Resource characterization of sites in the vicinity of an island near a landmass

15 Renewable energy technologies are undergoing rapid development, the global aim being to

-Resource characterization of coastal sites defined as an island near a landmass -Undisturbed kinetic or dissipated power do not approximate maximum power extracted -Numerical results exceed those from an analytical model except for long islands -Increased offshore depth and lower blockage both reduce the maximum power extracted -Power extracted can be maximized with extraction in strait and offshore of island

A C C E P T E D M A N U S C R I P T A C C E P T E D M A N U S C R I P T 1 Introduction
Development of renewable energy technologies has undergone remarkable progress in the past decades motivated by the security of supply, finiteness and unstable price of fossil fuels [1] [2] and the effects on the climate associated with carbon emissions [3].Renewable energy sources such as wind and solar are stochastic and as such, backup generation is required during those time periods when generation is unable to meet demand.Tidal currents have the advantage of being completely deterministic, and therefore quite predictable, making power-grid integration more straightforward.The ebb and flow motions of tidal currents make tidal power production intermittent, and so backup would be required during slack water as the tide turns and possibly during neap tides.Tidal farms exploit the relatively high energy densities of tidal streams, thus limiting their footprint in comparison to wind and solar farms.
The first pre-commercial tidal arrays are under construction and in the next ten to twenty years it is expected that the first multi-megawatt commercial arrays will become operational.The success of such tidal projects depends on correct estimation of the tidal resource and assessment of the associated environmental impacts.Tidal energy comprises both potential and kinetic energy; hence resource assessment requires information on sea surface elevations and current velocities.Typically, data are measured at the site using acoustic Doppler current profilers (ADCP), and the tidal signal time history reproduced using harmonic analysis [4].The data are very useful for validation of tide models.However, there are limits to ADCP deployment, owing to the cost of field measurement campaigns.Lack of spatial data coverage and measurement errors add to uncertainty in theoretical model calibration.
Power extraction alters the local flow hydrodynamics, and this must be accounted for in predictive models used for tidal resource assessment.Such models can be classified into three categories.Analytical one-dimensional (1D) models determine the maximum average power extracted from an idealised channel connecting two infinite ocean basins [5] or an infinite ocean basin with an enclosed bay [6] based on accessible parameters such as amplitude of tidal head difference driving the flow, peak flow through the channel, seabed friction, and channel dimensions.However, such analytical models assume idealised seabed conditions and channel geometry, and uniform power extraction.These limitations are largely overcome by using twodimensional (2D) and three-dimensional (3D) models.2D models solve the shallow water equations (SWE) to compute free surface elevations and depth-averaged velocities, and permit a localised representation of power extraction by tidal turbines.Although 2D models are computationally efficient, they neglect vertical flow behaviour.3D models compute the flow velocity over the entire water column and model the power extraction profile over the water column, leading to a more realistic representation of power extraction.The resulting improvement in accuracy is at the expense of greatly increased computational load, limiting 3D models to small-and medium-scale domains, unlike 2D models which are routinely applied to medium-to large-scale domains [7].
Draper [8] identified four generic coastal sites suitable for tidal energy exploitation: strait between two infinite ocean basins; enclosed bay; headland; and strait between an island and a semi-infinite landmass.The case of a channel linking two infinite ocean basins has been analysed analytically by Bryden and Couch [9], Vennell [10] and Garrett and Cummins [5] (GC2005).The GC2005 channel model computes the maximum average power available for extraction, also called the potential of the channel, based on the head driving the flow, the maximum volumetric flow rate through the channel and the phase difference between the driving head and flow in the channel.The model assumes that the flow is driven by a constant head, independent of the level of power extraction, and that the flow cannot divert from the A C C E P T E D M A N U S C R I P T channel.The model predicts that the maximum average power available is greater, for a short channel carrying a strong current, and lower, for a long channel carrying a slower current, than the average undisturbed kinetic power through the most constricted cross-section of the channel.In addition, the model predicts that at maximum power extracted, the flow through the channel is reduced to 57.7% of the flow in undisturbed conditions.Draper et al. [11] assessed the limits to power extraction in the Pentland Firth, a strait located between the north coast of Scotland and the geometrically long and wide Orkney Islands, and found the results to agree with the power extraction predictions by GC2005.Agreement between numerical results and GC2005 model was also found by Sutherland et al. [12] for the Johnstone Strait, located between the geometrically long Vancouver Island and the west coast of Canada.The potential of a channel linking an infinite ocean basin to an enclosed bay has been analysed analytically by Garrett and Cummins [13] and Blanchfield et al. [6].Numerical results by Draper [8] compared favourably to predictions by Blanchfield et al. [6] for an isolated bay.Draper et al. [14] analysed the potential of an array deployed near an idealised headland and the effects of power extraction by the array on the environment.The potential of the array was generally not well approximated by either the local undisturbed power or the power naturally dissipated by the seabed.Serhadlıoğlu et al. [15] obtained similar findings in their assessment of power extraction off the Anglesey Skerries, north-west of Wales.The coastal site defined as a strait between an island and a semi-infinite landmass may be sub-classified as follows: island of similar length and width in the vicinity of a landmass; isolated offshore island; island that is geometrically long and/or wide in the vicinity of a landmass; and isolated offshore multi-island system.Draper [8] numerically investigated the potential of a strait between a long and wide island and a landmass, and found that the maximum averaged power extracted was not well approximated by the GC2005 channel model.The disparity in the results arose from changes in the driving head induced by power extraction, with minimal bypass flow offshore of the island.Limits to power extraction in multiple-channel coastal sites can also be assessed through an electrical circuit analogy, whereby the head driving the flow is represented by an alternating voltage, the flow is represented by the electric current, and bed friction and turbines correspond to non-linear resistances [8].The electrical analogy theory has been employed by Draper et al. [16] to assess the resource of the Pentland Firth, located between north coast of Scotland and the Orkney Islands, and by Cummins [17] to investigate the power potential of a split tidal channel.Coastal sites categorized as a channel linking two infinite ocean basins could also be categorized as a strait between an island and landmass.This paper analyses numerically the limits to power extraction at idealised sites in the vicinity of an island near a landmass by means of a sensitivity analysis, and explores under which conditions the flow dynamics in the strait behave similarly to that in a channel linking two infinite ocean basins.This paper is structured in four sections.Section 2 details the methodology employed in the analysis of the coastal site.Section 3 presents the analysis and discussion of the island-landmass coastal site.Section 4 summarises the conclusions.

