GENERATING RENEWABLE ENERGY ON LAKE ERIE WITH WAVEENERGY CONVERTERS: A FEASIBILITY STUDY

Principal Investigator:

Ethan J. Kubatko, Assistant ProfessorDepartment of Civil & Environmental Engineering & Geodetic ScienceThe Ohio State University

1 Statement of regional or State water problem

The State of Ohio currently generates around 90 percent of its power from coal [23]. Inaddition to being the largest single man-made source of greenhouse gases, the burning of fossilfuels, such as coal, is also the biggest contributor to acid rain, which is responsible for a largepercentage of the toxins found in the Great Lakes [22]. So-called nonpoint source pollution,such as acid rain and also agricultural runoff (pesticides, fertilizers, manure), now accountsfor most of the water quality problems found in Lake Erie and its tributaries [17]. While largepoint source polluters are relatively easy to identify and regulate, controlling nonpoint sourcepollution, such as acid rain, poses a much greater challenge and requires cooperative effortsamong many different industries and governments; see, for example, [6], which outlines theU.S.-Canada Air Quality Agreement, the impetus of which was transboundary acid rain ineastern North America.

One measure that can be taken to help reduce the amount of airborne toxic contami-nants introduced into the atmosphere and entering Lake Erie in the form of acid rain is thereduction of Ohio’s dependence on electricity generated from coal-burning power plants. Inefforts aimed at reducing this dependence, the State of Ohio is requiring that 25 percent ofall electricity sold in 2025 come from alternative energy sources [3]. While some progress hasbeen made in outlining sources that will be used to help generate this alternative energy,such as General Electric’s proposed wind turbine farm in Lake Erie [20], a significant amountof work remains to be done before these energy goals can be met.

2 Statement of results or benefits

The project proposed herein aims to make progress towards meeting these alternative energygoals and towards reducing the State of Ohio’s dependence on coal-burning power plants forgenerating electricity by investigating the feasibility of generating clean, renewable energy onLake Erie through the use of so-called Wave Energy Converter devices (described in detailin the next section). Such progress will in turn have a direct effect on the water qualityof Lake Erie and the Great Lakes at large by significantly reducing the amount of airbornetoxic chemicals that enter Lake Erie in the form of acid rain from the burning of fossil fuels.

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3 Nature, scope, and objectives of the project

The primary objective of this proposal is to investigate the feasibility of generating clean,renewable energy on Lake Erie by harnessing the Lake’s wave energy through the use of anovel kinetic energy harvesting technology called nPowerR© developed by Tremont Electric,LLC, a Cleveland-based alternative energy company; see [21] and the attached letter ofsupport.

Through the development of the nPowerR© Personal Energy Generator (PEG), TremontElectric has shown that the nPower technology provides a practical and commercially viablemeans of generating clean electricity for certain applications, e.g., for recharging mobileelectronic devices (see Figure 1), by harnessing the kinetic energy generated from one’smovements. Specifically, the nPower PEG is equipped with a magnet and an induction coilthat move past each other under low frequency vibrations to generate pulses of current.Since such a system extracts maximum energy when the the input frequency is close to thenatural frequency of the generator (resonance), the nPower device is also equipped with anadaptive tuning mechanism that dynamically adjusts damping in the system based on thegiven input frequency in order to maintain resonance over time as the input frequency varies.This design feature allows the nPower PEG to operate efficiently and effectively under a widerange of different walking frequencies and amplitudes.

Figure 1: The nPower R© Personal Energy Gen-erator (PEG), which can be used to recharge mo-bile devices by harvesting the kinetic energy gen-erated from walking.

Preliminary scaling studies indicate thata larger-scale version of the nPower PEG,based on the same physical principles, couldbe used to extract energy from the verticalmotion of coastal waves on Lake Erie. Thisscaled-up nPower PEG, called the nPowerWave Energy Converter (WEC), would be en-cased in an airtight buoy and deployed in theLake, see Figure 2. Power generated by thenPower WEC would be routed directly backto the power grid on land. Tremont Electrichas proposed to use these devices in a “wavefarm” setting, where a large number of WECswould be deployed in an array to generate asignificant amount of power for delivery backto the grid, see Figure 3.

