetry data, from the Coastal Channel Observatory, were
interpolated onto this grid (Fig. 4), which comprised elevation
values from -20 m to more than 60 m with reference to the
local chart datum (LCD). The maximum values correspond to
the top of the dune, which backs most part of the beach (from
Profile P3 in Fig. 4 to the northernmost point of the beach),
and it is characterised by a very steep section (from Profile P3
to Profile P2) that will be of relevance in the beach
morphodynamics.
Fig. 4: Bathymetry of Perranporth Beach computed in XBeach. Profiles P1,
P2 and P3 included. Water depth in relation to local chart datum [in m].
The effects of the wave farm on the beach were determined
based on a comparison of the different wave farm scenarios
with the baseline (no farm) case. The impact indicators
defined by Abanades, et al. [12] are considered:
- Bed Level Impact (BLI) that represents the sea bed
level difference between the baseline and the wave
farm scenario at a generic point of the beach. A
positive value signifies that the seabed level is higher
in the presence of the wave farm, and, therefore a
reduction of the erosion in that point.
- Beach Face Eroded Area (FEA
b
or FEA
f
) that
quantifies the erosion in the beach face (area over the
mean water level exposed to the action of the waves) in
the baseline and the wave farm scenario. A negative
value means an accretion in this area.
- Non-dimensional Erosion Reduction (NER) that
computes the variation in the eroded area as a fraction
of the total eroded area brought about by the wave
farm. A positive or negative value implies a reduction
or increase in the eroded area, respectively, as a result
of the wave farm.
C. Beach modal state
The conceptual beach classifications are empirical models
based on the relationships between the characteristics of
different types of beaches (wave climate, sediment size and
tidal regime) and field observations. Therefore, these models
allow the evolution of beach dynamics as a function of the
beach features to be predicted, and also, the quantification of
the potential changes induced by a modification of these, such
as the reduction of wave energy brought about by a wave farm.
The empirical classification presented by Masselink and
Short [28], based on the classification of Wright and Short
[29], depends on two parametes: the dimensionless fall
velocity parameter, (Ω), also known as Dean’s number [30]
and the Relative Tide Range (RTR), defined as
b
s
H
wT
Ω=
(1)
b
MSR
RTR
H
=
(2)
where H
b
is the breaking wave height, T is the wave peak
period corresponding to the breaking conditions, w
s
is the
sediment fall velocity and MSR the Mean Spring tidal Range
(MSR = 6.3 m at Perranporth).
Fig. 5 shows the relationships between the dimensionless
fall velocity and the relative tide range parameters that are
used to establish the modal beach state. As the RTR parameter
increases the beach evolves from a classic reflective state
through the formation of a low tide terrace at the toe of the
beach face and low tide rips to a steep beach face fronted by a
dissipative low tide terrace. In the case of an intermediate
barred beach, the increase in the tidal range moves the bar
down to the low tide level generating a low tide bar and rips.
Finally, for barred dissipative beaches characterised by
multiple subdued bars at different water depths, the increase
of RTR results in the disappearance of these bars. The latter
two groups shift to ultra-dissipative beaches with values of
RTR between 7-15. For values of RTR greater than 15 the
resulting beach is fully tide-dominated.
Figure 5: Conceptual beach model [28].
To determine the wave conditions necessary to establish the
morphological beach state breaking wave height (H
b
) and
peak period (T
p
) the results from SWAN are coupled to the
Kamphuis’ formulae [16], a breaking criterion for irregular
waves based on the following expressions:
4
2
0.095 tanh( )
m
b
sb bp
bp
d
H eL
L
Π
=
, and (3)
3.5
0.56
m
sb
b
H
e
d
=
, (4)
where H
sb
represents the breaking significant wave height,
m the beach slope, L
bp
the breaking wave length and d
b
the
breaking water depth. Once he breaking wave height was
determined, the corresponding period was selected.
III. R
ESULTS AND DISCUSSION
The wave propagation model was validated using the wave
buoy data at Perranporth Beach from November 2007 to
October 2008, missing out January 2008 owing to the lack of
data. Fig. 6 shows the good fit achieved between the
significant wave height computed by SWAN and the values
from the wave buoy. The coefficient of determination, R
2
, and
the Root Mean Square Error, RMSE, confirm the goodness of
the fit: R
2
= 0.94 and RMSE = 0.38 m.