Methodology
This section describes the methodology employed to undertake a resource assessment of power extraction from a strait between an island and landmass.First, the numerical model employed for the analysis is described.Second, the parameterization of the numerical model is outlined.Third, the process of mesh convergence and spatial discretization of the domain is presented.The resource assessment methodology presented herein has previously been verified and validated by Pérez-Ortiz et al. [18] [19].

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Numerical Model
This study is carried out using the finite element numerical code Fluidity [20] which solves the non-conservative form of the shallow water equations: 2) where η is the elevation of the free surface above mean water level, is the horizontal velocity  vector, t is time, is the horizontal gradient vector, h is the total water depth, g is the ∇ acceleration due to gravity, and C d is the bottom drag coefficient.The model setup follows guidelines for coastal and tidal power extraction modelling provided by the Fluidity developers [21] [22].Based on results from Cotter et al. [20] for large-scale ocean applications solving the SWE, a mixed finite element discretization scheme P 1DG P 2 is employed, which is linear discontinuous Galerkin for velocity and quadratic continuous Galerkin for pressure.The backward Euler scheme is employed to temporally discretise the momentum equation [23].Velocity and pressure fields are resolved using a Generalised Minimal Residual Method (GMRES) solver with a Successive Over-Relaxation (SOR) pre-conditioner [21].The tolerance in the absolute error solution and maximum number of iterations are specified as 10 -7 and 1,000 respectively for both pressure and velocity fields.The geometry of the domain is defined by its length L, width B and water depth h o .The width B is set so that the free stream velocity U ∞ is fully developed north of the island.The island geometry is ellipsoidal with length L i and width B i .The parameter s, corresponding to the minimum distance between island and landmass, defines the width of the strait.Sea surface elevations above mean sea level at the west and east open boundaries are defined as δ w and δ e respectively.Unless otherwise stated, model seabed friction is characterized by a dimensionless drag coefficient C d = 0.0025.Turbulence is included using an empirical depth-averaged parabolic eddy viscosity [24].

Model Parameterization
3) where k = 0.41 is the von Kármán constant, u and v are the stream-wise and transverse velocity components.Unless otherwise stated, the water depth h o in the domain is fixed at 40 m in the stream-wise direction between (transverse) cross-sections located 0.36L upstream and downstream of the centre of the island.From cross-sections located 0.36L to 0.43L upstream and downstream of the island's centre, the water depth is linearly increased from h to 75h in the stream-wise direction, and kept to 75h in the remaining part of the domain.The increase in water depth near the open boundaries mimics conditions at the edge of the continental shelf.The deep water zone attenuates reflected long waves from the island and power extraction zone and reflects them back onto the shelf before such waves reach the open boundaries [25].Three scenarios are considered in order to define conditions at the solid boundaries of the island and landmass: a free-slip condition; a no-slip condition; and a non-uniform seabed scenario where the water depth is increased linearly from 0.125h o at the island and landmass boundaries to h o at a distance 0.1Ø i away from both solid boundaries, and a free-slip condition is applied to island and landmass.Here, Ø i is the diameter of the island in the case where the length of the island L i is the same as its width B i .In all scenarios, a free-slip boundary condition is set at north solid boundary Γ 2 .Open boundary conditions are prescribed as follows: zero surface elevation at Γ 4 ; and free surface elevation at Γ 1 computed for the M 2 tidal constituent from: where a and ω t are the amplitude and frequency of the M 2 tidal wave (3 m and 1.41 x 10 -4 rad/s respectively).The parameter a o is used to minimize the formation of perturbations by ramping up the tidal signal over the first two tidal cycles:   = 0.5 ( 1 -cos (    4 ) ) 5) Other site-dependent parameters such as Coriolis force, atmospheric pressure, wind or wave conditions are not included in the numerical model.The time step is chosen accordingly, to limit the Courant-Friedrichs-Lewy number to be within O(1).The area of power extraction, or tidal farm, is located at the central and narrowest section of the strait, and it is defined by a length L f and a width B f .The presence of turbines is included in the model through the addition of an equivalent seabed friction coefficient k f in the farm area A f , which is treated implicitly in the same way as natural seabed friction [12] [26].This methodology of power extraction does not account for turbine-scale losses, for example due to mixing behind fences or arrays of tidal turbines; consequently the results represent an upper limit to power extraction [27].

Spatial discretization of the Model
The domain is spatially discretized based on the results of a mesh convergence analysis for the case of a circular island (L i = B i = Ø i = 50h o ) and strait width s = L i for free-slip and no-slip scenarios under steady-state conditions with the flow travelling from west to east of the domain.The mesh is defined by specifying the element edge length on four different boundary regions: on the landmass and within 2Ø i of the island, the rest of the landmass, on the island, and the north boundary.Six meshes are generated using Gmsh [28] with Table I listing the mesh-

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M A N U S C R I P T edge length definition and the total number of mesh elements.Convergence of the velocity solution is analysed at four transverse cross-sections of length 5Ø i extending from the landmass located Ø i west of the island centre, at the island centre, and Ø i and 2Ø i east of the island centre.For the no-slip scenario, analysis of the stream-wise velocity component at the island centre cross-section shown in Figure 2a appear to indicate that mesh convergence is satisfied at the island using Mesh 4.However, results at cross-section 2Ø i east (downstream) of the island (Figure 2b) indicate that full convergence of the velocity field has not been achieved.Although the wake behind the island is not accurately reproduced in the no-slip scenario, results from a validation test of flow past a surface piercing circular cylinder by Pérez-Ortiz et al. [18] have shown that Mesh 4 is able to capture the main flow features around the island.In the next section several scenarios are considered to assess the influence of the parameters defining the geometry (see Figure 1).Meshes for each of these scenarios are created based on the Mesh 4 edge-length specifications in Table I; Figure 3 presents these domains.

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Analysis
This section presents and discusses results from a sensitivity analysis of the tidal power resource of sites in the vicinity of an island near a landmass, hereby referred to as the islandlandmass system.For each case presented, simulations are run for seven tidal periods T: during

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M A N U S C R I P T the first two tidal periods the system is ramped up; the following two tidal periods correspond to spin-up of the system; the final three tidal periods are used for resource assessment.