In 2009, in collaboration with Case West-ern Reserve University and The Universityof Akron, Tremont Electric undertook a pre-liminary feasibility study of nPower technol-ogy for wave energy harvesting. Specifically,extrapolation of the performance data avail-able from the nPower PEG suggested that theWEC would be capable of generating electric-ity with zero carbon emissions at a cost per kilowatt equal to the average cost per kilowattof a new coal-fired power plant [21], see Table 1.

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Table 1: Estimated cost per kilowatt hour of various energy sources.

nPower R© Wave Energy Converter (WEC) $ 0.05 per kilowatt hour

Solar $ 0.10 – $ 0.25 per kilowatt hour

Offshore wind $ 0.07 – $ 0.09 per kilowatt hour

Coal-burning power plant $ 0.05 per kilowatt hour

The work proposed for this project builds on these prior efforts and the ongoing work ofthe PI in the development of a nearshore model for Lake Erie. Specifically, in order to betterquantify the amount of energy that could potentially be generated using the WEC farmconcept and to identify optimal placement of the devices within the Lake, computer-basedwave simulations will be performed to characterize the wave energy density of Lake Erie.The methods, procedures, and facilities used to perform these simulations, and to analyzethe results, are outlined in detail in the next section.

Figure 2: A schematic of a proposed nPower R© Wave Energy Converter (WEC) encased in anairtight buoy. Power generated by the WEC would be directly routed to the power grid on land.

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Figure 3: An artist’s rendering of an nPowerR© Wave Energy Converter (WEC) “farm” inLake Erie.

4 Methods, procedures, and facilities

4.1 Methods and procedures

The wave energy simulations proposed for this project will be performed to address thefeasibility of generating energy using the WEC farm concept. These simulation effortswill make use of two critical modeling components described in detail below: 1) a high-resolution, unstructured mesh of Lake Erie that provides highly accurate measurements ofthe bathymetry and the shoreline of the Lake, see Figure 4; and 2) a computational model

that consists of a tightly coupled two-dimensional shallow water circulation/spectral waveenergy evolution model.

1) High-resolution mesh of Lake Erie: In a recent NOAA/Ohio Sea Grant project,the PI and his research group have constructed a very high-resolution, unstructured meshof Lake Erie that provides detailed and highly resolved coverage of nearshore areas. Theresolution of these nearshore areas is particularly relevant for the proposed project as theseareas would likely be good candidates for the deployment of the WEC devices, see Figure 4.In contrast to structured grids that have been used in past modeling efforts on Lake Erie,this new unstructured mesh allows the use of variable grid spacing. Specifically, a domain isrepresented by a set of “elements” comprised of triangles, quadrilaterals, or a combinationof the two, of varying sizes (tetrahedra and triangular prisms are commonly used element

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CLEVELANDMAUMEE BAY ERIEFAIRPORT HARBOR

Figure 4: The recently constructed unstructured mesh of Lake Erie showing bathymetricdepths (top) and details of the grid in four locations on the Southern shore of the Lake.

shapes in 3D). This allows unstructured meshes to accurately represent complex geome-tries introduced by both the bathymetry/topography and the shoreline with relative ease.Furthermore, unstructured meshes provide a natural and computationally efficient way ofresolving the large range of scales that is typically associated with wave problems. In manyrespects, this mesh represents the state-of-the-art in digital mapping of the Lake as it incor-porates up-to-date and accurate shoreline and bathymetric data and U.S. Geological Survey(USGS) land use/land cover data.