Figure 6: Time series of simulated (Hs, SWAN) and measured (Hs, buoy)
significant wave height.
In first place, the wave farm impacts on sediment transport
are analysed. The nearshore significant wave height (H
s
) for
the different scenarios (baseline and with the wave farm at
distances of 2 km, 4 km and 6 km from the reference contour)
is shown in Figure 7 for CS1 (Table 1). The reduction in the
significant wave height in the lee of the farm caused by the
energy extraction is apparent. The maximum values of the
reduction were achieved in all the wave farm scenarios behind
the second row of WECs with values of up to 50%. At a
distance of 1.5 km from the second row of devices, the
reduction reached a peak of 40% due to the merging of the
shadows caused by the first and the second row of devices.
However, this reduction decreased moving towards the coast
due to the redistribution of the energy from the edges into the
shadow caused by the wave farm. At a water depth of 10 m in
the area of Perranporth Beach, the average reduction along
this contour in the area of caused by the wave farm closest to
the coast (2 km) was approx. 25%, whereas for the wave farm
at 4 and 6 km the average reduction was approx. 15% and 9%,
respectively.
The relevance of the farm-to-coast distance may be readily
observed in the shadows caused by the wave farm at different
distances. The area affected at the coastline by the wave farm
furthest to the coast (6 km) was greater than 7 km, however
the average reduction of the significant wave height in this
area was less than 5%. On the other hand, the wave farm at 2
km affected a smaller area in the coastline, around 4 km, but
the reduction exceeded 10%.
Figure 7: Significant wave height [m] in the baseline scenario and in the
presence of the farm at distances of 2 km, 4 km and 6 km from the reference
(10 m water depth) contour in CS1 (clockwise from above left).
The results along the 20 m water depth contour (Figure 7)
are the input of the coastal processes model to study in which
manner the modification of the wave patterns affected the
coastal processes and, consequently, the beach morphology.
To quantify this alteration the results were analysed by means
of the impact indicators defined in Section 3.2. The first
indicator was the bed level difference, BLI, which represented
the difference of the bed level between the baseline and the
wave farm scenarios at a point in time. Figure 8 shows BLI
values at the end of the storm for CS1 with the wave farm at a
distance of 2 km (left), 4 km (middle) and 6 km (right). It was
observed that the main impact caused by the wave farm was
located at the beach face, where reductions of the erosion up
to 1.5 m were found. In the comparison between scenarios, the
wave farm at a distance of 2 km caused greater reduction of
the erosion in the beach than the other scenarios, in which
areas with significant reductions of erosion were combined
with negligible values or even accretion.
Figure 8: Bed level impact in the area of interest with the wave farm at a
distance of 2 km (BLI
2km
), 4 km (BLI
4km
) and 6 km (BLI
6km
) at the end of the
storm in CS1.
The impacts on the beach face were analysed through the
FEA and NER indicators. The FEA factor was defined to
quantify the erosion in the beach face along the beach (Fig. 9).
The greatest values of this indicator along the beach were
focussed in the southern area because this section was not
backed by the dune. The erosion in the baseline scenario was,
in general, greater than the scenarios with the wave farm,
especially in the middle and northern area of the beach, y
coordinate (along the beach) > 1250 m. To compare the
reduction between the different wave farm scenarios the
indicator NER was defined, which showed the variation of the
erosion in terms of the eroded area in the baseline scenario
(Figure 10). The NER values fluctuated considerably along
the beach, but it was observed that the reduction using a wave
farm at a distance of 2 km was greater than the other two
scenarios.
Figure 9: Beach face eroded area in the following scenarios: baseline (FEA
b
)
and with the wave farm at a distance of 2 km (FEA
2km
), 4 km (FEA
4km
) and 6
km (FEA
6km
) along Perranporth Beach (y - coordinate, with y increasing
towards the north of the beach) at the end of the storm in CS1 (above) and
CS2 (below).
In the area of the steep dune (500 m < ycoordinate < 1250
m), the erosion in the beach face was very low (negligible in
some sections), and very few profiles presented an isolated
response taking the NER factor negative values (greater
erosion with the farm than without it). However, in terms of
the average reduction of the beach face erosion along the
whole beach, it was confirmed that the wave farm at 2 km
offered a greater degree of coastal protection, around 15% in
both case studies, than the scenario with the wave farm at 4
and 6 km, which presented an approximate reduction of
approx. 10%. Considering particular sections of the beach, the
impact was much more significant, for instance, the reduction
exceeded 20% for the wave farm at 2 km for values of the y
coordinate between 1200 and 2000 m in CS2, which was the
area most affected by the reduction of the significant wave
height (Figure 7).