Island in Proximity of a Semi-infinite Landmass
First the tidal resource of an island-landmass system is assessed.Then a sensitivity analysis is carried out concerning the impact of changing the friction, eddy viscosity, offshore water depth, blockage ratio, and combined strait-offshore power extraction.The island has dimensions L i = B i = Ø i = 50h o , and is located a distance s = Ø i from the landmass.The domain has length L = 70Ø i and width B = 20Ø i .The mesh contains 8,027 vertices and 16,054 elements, and a regular grid of 80 biased-right isosceles triangles defines the area where power extraction is implemented, located at the narrowest section of the strait (Figure 3a).Three scenarios are considered for the boundary conditions (as mentioned in Section 2.2). Figure 4 presents vorticity contour plots for the three scenarios, at times T/2 and T. Vortex shedding occurs in the lee of the island for a noslip boundary condition set at the island, and for the non-uniform seabed scenario, but not for a free-slip boundary at the island.Figure 5 shows contour plots of the speed and kinetic power density, computed from the stream-wise and transverse velocity components, averaged over three tidal cycles, obtained for the free-slip scenario.Higher velocities and consequent kinetic power densities are predicted to occur in waters to the immediate south and north of the island.For the three scenarios, power extraction levels k f between 0 and 4.5 are implemented at the tidal farm in the strait.Figure 6 shows three tidal period-averaged results: undisturbed kinetic power , defined as the kinetic power evaluated at the narrowest section of the strait with no power extraction and computed from the stream-wise and transverse velocity components; natural power dissipated at the seabed in the strait in the absence of power extraction ;

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M A N U S C R I P T kinetic power in the strait with the tidal farm present; and power extracted from the flow by   the tidal farm .There is a clear disparity in the predictions between the three scenarios   evident in the kinetic and extracted power plots.The discrepancy in results between the freeslip and no-slip scenarios may be explained by flow separating at the island in the no-slip scenario.The no-slip and free-slip scenarios may represent upper and lower bounds to power extraction in the strait, with the value of power extracted for the non-uniform seabed scenario falling in-between the values for the no-slip and free-slip scenarios.No clear relationship is found between the maximum in the strait and .For the no-slip scenario, the results

𝑃 𝑒
indicate that maximum power extracted could be approximated by ; however this is not the   case for the free-slip and non-uniform seabed scenarios.Rates of decrease of are higher for   the free-slip and non-uniform seabed scenarios than for the no-slip scenario at low extraction levels k f < 0.5, but they are relatively similar when k f > 0.5.  Unlike a channel connecting two infinite ocean basins, the island-landmass is a two-path flow system, where under equal water depths and bottom friction conditions, both paths exert relatively similar resistance to the flow, noting that the presence of the landmass increases the resistance of the strait path.The volumetric flow rate, , is computed along two cross- = ℎ   sections of length l = s; one across the narrowest section of the strait, and the second spanning offshore from the northern limit of the island.Figure 7 plots the volumetric flow rates in the strait and offshore for the three scenarios.Values are normalised by the volumetric flow rate in the absence of power extraction .Diminishing trends of volumetric flow rate across the strait   are in agreement with the trends of kinetic power shown in Figure 6.In all three scenarios, the reductions in volumetric flow rates across the strait do not yield equivalent increases in volumetric flow rate offshore of the island, implying that there is some energy lost in the system      and 1.14 for the free-slip, no-slip and non-uniform seabed scenarios respectively.

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M A N U S C R I P T Figure 8 plots the head driving the flow in the strait δ wi -δ ei (Figure 1) over three tidal periods for the free-slip scenario with varying values of k f .The driving head increases as power extraction level in the strait rises from low (k f = 0.14) to high (k f = 2.24) power extraction levels.This agrees with numerical results from Draper [8] for a strait between an island with a high width to length ratio and a landmass.
In the free-slip scenario, based on the amplitude of the head driving the flow and maximum   in the strait, the GC2005 channel model with γ = 0.22, where γ accounts for the phase difference between the driving head and flow in the channel, predicts a maximum extracted power in the order of about 45 MW.If γ is approximated by 0.2, as the peak flow lags the peak head drop along the strait by 35°, this leads to a predicted maximum power extracted of 40.7 MW.These values are 67.7 % and 78.3 % lower than the numerically computed free-slip values.For the noslip scenario, the maximum power extracted is predicted to be 81.6 and 77.9 MW for γ = 0.22 and 0.21 (corresponding to peak flow lagging the peak head drop by 5º), which are 60.5 % and 62.3 % lower than the numerical estimates of maximum power extracted.It may be concluded that the GC2005 channel model is not applicable in this case, where the island geometry scale does not prevent bypass flow effects, and where the head driving the flow increases significantly with power extraction.The increase in driving head across the strait may also lead to higher bypass flow rates, distorting furthermore the comparison between the numerical predictions and GC2005.

Friction and Eddy Viscosity
Bottom friction is often used as a calibration parameter when modelling actual coastal sites [30].Sensitivity of in the strait to the choice of bottom friction is tested for three dimensionless   coefficients C d = 0.00125, 0.0025 and 0.005 [31].Figure 9    achieved for lower C d as less power is naturally dissipated by the bottom and there is more power available for extraction by the tidal farm in the strait.Figure 9 highlights the sensitivity of the tidal resource assessment to the parameterization of the domain friction environment, as analysed by Adcock et al. [30] for the Pentland Firth.

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M A N U S C R I P T   The changes to the domain's frictional environment are also reflected in the bypass flows.At maximum , the offshore ratios are 1.25, 1.21, and 1.17 for C d equal to 0.00125, 0.0025,      and 0.005, respectively.Higher bypass flows are obtained with lower C d .Calibration of actual coastal site numerical models is also often performed using the eddy viscosity [32].Sensitivity of to the choice of eddy viscosity is assessed in the free-slip and no-  slip scenarios using Eq. ( 3) with constant kinematic viscosity values of ν t = 10 -6 , 1, and 100 m 2 s -1 , which correspond to the water molecular kinematic viscosity and two typical eddy viscosity values used in the calibration of numerical models [32].For k f levels equal to 0, 0.14 and 2.24, the resulting and are very similar, for both free-slip and no-slip scenarios, with the     empirical depth-averaged parabolic (range of ν t = 10 -2 -1 m 2 s -1 in the vicinity of the island) and constant (ν t = 10 -6 and 1 m 2 s -1 ) values of depth-averaged eddy viscosity coefficient.The case with ν t = 100 m 2 s -1 yields different kinetic and extracted power results, and this difference is greater for the no-slip than free-slip scenario.At k f = 2.24, comparison of results for constant ν t = 100 m 2 s -1 with those from the empirical formula for depth-averaged parabolic viscosity showing that and both increase by 19 % for free-slip and both reduce by 47 % for no-slip.