2) Computational models: The energy spectrum exhibited in oceans and large lakes isvery broad, consisting of energy generated from both short and long waves. Short waves, suchas wind waves and swell, have periods ranging from 0.5–25s, while long waves, associatedwith such things as storm driven surges and seiches, have much longer periods. These shortand long waves are well-separated in the energy spectrum and have well-defined spatialscales, which leads to two distinct modeling approaches. Most short-wave models in usetoday do not attempt to explicitly resolve individual winddriven waves but instead treat the

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wave field as an energy spectrum by solving an equation for the conservation of wave actiondensity (discussed in more detail below). Short wave models that use such an approach arecalled spectral or non-phase resolving wave models. Long-wave models on the other hand,or so-called circulation models, explicitly resolve the associated spatial and temporal scalesby solving forms of the equations for the conservation of mass and momentum (the so-calledshallow water equations when a hydrostatic approximation is used in the vertical). Althoughshort and long waves are separated in the energy spectrum, they do interact. For example,water levels and currents associated with long waves affect the propagation of short waves,and, in turn, short waves generate radiation stress gradients that drive set-up and currents.Short wind waves also affect the vertical momentum mixing and bottom friction, which inturn affect the circulation. These facts necessitate using a tightly coupled modeling systemapproach, consisting of both circulation and spectral wave modeling components, in orderto properly model the wave energy spectrum of Lake Erie. Many recent examples of variouslevels and degrees of sophistication of coupling between circulation spectral wave modelsused for various applications exist; see [7] and the references therein.

Lake simulations performed for this project using this type of coupled model approachand the unstructured mesh outlined above will be performed with a tightly coupled shallowwater circulation/spectral wave energy evolution model system developed in part by thePI [10, 11, 12, 13]. The shallow water component of this model system is the ADCIRC(ADvanced CIRCulation) hydrodynamic model [1]. The spectral wave model component ofthis system is the third generation SWAN (Simulating Waves Nearshore) model [2]. Theseindividual model components, as well the coupled ADCIRC + SWAN model system, aredescribed in detail below.

The ADCIRC model: ADCIRC is a computational model for solving time-dependent,free surface circulation and transport problems in two- and three-dimensions. The hydrody-namic component of this model employs a finite element method to solve the so-called shallowwater equations (SWE), which consist of equations for the conservation of momentum andmass. The 3D momentum equations in conservative form are given by [24]

∂tuxy + ∇ · (uxyu − D∇uxy) + g∇xyξ +g

ρ0

∇xy

∫ ξ

z

(ρ − ρ0)dz̃ − fck × uxy = F,

where ρ0 is the reference density and ρ is the density computed from an equation of stateand may depend on salinity and temperature.; see e.g. [9]. Surface stresses, for example,wind stress, atmospheric pressure gradient, and tidal potential are combined into a surfaceforce term F, ∇xy = (∂x, ∂y), u = (u, v, w) is the velocity vector, uxy = (u, v) is the vector ofhorizontal velocity components, fc is the Coriolis coefficient, k = (0, 0, 1) is a unit verticalvector, g is acceleration due to gravity, and D is the tensor of horizontal and vertical eddyviscosity coefficients. The continuity, or conservation of mass, equation is

∇ · u = 0.

Suitable initial conditions must also be specified on all primary variables along with lateral,free surface, and bottom boundary conditions.

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The SWE are extensively used to model flows for processes such as tides, storm surge, andflows within ocean basins, on shelves, in bays, through inlets, in lakes, in rivers, and adjacentflood-plains. The “operational” version of ADCIRC, though an evolving community basedresearch code, is robust, accurate and has been thoroughly validated. It has been extensivelyapplied by the federal and state governments and private entities including: the U.S. ArmyCorps of Engineers, who use the code to determine design elevations for the levee systems andclosures being built in Southern Louisiana; by the Federal Emergency Management Agencywho use ADCIRC to develop the coastal Digital Flood Insurance Rate Maps (DRIRMs) inLouisiana, Mississippi, North Carolina, South Carolina, Georgia, and Florida; the NationalOceanic and Atmospheric Administration who use the model for tidal and hurricane studies;the U.S. Navy; and numerous universities and private sector companies worldwide.