Figure 11: Non-dimensional erosion reduction (NER) at the beach face in the
following scenarios: with the wave farm at a distance of 2 km (NER
2km
), 4 km
(NER
4km
) and 6 km (NER
6km
) along Perranporth Beach (y-coordinate, with y
increasing towards the north of the beach) at the end of the storm in CS1
(above) and CS2 (below).
In second place, the modal state of the beach was
determined based on the results of the wave propagation
model. In order to investigate the spatial variability of the
impact three profiles (Fig. 4) were selected: profiles P1, P2
and P3 corresponded with the south, middle and north section
of the beach.
Profile P1: South section
Reflective
Barred
Barred dissipative
Baseline 0.00% Baseline 0.07% Baseline 16.04%
6 km 0.00% 6 km 0.07% 6 km 15.96%
4 km 0.00% 4 km 0.07% 4 km 15.90%
2 km 0.00% 2 km 0.07% 2 km 15.70%
Low tide Terrace +
rip
Low tide bar/rip
Non-barred
dissipative
Baseline 0.00% Baseline 25.50% Baseline 26.59%
6 km 0.00% 6 km 25.70% 6 km 26.39%
4 km 0.00% 4 km 25.98% 4 km 26.18%
2 km 0.00% 2 km 26.18% 2 km 25.77%
Low tide terrace
Ultra-dissipative
Baseline 3.36% Baseline 22.89%
6 km 3.36% 6 km 22.89%
4 km 3.43% 4 km 22.82%
2 km 3.36% 2 km 23.24%
Transition to tide-dominated tidal flat
Baseline 5.55%
6 km 5.63%
4 km 5.62%
2 km 5.69%
Table 2: Percentages of the beach modal state for the south section of the
beach (Profile P1) from 1st November 2007 to 31st October 2008
The south section of the beach is predominantly dissipative
(third column in the table), although the percentage that the
beach is found to be intermediate (second column) is far from
negligible. Indeed, in the case with the farm at a distance of 2
km, the low tide bar/rip becomes the most frequent state. The
comparison between the baseline and farm scenarios reflects a
slight modification of the modal state of the beach owing to
the low impact of the wave farm on the wave conditions in
this area. The maximum difference between the baseline and
the farm scenarios is the case of the non-barred dissipative
state, in which the reduction does not exceed 1%. In any case,
the trends due to the reduction of the significant wave height
are shown in the results; for instance, the percentage of low
tide bar/rip state increases as the wave farm become closer,
because the Relative Range Tidal parameter (RTR) is
inversely proportional to the breaking wave height. On the
other hand, the dimensionless fall velocity parameter (Ω) is
directly proportional to the breaking wave height, and,
therefore the barred dissipative state occurred more frequently
in the baseline scenario than in the cases with the farm.
Profile P2: Middle section
Reflective Barred Barred dissipative
Baseline 0.00% Baseline 0.14% Baseline 16.59%
6 km 0.00% 6 km 0.07% 6 km 15.49%
4 km 0.00% 4 km 0.07% 4 km 14.39%
2 km 0.00% 2 km 0.07% 2 km 6.18%
Low tide Terrace +
rip
Low tide bar/rip
Non-barred
dissipative
Baseline 0.00% Baseline 28.10% Baseline 28.71%
6 km 0.00% 6 km 27.55% 6 km 28.92%
4 km 0.00% 4 km 28.24% 4 km 28.71%
2 km 0.00% 2 km 31.11% 2 km 22.62%
Low tide terrace Ultra-dissipative
Baseline 0.89% Baseline 22.68%
6 km 0.96% 6 km 23.99%
4 km 1.03% 4 km 24.40%
2 km 3.49% 2 km 32.28%
Transition to tide-dominated tidal flat
Baseline 2.89%
6 km 3.02%
4 km 3.16%
2 km 4.25%
Table 3: Percentages of the beach modal state for the middle section of the
beach (Profile P2) from 1st November 2007 to 31st October 2008
In the case of the middle of the beach (Table 3), the results
were slightly different compared with the south section. In this
area, the wave farm impacts are greater compared to the south
section. Whereas the wave farm at 4 km and 6 km do not
present significant differences compared with the baseline
scenario, the wave farm at 2 km changes the behaviour of the
beach significantly, reducing the barred dissipative state by
more than 5% or 20 days per year, and increasing the
ultradissipative state by more than 15 days. Overall, with the
wave farm at 2 km the most frequent state shifted from non-
barred dissipative (baseline) to ultra-dissipative due to the
reduction of breaking wave height.