Water depth
In nature, the water depth offshore of an island is usually greater than in the strait of an islandlandmass system.To analyse this effect on tidal resource estimates for the idealised strait, the water depth offshore of the island in the non-uniform seabed scenario is increased linearly northwards from 0.125h o at the island to 4h o at a distance 0.4Ø i north of the island.Water depth is increased linearly from h o to 4h o west and east of the island along the landmass from the island centre plane until the continental shelf limits are encountered.Figure 10

Farm Strait Blockage
Deployment of tidal turbines at coastal sites is constrained by technical, commercial, environmental and social factors.Resource estimates may be sub-optimal if the tidal farm cannot block the entire strait [33].Based on the non-uniform seabed scenario of the islandlandmass system, three cases are analysed: turbines installed across the entire cross-section of the strait, independent of water depth, hence the strait is 100 % blocked by the farm; turbines solely installed at depths equal or greater to h o , representing an effective 80 % blockage of the strait; and turbine installation constrained by minimum water depth and environmental regulations setting minimum clearances between farm and island, and farm and landmass of 0.2Ø i in both cases, leading to an effective strait blockage of 60 %.The reduction in strait blockage leads to two alternative bypass paths in the strait: between tidal farm and southern tip of island; and between tidal farm and landmass.Figure 11 plots the three-tidal-period-averaged , , and profiles for three strait-        blockage ratio cases, as functions of the equivalent number of turbines in the farm N T , derived from k f as follows: ) where A T and A S are respectively the projected area of the rotor and support structure (A S = 0.1A T ) of a 1 MW power-rated P R tidal turbine with 20 m diameter rotor; C T and C D are the thrust and drag turbine coefficients (assumed constant and equal to 0.8 and 0.9 respectively).  Similar values of maximum are obtained for the 100 % and 80 % blockage ratio cases, and a   lower maximum is predicted for the 60 % case.The increase in frictional resistance due to   reduction in water depth between farm and island and farm and landmass is found to limit bypass flow; this explains why the 80 % and 100 % blockage ratio cases yield similar estimates of maximum .From these results, it appears that implementation of power extraction in   shallow regions of the strait using turbines of smaller size and power rating may not be necessary to reduce or prevent bypass flow.As the strait blockage ratio reduces, so do the rates of reduction of in the strait with power extraction, as the flow reduction through the farm is   counterbalanced by an increase of flow in the strait bypass regions.At high levels of power extraction and partial strait blockage, the increase of velocity in the bypass regions could lead to local seabed erosion in the long term.

Offshore Power Extraction
Although the water depth is likely to be deeper on the offshore side of an island, such a flow regime may still be suitable for tidal power generation (e.g. the Outer Sound, Pentland Firth, Scotland [30]).With development of deep water tidal technology, it is therefore worth exploring the limits to power extraction offshore of the idealised island as well as those for the two-path island-landmass system.Based on the free-slip scenario, power extraction is included on the offshore side of the island over a rectangular area of equal dimensions (L f x B f ) to the tidal farm in the strait used in the island-landmass system.The farm extends towards the north of the

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M A N U S C R I P T domain from the northern limit of the island, and is located at the same stream-wise coordinates as the farm in the strait.The addition of the offshore farm increases blockage of the domain by 50 %; however, no effect on the resource assessment is expected because of the large width of the domain.The averaged power generated by the farm is computed from the local   velocities and the following C P function (based on the turbine described in Section 3.1.3): ) with cut-in speed U C of 1m/s and rated speed U R of 2.5 m/s.Based on N T and P R , the capacity factor CF of the tidal farm during the three tidal cycles is   , computed from:   same k f value.When k f = 0.14 is applied both in the strait and offshore of the island (Scenario 5), there is a 50 % increase in compared to Scenarios 1 and 3 where k f = 0.28 is applied solely at   one side of the island, in agreement with the lower and also evident for Scenario 5.
*   *  Similar results are observed when comparing results from Scenario 6 with k f = 0.28 applied to both sides of the island, against those from Scenarios 2 and 4. The data listed in Table II indicate that power generation in an island-landmass system may be optimized if considered as a two flow path problem, although complex bathymetry and flow conditions may require numerical optimization.

Isolated Offshore Island
This section assesses the limits to power extraction in the vicinity of an isolated offshore island of dimensions L i = B i = 50h o , centred midway across the domain in the transverse direction, at a distance s = 9.5Ø i from the landmass.The computational mesh has 7,341 vertices and 14,682 elements (Figure 3b).Power is extracted south of the island over a rectangular area, of the same dimensions L f x B f as the farm in the strait of the island-landmass system, and extending south from the southern limit of the island.Both free-slip and no-slip scenarios are considered for the island, and the north and south domain limits are defined as free-slip boundaries.Figure 12 compares the three-tidal-period-averaged , , and profiles with k f for the         free-slip and no-slip scenarios.As for the island-landmass system, both free-slip and no-slip scenarios may represent lower and upper bounds to in the vicinity of the island.There is no   evident relationship between maximum and or .For no-slip, the maximum is 17 %         lower than that reached in the island-landmass case, indicating that the presence of the landmass benefits power extraction from the coastal site.As in the island-landmass system, the rate of decrease of at k f < 0.14 is higher for the free-slip than for the no-slip condition.The   ratios at maximum are equal to 1.19 and 1.05 for the free-slip and no-slip scenarios      respectively, indicating similar dynamic behaviour to the island-landmass system.