The SWAN model: The SWAN simulator is a well-known spectral wave model de-veloped at Delft University of Technology that predicts the evolution in geographical spacex and time t of the wave action density spectrum N(x, t, σ, θ) as governed by the so-calledaction balance equation [2, 18],

∂N

∂t+ ∇ ·

[(

cg + u)

N]

+∂

∂σ

(

cσN

)

+∂

∂θ

(

cθN

)

=Stot

σ,

where N is the action density, cg is the group velocity, u is the ambient current, cσ and cθ

are the propagation velocities in spectral space (σ, θ), and Stot represents all the source/sinkterms that generate, dissipate, or redistribute wave energy [19, 26].

Figure 5: Schematic of the coupling and parallel communica-tion between models and cores for the ADCIRC+SWAN model.Dashed lines indicate communication for all nodes within a sub-mesh, and are inter-model and intra-core. Solid lines indi-cates communication for the edge-layer-based nodes between sub-meshes, and are intra-model and inter-core.

In particular, the source term, Stot,used in SWAN includes effects ofwave growth by wind; action lostdue to whitecapping, surf breakingand bottom friction; and action ex-changed between spectral compo-nents in deep and shallow waterdue to nonlinear effects. The as-sociated SWAN parameterizationsare given in [2]. The modelhas been extensively validated incoastal regions, lakes and estuaries[18].

The ADCIRC + SWANmodel: In a collaborative effortamong several U.S. Universitiesand researchers at the Techni-cal University-Delft, Netherlands,a tightly coupled two-dimensionalshallow water circulation/spectralwave energy evolution model usingthe ADCIRC and SWAN modelshas been developed. The implementation allows for two-way dynamic coupling of long wavecirculation and short wave physics on common unstructured meshes. The two-way coupling

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is accomplished using the following procedure. ADCIRC solves the depth-averaged shallowwater equations using time steps on the order of seconds or minutes, while SWAN solves forthe wave physics over time steps of several minutes. Given ADCIRC currents, SWAN solvesfor wave radiation stresses. These stresses are then fed into ADCIRC at approximately 15minute time intervals, at which point currents are updated and fed back into SWAN. Themodels have been coupled into a single, MPI-based parallel framework, and run on the samemesh; see Figure 5. Testing of the coupled model, for example on data from HurricanesKatrina and Rita, show dramatic improvement over previous wave/current couplings [7].

Simulations with the coupled ADCIRC + SWAN model will be performed using availablewind and atmospheric condition data to force the models. The obtained results will be ana-lyzed to assess the evolution of the wave energy density of the Lake over an extended periodof simulation time (possibly a year or two) in order to observe seasonal variations. Morespecifically, simulation results will be analyzed and post-processed to estimate the amountof energy that could be potentially generated using the WEC farm concept. Additionally,“hot spots” of wave energy within the Lake will also be identified in an effort to maximizethe amount of energy that could be generated. However, placement of the WEC buoys willnot only be dictated by the wave energy density of a particular spot but also by additionalfactors such as the proximity to shore and populated areas. Collectively, these factors willbe taken into account in an attempt to identify optimal spots for the deployment and set-upof an initial WEC farm.

4.2 Facilities

Computing resources required for this project are housed in the PIs computing lab facilityin the Department of Civil and Environmental Engineering and Geodetic Science (CEEGS)at OSU. This lab facility has dedicated space for the graduate student working under thedirection of the PI for this project. Computer workstations equipped with the EnvironmentalModeling System, Incs (EMSIs) Surface Water Modeling System (SMS) mesh developmentand visualization software [5] are available. SMS is a comprehensive software package for one-, two- and three-dimensional hydrodynamic modeling. It includes a complete set of toolsfor importing, creating and manipulating various formats of geometric data and includesseveral robust algorithms to insure that acceptable aspect ratios for individual elements andsmooth element size transitions are met in order to insure stable and accurate calculationswith unstructured mesh models. Additionally, the resources of the CEEGS Mapping andGIS Lab will be available.