Finally, the north section of the beach is the area that
presented the greatest differences between the baseline and the
farm scenarios (Table 4). The trends mentioned in previous
paragraphs are accentuated in this area, the reduction in the
barred and non-barred dissipative states results in a greater
occurrence of the ultra-dissipative beach, from 5 days to 36
days per year in the case of the farm at 6 and 2 km,
respectively a very substantial change in the morphological
behaviour of the beach. As regards the Ω parameter, it is
observed that the closest wave farm make the low tide terrace
and the low tide bar and rip states more frequent by 10 and 12
days per year, respectively, compared with the baseline
scenario.
Profile P3: North section
Reflective Barred Barred dissipative
Baseline 0.00% Baseline 0.07% Baseline 21.73%
6 km 0.00% 6 km 0.07% 6 km 20.90%
4 km 0.00% 4 km 0.07% 4 km 20.29%
2 km 0.00% 2 km 0.00% 2 km 16.04%
Low tide Terrace +
rip
Low tide bar/rip
Non-barred
dissipative
Baseline 0.00% Baseline 22.76% Baseline 26.11%
6 km 0.00% 6 km 22.69% 6 km 25.63%
4 km 0.00% 4 km 22.62% 4 km 25.29%
2 km 0.07% 2 km 23.85% 2 km 25.29%
Low tide terrace
Ultra-dissipative
Baseline 2.06% Baseline 22.69%
6 km 2.19% 6 km 23.85%
4 km 2.19% 4 km 24.81%
2 km 3.29% 2 km 26.32%
Transition to tide-dominated tidal flat
Baseline 4.59%
6 km 4.66%
4 km 4.73%
2 km 5.14%
Table 4: Percentages of the beach modal state for the north section of the
beach (Profile P3) from 1st November 2007 to 31st October 2008
In summary, the presence of the wave farm affects the
modal state of the beach drastically, decreasing the occurrence
of wave-dominated states (barred and non-barred dissipative
states) in the favour of tide-dominated (low tide bar and rip in
winter and ultra-dissipative in summer). The reduction of the
wave-dominated states would seem to lead to an increase in
the onshore sediment transport and the removal of the
offshore bar, the materials of which would cause accretion on
the beach in line with the findings by Abanades, et al. [11],
[12].
IV. C
ONCLUSIONS
In view of the accelerated pace of development of wave
energy, a thorough understanding of the effects of nearshore
wave farms on beach morphodynamics will soon be
fundamental to coastal management. In this context, this paper
analyses the role played by the farm-to-coast distance to
protect the coast.
It was observed that the closer the farm to the coast, the
lesser wave energy resource but the greater the reduction of
the erosion. The overall reduction of the erosion on the beach
face compared to the baseline scenario was 15% for the
closest wave farm and approx. 10% for the other two. These
values fluctuated significantly along the beach, and in some
sections, especially in the northern area of the beach,
exceeded 40%.
In the analysis of the beach modal state, it was observed
that the wave farm can transform the predominant character of
the beach from wave- to tide-dominant. The reduction in the
occurrence of the barred states corresponds to an increase of
the onshore sediment transport and the removal of the
offshore bar, which would in turn lead to accretion of the
beach.
In sum, this work showed that a wave farm can alter the
behaviour of a beach in its lee considerably. This in itself need
not be regarded as a negative impact; on the contrary, the
wave farm can lead to beach accretion and thus serve to
counter erosional trends. Moreover, the effects of the wave
farm on the beach can be controlled by locating the farm
closer to, or further from, the shoreline.
A
CKNOWLEDGMENT
This research was carried out in the framework of the
Atlantic Power Cluster Project, funded by the Atlantic Arc
Programme of the European Commission (2011-1/151) and
the School of Marine Sciences and Engineering of Plymouth
University. The authors are grateful to the Coastal Channel
Observatory and DIGIMAP for providing the data.
R
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