Geometrically Long Island
This section analyses the sensitivity of the tidal resource at the strait to the length of the island.The length of the island is increased to L i = 800h o while the width of the island and strait dimensions remain B i = s = 50h o .The computational mesh contains 19,335 vertices and 38,670 elements (Figure 3c).Power extraction is implemented in the strait over a rectangular area (of identical dimensions to that in the island-landmass system midway along the island in the Based on the tidal head difference and the maximum volumetric flow rate in undisturbed conditions with γ = 0.22 for the free-slip scenario, the GC2005 channel model predicts =   411.4 MW, which is 8.6 % lower than the numerical prediction.For γ = 0.2 the prediction   using the GC2005 model is 16.9 % lower than the numerical value.Similar discrepancies between analytical and computed results are observed for the no-slip scenario.Although the GC2005 model appears to underestimate relative to the numerical model, there is better   agreement between the two approaches than for the island-landmass system.This indicates that the longer the island length, the more the strait dynamics resemble those in an idealised channel, in concurrence with a similar finding by Sutherland et al. [12] in a study of the Johnstone strait.

Geometrically wide island
This section assesses the effects of the width of the island on the resource in the strait.L i and s are kept equal to 50h o and the island width is increased to B i = 200h o .In order to keep the same domain blockage ratio, B is increased by a factor of 4. The computational mesh comprises 10,465 vertices and 20,930 elements (Figure 3d).A free-slip boundary condition is applied to both island and landmass boundaries, leading to large-scale vortical structures shedding from the island.Figure 15 plots the three-tidal-period-averaged power coefficients, , , and       , as functions of k f as its value is increased from 0 to 4.5.As in Section 3.1, maximum is not     well approximated by either or .Maximum is found to be almost triple that of the no-      slip scenario of the island-landmass system.The ratio at maximum is equal to 1.08.
exhibits a higher rate of decrease than for the corresponding case in Section 3.1.Figure 16 plots the head driving the flow in the strait for no extraction and for an extraction level of k f = 2.24.The fluctuation in the sinusoidal signal originates from eddy shedding in the lee of the island.The increase in head driving the flow with extraction level and the increase in path distance offshore of the island are the main reasons why maximum is higher than for the island-  landmass system.    Based on the flow conditions and head amplitude in the natural state, the GC2005 channel model predicts maximum power extracted of 169.5 and 161.8 MW for γ = 0.22 and 0.21 (derived from the phase difference between maximum head and flow in the strait) respectively.This value under-predicts the numerically computed results by 72.5 % and 73.7 % respectively.Perhaps a more suitable analytical model for geometrically wide islands is that recently derived by Mei [32] for barriers oriented orthogonal to landmass.Mei's analytical model can be used to compute the maximum head difference between a barrier and a landmass based on tidal frequency, maximum tidal flow velocity along the landmass without the barrier, gravitational acceleration, and the length of the barrier.

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Conclusion
This paper has characterized numerically the tidal resource at idealised sites representing an island-landmass system.It is shown that the maximum power extracted in the strait between the island and landmass is generally not well approximated by either the power dissipated naturally at the seabed in the strait or by kinetic power in the absence of the turbines.Both parameters have been used in the past to assess the exploitable resource at tidal coastal sites.An exception is the case of a geometrically long island, where the maximum power extracted is reasonably well approximated by the power dissipated by seabed friction.No-slip and free-slip conditions applied to the island and landmass boundaries may provide lower and upper bounds to maximum power extraction in the strait.The GC2005 model consistently predicts a lower value than the numerical prediction of maximum averaged power extracted in the strait.The longer the island, the better the agreement between the analytical and numerical predictions.Primary reasons for discrepancies between the numerical and analytical results are: the non-inclusion in the latter of changes to the head driving the flow due to power extraction in the strait; and flow diversion on the offshore side of the island.The choice of parameters representing bed friction and eddy viscosity, which are commonly used to calibrate numerical models, is demonstrated to have a significant influence on the predicted value of power extracted in the strait.As would be expected, less extractable power is available in a strait with high bed friction.The results are much less sensitive to choice of eddy viscosity, with changes only becoming apparent at relatively high values (e.g. 100 m 2 s -1 ).Lower flow resistance in deeper water offshore of the island leads to reduced power extraction from the strait.This highlights the necessity for developers to be aware of the effect of far-field bathymetry.

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M A N U S C R I P T The maximum power extracted from the strait reduces as the blockage decreases; this occurs because two additional bypass flow routes in the strait are available: one between the array and island; the other between the array and landmass.Bypass flow routes in the strait are relatively shallow, increasing flow resistance.A blockage ratio of 80 % yields similar maximum power extracted to that of 100 % blockage ratio.Reduction of strait blockage to 60 %, which included deep regions of the strait, leads to lower maximum power extracted than at the higher blockage values.Power generation is similar in the strait and at the offshore side of the island for identical extraction levels.In this case, the total power generated is higher than for an equivalent extraction level applied solely to one side of the island.Inclusion of power extraction offshore of the island increases flow resistance along the bypass route which lowers bypass flow rates and velocity deficits; this is then converted into higher power outputs generated by the islandlandmass system.This implies an opportunity for optimal power generation if the islandlandmass system is considered as a two-flow path problem.Analysis of power extraction off an isolated offshore island reveals that absence of a nearby landmass lowers the maximum power extracted from a coastal site.Maximum power extracted from the strait is found to increase with length and width of the island.This study has provided a comprehensive characterization of the limits to power extraction in island-landmass systems, examined differences in estimates of maximum power extracted obtained using the undisturbed kinetic power and the power dissipated naturally at the seabed, and highlighted limitations in the applicability of an analytical channel model to island-landmass systems.This information should be of particular use to policy makers and tidal developers in preliminary assessment of coastal sites for tidal energy development.