Several HPC platforms are available to perform the simulation pertaining to this project.The PI has a small-scale, in-house computing cluster, which has dedicated compute nodesfor the PI. The availability of this cluster will aid greatly in the initial testing of the codes. Interms of larger-scale computing clusters that will be necessary for many of the simulations,HPC resources are available at both The Ohio Supercomputer Center (OSC) and the TexasAdvanced Computing Center (TACC). The OSCs flagship supercomputing system is Glenn,an IBM e1350 system with more than 4200 Opteron processor cores connected together by10 Gbps Infiniband. Other supercomputing resources available at the Center include severalsmaller Opteron clusters as well as Itanium-2 based systems from HP and SGI. OSC alsohouse a Mass Storage Environment, which consists of servers, data storage systems, and

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networks that provide a number of storage services to OSC HPC systems. TACCs flagshipcluster, Ranger, which is the largest HPC system in the world for open science research,has over 62,000 processing cores. Although the ADCIRC code has been previously run onnumerous HPC platforms (including TACCs Ranger), this project will be the first attempt tocompile and execute ADCIRC on OSCs HPC machines. This process, while being relativelystraight forward, will require a cooperative effort with OSC personnel.

4.3 Timeline of proposed work

The proposed work for this project will follow the schedule outlined in detail in the tableon the following page. Briefly, initial collection and processing of wind and atmosphericcondition data for forcing the model will take place in the first quarter along with thebeginning of model compilation and initial testing of the model on OSCs super computers,which will extend into the second quarter. Model simulations and an initial analysis of modelresults will take place in the third quarter followed by a final assessment of model resultsand the formulation of recommendations based on these results.

Table 2: Timeline of proposed work

Task 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter

Collection and processing of wind and X X X

atmospheric condition model inputs X X XX

X

Model compilation and initial model X X X

testing on OSCs supercomputers X X X X X XX

X

Performance of model simulations and X X X

initial analysis of results X X X X X XX

X

Final assessment of model results X X X

and recommendations X X X X X XX

5 Related research

While there have been several modeling efforts on Lake Erie (see, for example, [8, 14, 16, 25]),to the PIs knowledge there have be no coupled circulation/spectral wave model simulationsperformed to assess the wave energy density of the Lake and its potential to be used asan alternative energy source. It should be noted that the most notable modeling effort onLake Erie in the past resulted in the existing predictive modeling framework for the Lakeknown as the Lake Erie Operational Forecast System (LEOFS), which is a National Oceanic

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and Atmospheric Administration (NOAA) project that aims to provide predictions of waterlevels, water currents and water temperatures in Lake Erie to user communities [4]. A currentNOAA/Ohio Sea Grant project obtained by the PI aims to improve the modeling capabilityof this system by using unstructured meshes to correct some deficiencies of LEOFS in thenearshore as noted in a 2007 NOAA skills assessment report. As noted previously, it willbe particularly relevant to model these nearshore areas correctly for the proposed project asthese areas would likely be good candidates for the deployment of the WEC devices. Thus,there would be a strong synergy between the PIs current NOAA/Ohio Sea Grant projectand the project proposed here.

6 Training potential

The success of this project will rely on the direct involvement of a graduate student. The PIcurrently has three graduate students that could potentially work on this project. In additionto furthering the education and training of a graduate student, the work developed under thisproject will also result in the dissemination of results through journal publications, conferenceproceedings and presentations at international conferences, seminars and workshops and leadto the transfer of technology and findings to federal agencies such as NOAA and USGS andstate agencies such as Ohio Sea Grant and the Ohio Department of Natural Resources, forexample.

7 Investigator’s qualifications

See attached CV.

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References

[1] ADCIRC development group website, http://www.nd.edu/~adcirc/

[2] N. Booij, R.C. Ris and L.H. Holthuijsen, 1999, A third-generation wave model for coastalregions, Part I, Model description and validation, J. Geoph. Research, C4, 104, pp. 7649-7666, 1999.