RENE-D-16-00922 Resource Characterization of Sites in the Vicinity of an Island near a Landmass
Dear Editor-in-Chief, Thank you very much for your kind email concerning our manuscript entitled "Characterization of Sites in the Vicinity of an Island near a Landmass" (ID: RENE-D-16-00922) which was submitted to Renewable Energy for possible publication.Following your suggestion, we have made a considerable effort to modify the paper taking full consideration of all the comments and suggestions from the three Reviewers.
Corresponding revisions have been made and are highlighted in yellow in the new version of our manuscript.A detailed list of the revisions is provided along with itemized responses to each comment and suggestion, which we believe have led to significant improvement in the quality of the manuscript.Additional references have been added to support our thesis.We confirm that all the format, style and referencing style of the manuscript should fit the requirements of the Journal.
We would like to thank you again for your detailed suggestions.Sincere thanks are also due to the anonymous reviewers for their very helpful comments.
With best regards.
Sincerely yours, The work is of good quality, and it appears to be technically sound.But the application is idealised and rather limited in scope.Perhaps some more generic conclusions, for example conclusions that a policy maker might be interested in, could be added to the final section.
Response: Thank you for your suggestion.We have included the following paragraph at the end of the Conclusion section at Page 20: "This study has provided a comprehensive characterization of the limits to power extraction in island-landmass systems, examined differences in estimates of maximum power extracted obtained using the undisturbed kinetic power and the power dissipated naturally at the seabed, and highlighted limitations in the applicability of an analytical channel model to island-landmass systems.This information should be of particular use to policy makers and tidal developers in preliminary assessment of coastal sites for tidal energy development." Minor comments: 1.In the first paragraph of the introduction, should also mention that tidal energy, although predictable, is intermittent, especially as mention is made of "backup" being required during times of low wind energy, for example.Same situation would apply during times of slack water or neaps.
Response: We agree with the reviewer's suggestion.Although tidal energy is deterministic, the grid will require backup generation during slack water and during neap tides.
We have added the following sentence in the first paragraph of the Introduction section, Page 2, Lines 8-10: "The ebb and flow motions of tidal currents make tidal power production intermittent, and so backup would be required during slack water as the tide turns and possibly during neap tides." 2. Line 16 -ADCP, not ADP.
Response: Thank you for the suggestion.We have substituted the acronym ADP for ADCP in the manuscript at Page 2 Lines 18 and 19.

A C C E P T E D
M A N U S C R I P T 3. I suggest one or two opening sentences in the abstract setting the research problem within the wider context of renewable and marine renewable energy.
Response: Thank you for your suggestion.We agree with the reviewer's comment and we have added the following lines at the start of the Abstract section (Page 1): "Renewable energy technologies are undergoing rapid development, the global aim being to achieve energy security and lower carbon emissions.Of marine renewable energy sources, tidal power has inherent predictability and large theoretical potential, estimated to exceed 8,000 (TW.h)a -1 in coastal basins.Coastal sites in the vicinity of an island near a landmass are prime candidates for tidal stream power exploitation by arrays of turbines"

Reviewer #2
This paper uses a 2D depth-averaged model to explore the tidal stream resource of a small channel constrained between an island and a semi-infinite landmass.The sites analysed are idealised, with geometric parameters varied to explore the resource parametrically.
Over all I think this is a good paper and is suitable for publication in Renewable Energy.However I have some comments below which I feel the authors should consider prior to publication.
Main Comments: 1.The authors show that the Garrett and Cummins (2005) analytical model gives reasonable predictions when the island is long.An alternative analytical model (which one might expect is most accurate for a wide island) is that due to Mei (2012) ("Note on tidal diffraction by a coastal barrier", Applied Ocean Research, .I suggest the authors read this work and make a comparison to their analysis too. Response: Thank you for your suggestion.We agree with the reviewer's suggestion; however, for consistency with other sections in the paper, we have restricted the comparison of numerical results to the Garrett and Cummins (2005) model.Nevertheless, we have added the following text at the end of Section 3.4 (Page 19) which we believe highlights that the Garrett and Cummins (2005) model may not be the most suitable analytical model for this island aspect ratio, and that in this case other analytical models such as Mei (2012) may provide a better approximation to the limits to power extraction.

A C C E P T E D M A N U S C R I P T
"Perhaps a more suitable analytical model for geometrically wide islands is that recently derived by Mei [32] for barriers oriented orthogonal to landmass.Mei's analytical model can be used to compute the maximum head difference between a barrier and a landmass based on tidal frequency, maximum tidal flow velocity along the landmass without the barrier, gravitational acceleration, and the length of the barrier." 2. The authors refer throughout the paper to "bypass flow" which is used to define the flow on the seaward side of the island.While it is correct that changes in the flow on the seaward side of the island may be related to bypass, the changes might also be due to changes in the driving head with power extraction (i.e. the general change in the amplitude of the free surface fluctuations in the vicinity of the Western and Eastern ends of the island).This driving head not only alters the momentum balance within the channel but may also alter the momentum balance in the flow seaward of the island leading to an increase in flow without any need for bypass flow.

Response:
We agree with the reviewer's comment.Changes in the flow on the seaward side of the island are due both to bypass effects and changes in the driving head induced by power extraction in the strait.We have added the following text to the manuscript at Page 11, Line 14: "The increase in driving head across the strait may also lead to higher bypass flow rates, distorting furthermore the comparison between the numerical predictions and GC2005."Additional Comments: 1. Abstract, Sentence 2: This sentence should stress that natural power dissipation and kinetic flux do not generally explain the power potential.This is because you actually show that in the special case of a long channel natural power dissipation is correlated with potential.
Response: Thank you for the suggestion.We have included the word "generally" in both abstract (Page 1, Line 21) and conclusion (Page 19, Line 14) sections as follows: "This paper characterizes numerically the upper limit to power extraction of turbines installed at such sites.It is demonstrated that the maximum power extracted from the strait is generally not well approximated by either the power dissipated naturally at the seabed or the undisturbed kinetic power of flow in the strait."

A C C E P T E D M A N U S C R I P T
"It is shown that the maximum power extracted in the strait between the island and landmass is generally not well approximated by either the power dissipated naturally at the seabed in the strait or by kinetic power in the absence of the turbines." 2. Abstract, Sentence 3: Flow diversion would lead to less power in the numerical model not more.
Response: Thank you for your comment.We agree with the reviewer that flow diversion would lead to less power in the numerical model.However, the sentence in the abstract aims to highlight that differences between the analytical and numerical results arise from two factors: increase in head driving the flow with power extraction in the strait, and flow bypassing on the offshore side of the island.Response: Thank you for your comment.We have edited the text as follows in Page 5, Line 8: "The deep water zone attenuates reflected long waves from the island and power extraction zone and reflects them back onto the shelf before such waves reach the open boundaries [23]." 5. Figure 5b and generally: Kinetic flux is a vector quantity -i.e.you need to indicate the direction in which it is flowing.Also, it would be useful to define 'kinetic power', which is a phrase used a lot in the paper, to be the 'streamwise' kinetic flux evaluated at a specific location along the channel (or elsewhere).
Response: Thank you for your comment.We have added the following text to the caption of Figure 5b (Page 8) to indicate the direction of the flow:

A C C E P T E D M A N U S C R I P T
"Figure 1. Contour plots of the three-tidal-cycle averaged speed (a) and kinetic power density (b) for the free-slip scenario, where flow travels from west to east and east to west at flood and ebb tide respectively." In addition, we have amended the text above Figure 5 in Page 8 as follows: ""Figure 1 shows contour plots of the speed and kinetic power density, computed from the stream-wise and transverse velocity components, averaged over three tidal cycles, obtained for the free-slip scenario." Furthermore, we have amended the text below Figure 5 in Page 8 as follows: "Error!Reference source not found.shows three tidal period-averaged results: undisturbed kinetic power , defined as the kinetic power evaluated at the narrowest   section of the strait with no power extraction and computed from the stream-wise and transverse velocity components;" 6. Page 9, line 7: This sentence is incorrect.Even with equal water depths both paths will not exert identical resistance because of the presence of the semi-infinite coastline.
Response: Thank you for your comment.We agree that the presence of landmass adds additional friction to the strait path and we have consequently amended the sentence as follows (Page 9, Line 20): "Unlike a channel connecting two infinite ocean basins, the island-landmass is a twopath flow system, where under equal water depths and bottom friction conditions, both paths exert relatively similar resistance to the flow, noting that the presence of the landmass increases the resistance of the strait path." 7. Section 3.3: How long do you think the island must be for the Garrett and Cummins 2005 model to be a good approximation?
Response: Thank you for the reviewer's question.We did not identify the island geometry length at which the Garrett and Cummins (2005) model provides a good approximation to the limit of power extraction in the strait.We believe this requires substantial further analysis and we aim to assess this in future publications.

Reviewer #3:
This a technically sound paper presenting an analysis of the tidal stream resource assessment of an idealised scenario using numerical modelling.The paper is well written and the structure is clear.
My only query is over the novelty of the work.The results presented here are entirely expected and, whilst a contribution to the literature and should be published, perhaps an alternative journal with lower prestige (e.g.International Journal of Marine Energy) could be considered.
Response: Thank you for your comment.We believe this work performs a comprehensive analysis of the island-landmass coastal site for tidal energy generation purposes.Other types of coastal sites have been analytically and numerically assessed, such as a channel connecting two infinite ocean basins, a channel connecting an infinite ocean basin and an enclosed bay, and a headland.In addition, the Garrett and Cummins (2005) analytical channel model has been utilised systematically to assess the limits to power extraction in island-landmass coastal sites.This paper characterizes the tidal resource in island-landmass sites, identifies and assesses the sensitivity of the limits to power extraction in the strait to different drivers, and explores the limits of application of the Garrett and Cummins (2005) channel model.Consequently, we think that this paper includes new research findings that will benefit the tidal energy industry and is particularly relevant to developers and policy makers.
Minor points I am surprised that no reference has been made to the analytical work on this problem by Cummins (2013) or Draper et al. (2014).
Response: Thank you for your comment.We agree that the addition of both references and a short explanation of the electrical analogy theory will benefit the paper, as this technique has previously been employed with considerable success to assess the resource in multiple-channel coastal sites.We have added the following text at Page 3 Line 26 which includes the citation of the works by Cummins (2013)  "Limits to power extraction in multiple-channel coastal sites can also be assessed through an electrical circuit analogy, whereby the head driving the flow is represented by an alternating voltage, the flow is represented by the electric current, and bed friction and turbines correspond to non-linear resistances [8].The electrical analogy theory

A C C E P T E D
M A N U S C R I P T has been employed by Draper et al. [16] to assess the resource of the Pentland Firth, located between north coast of Scotland and the Orkney Islands, and by Cummins [17] to investigate the power potential of a split tidal channel." Page 2 Line 22 -The Authors' refer to the Garrett & Cummins model as (1D).This has zero spatial dimensions and 1 timescale.By contrast they refer to models have 2 or three spatial dimensions, plus time, as 2D and 3D.Although rarely used a model with one spatial dimension plus time could be considered for such applications (e.g.Rainey (2009)).As such this nomenclature is confusing.
Response: Thank you for your comment.However, we believe we have used nomenclature that is commonly used in environmental free surface flow modelling when referring to analytical, shallow water and three-dimensional models.
For example, hydrodynamic codes such as Telemac are usually referred to as Telemac-2D and Telemac-3D when solving the shallow water and the full Navier-Stokes equations respectively.Page 2 Line 47 -"The model predicts that the maximum average power available is lower than the 47 average undisturbed kinetic power through the most constricted crosssection of the channel".I find this sentence rather worrying given how important the paper referred to is for this work.Equation 2.10 in Garrett & Cummins (2005) (and the surrounding text) explicitly says that the power can be greater or lower than the undisturbed kinetic flux.
Response: Thank you for your comment.We agree that the sentence needs a revision as we may have misinterpreted the results from Garrett and Cummins (2005).We have rewritten the sentence, on Page 3 Lines 1 to 5 as follows: "The model predicts that the maximum average power available is greater, for a short channel carrying a strong current, and lower, for a long channel carrying a slower current, than the average undisturbed kinetic power through the most constricted crosssection of the channel.
In addition, the model predicts that at maximum power extracted, the flow through the channel is reduced to 57.7% of the flow in undisturbed conditions."Section 2.3 -are the elements at the boundary straight edged or curvi-linear?

A C C E P T E D M A N U S C R I P T
Response: Thank you for your question.We have used straight-edged elements at the boundaries of our domain, which can be seen in Figure 3.We are able to provide another figure to clarify this if requested.Response: Thank you for your comment.We are able to provide figures at journal resolution; however the format required for the manuscript causes this pixalation.This will disappear in the as-published version.

Figure 1
Figure 1 depicts the coastal model parameters.The model domain is defined by five boundaries: open boundaries Γ 1 and Γ 4 at the east and west limits of the domain; a solid boundary Γ 2 in the north; a solid boundary Γ 3 in the south corresponding to the semi-infinite landmass; and a solid boundary Γ 5 , corresponding to the island.Boundaries Γ 3 and Γ 5 define the strait.

Figure 1 .
Figure 1.Model geometry and tidal parameters for a strait between an island and a semi-infinite landmass.Grey area indicates the tidal array.

Figure 2 .
Figure 2. Stream-wise flow velocity profile at transverse cross sections at (a) the island centre crosssection, and (b) 2Ø i east of the island centre.The model is run with no-slip boundary conditions at island and coastline.Fluidity predictions for Mesh 3 (solid line), Mesh 4 (dashed line), Mesh 5 (dotted line) and Mesh 6 (dash-dot line).

Figure 3 .
Figure 3. Unstructured spatial discretization: (a) Island in the proximity of a semi-infinite landmass; (b) isolated offshore island; (c) geometrically long island; and (d) geometrically wide island.A regular biasedright isosceles triangles grid is used to delineate the tidal farm

Figure 5 .
Figure 5. Contour plots of the three-tidal-cycle averaged speed (a) and kinetic power density (b) for the free-slip scenario, where flow travels from west to east and east to west at flood and ebb tide respectively.

Figure 6 .
Figure 6.Power profiles as functions of k f for a strait between an island and landmass: free-slip (black), noslip (red) and non-uniform seabed (green) scenarios.Extracted power for a tidal farm located in the strait (solid line); kinetic power for the strait with the tidal farm present (dash-dot line); kinetic power for     undisturbed conditions in the strait (dotted line); and natural power dissipated on the seabed at the   strait (dashed line).Markers indicate output data from the numerical model.
A C C E P T E DM A N U S C R I P T due to power extraction in the strait.The ratios at maximum are equal to 1.21, 1.09

Figure 7 .
Figure 7. Changes in ratio of actual to undisturbed volumetric flow rate for free-slip (black), no-slip (red), and non-uniform seabed (green) scenarios at different levels of power extraction.Volumetric flow rates are calculated across the tidal farm (solid line) and through a cross-section of identical length at the offshore side of the island (dashed line).Markers indicate output data from the numerical model.Analysis of Figure6and Figure7reveals that the volumetric flow rate through the strait at maximum power extracted is reduced to a range between 60-40 % of for the three scenarios,   which approximates reasonably well to the 57.7 % volumetric flow rate predicted by GC2005 and Bryden and Couch[29].

Figure 8 .
Figure 8. Flow driving head between entrance and exit of the strait for the free-slip scenario: no power extraction (solid line); low extraction k f = 0.14 (dotted line); and very high extraction k f = 2.24 (dashed line).

Figure 9 .
Figure 9. Power profiles as functions of k f for a strait between an island and landmass: C d = 0.0025 (black), C d = 0.00125 (red) and C d = 0.005 (green) scenarios.Extracted power for tidal farm located in the strait   (solid line); kinetic power for the strait with the tidal farm present (dash-dot line); kinetic power for   undisturbed conditions in the strait (dotted line); and natural power dissipated on the seabed at the compares the three-tide-period-averaged , , and power profiles obtained when the water depth         A C C E P T E D M A N U S C R I P T offshore is set to h o and 4h o .No changes are observed in and , implying that increase in    water depth offshore does not alter the main undisturbed flow conditions in the strait.However, when the water depth is increased from h o to 4h o offshore, decreases at a higher   rate for the same k f level and maximum decreases from 180 MW to 130 MW.Increase in   water depth offshore of the island reduces resistance to the flow in the offshore path, leading to higher bypass flow rates when extraction level in the strait is increased.This observed reduction in maximum highlights the need for tidal site developers to have a detailed   understanding of the effect of far-field bathymetry on power extraction by a tidal farm.

Figure 10 .
Figure 10.Power profiles as functions of k f for a strait between an island and landmass: depth h o offshore (black) and depth 4h o offshore (red).Extracted power for tidal farm located in the strait (solid line);   kinetic power for the strait with the tidal farm present (dash-dot line); kinetic power for undisturbed   conditions in the strait (dotted line); and natural power dissipated on the seabed at the strait

Figure 11 .
Figure 11.Power profiles as functions of N T for a strait between an island and landmass for three extraction blockage ratios in the strait: 100 % (black); 80 % (red); and 60 % (green).Extracted power for tidal farm located in the strait (solid line); kinetic power for the strait with the tidal farm present     (dash-dot line); kinetic power for undisturbed conditions in the strait (dotted line); and natural power

Figure 12 .
Figure 12.Power profiles as functions of k f for a tidal farm located south of an isolated offshore island: freeslip (black); and no-slip (red) solid boundaries.Power extracted at farm located south of the island   (solid line); kinetic power measured across the tidal farm (dash-dot line); kinetic power measured   across the tidal farm in undisturbed conditions (dotted line); and natural power dissipated on the

Figure 14 .
Figure 14.Tidal head difference between entrance and exit of the strait between a geometrically long island and mainland with free-slip condition at the island: no power extraction (solid line); very high extraction k f = 8.95 (dashed line) in the strait.

Figure 15 .
Figure 15.Power profiles as functions of k f for a strait between an island with high width to length ratio and landmass.Extracted power for tidal farm located in the strait (solid line); kinetic power for the   strait with the tidal farm present (dash-dot line); kinetic power for undisturbed conditions in the strait   (dotted line); and natural power dissipated on the seabed at the strait (dashed line).

Figure 16 .
Figure 16.Flow driving head between the entrance and exit of the strait for the free-slip scenario of a geometrically wide island: no power extraction (solid line) and high extraction level k f = 2.24 (dashed line) at the strait.

3 .
Page 3, line 12: Please include the word 'generally' in this sentence.Response: Thanks for the suggestion.We have added the word generally to the indicated sentence in Page 3, line 15."The potential of the array was generally not well approximated by either the local undisturbed power or the power naturally dissipated by the seabed."4. Page 5, line 2: I don't understand the last two sentences of this paragraph.Deep water does not 'absorb' long waves (if it did we would have no such thing as swell waves!).

Figures 4 and 5
Figures 4 and 5 are rather pixalated in my version.

Table I .
Six spatial discretization cases considered in mesh convergence analysis.Element edge length used in the three mesh regions of the model, and total number of mesh elements.
plots the three-tide-period-averaged results of , , and for the three assessed C d values.Since the boundary conditions are         kept constant, the lowest value of C d consequently yields the highest kinetic power in the   strait.More power is naturally dissipated by the seabed as C d is increased.Higher is

Table II .
Extraction levels k f and equivalent number N T of turbines in the strait (S) and offshore side (O) of