[3] Chicago Tribune, http://www.chicagotribune.com/news/

chi-ap-in-renewableenergy-i,0,4249721.story

[4] Great Lakes Operational Forecast System (GLOFS), http://tidesandcurrents.noaa.gov/ofs/glofs.html

[5] Environmental Modeling System, Inc, http://www.ems-i.com/SMS/SMS_Overview/

sms_overview.html

[6] B. McLean and J. Barton, U.S.–Canada cooperation: the U.S.-Canada air quality agree-ment, Journal Of Toxicology And Environmental Health. Part A, 71 (9-10), pp. 564-569,2008.

[7] J.C. Dietrich, M. Zijlema, J.J. Westerink, L.H. Holthuijsen, C. Dawson, R.A. Luettich,R. Jensen, J.M. Smith, G.S. Sellig and G.W. Stone, Modeling hurricane waves andstorm surge using integrally coupled, scalable computations, submitted to Journal ofAtmospheric and Ocean Technology.

[8] J. Kaur, G. Jaligama, J.F. Atkinson, J.V. DePinto, A.D. Nemura Modeling dissolvedoxygen in a dredged Lake Erie tributary, Journal of Great Lakes Research, 33(1), pp.62–82, 2007.

[9] http://mason.gmu.edu/bklinger/seawater.pdf

[10] E.J. Kubatko, J.J. Westerink and C. Dawson, hp Discontinuous Galerkin methods foradvection dominated problems in shallow water flow, Computer Methods in AppliedMechanics and Engineering, 196, pp. 437-451, 2006.

[11] E.J. Kubatko, J. J. Westerink and C. Dawson, Semi-discrete discontinuous Galerkinmethods and stage exceeding order strong stability preserving Runge-Kutta time dis-cretizations, Journal of Computational Physics, 222, pp. 832-848, 2007.

[12] E.J. Kubatko, S. Bunya, C. Dawson, J.J. Westerink, Dynamic p-adaptive Runge-Kuttadiscontinuous Galerkin methods for the shallow water equations, Computer Methods inApplied Mechanics and Engineering, 198, pp. 1766-1774, 2009.

[13] E.J. Kubatko, S. Bunya, C. Dawson, J.J. Westerink, C. Mirabito, A Performance com-parison of continuous and discontinuous finite element shallow water models, Journalof Scientific Computing, 40, pp. 1573-7691, 2009.

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[14] L.K. Leon, I.J. Imberger, R.E.H. Smith, R.E. Hecky, D.C.L. Lam, W.M. Schertzer,Modeling as a tool for nutrient management in Lake Erie: a hydrodynamics study,Journal of Great Lakes Research, 31, pp. 309–318, 2005.

[15] G. Matisoff, D.R. Aguilera, M. Thullner, Reactive transport modeling of sediment oxygendemand in Lake Erie sediments, Proceedings of the 14th Annual V.M. GoldschmidtConference, 68(11), pp. A339-A339, 2004.

[16] M.H. Moeini, A. Etemad-Shahidi, Wave Parameter Hindcasting in a Lake Using theSWAN Model, Scientia Iranica Transaction A – Civil Engineering, 16 (2), pp. 156–164,2009.

[17] Ohio Department of Natural Resources, Lake Erie Coastal NonPoint Pollution Con-trol, http://www.dnr.state.oh.us/soilandwater/programs/coastalnonpoint/

default/tabid/8861/Default.aspx

[18] R.C. Ris, N. Booij and L.H. Holthuijsen, A third-generation wave model for coastalregions, Part II, Verification, J. Geoph. Research, C4, 104, pp. 7667-7681, 1999.

[19] W.E. Rogers, P.A. Hwang, and D.W. Wang, Investigation of wave growth and decay inthe SWAN model: three regional-scale applications, J. Phys. Oceanogr., 33, pp. 366-389,2003.

[20] Rueters, http://www.reuters.com/article/idUSTRE64N49H20100524

[21] Tremont Electric, LLC, http://www.npowerpeg.com/

[22] U.S. EPA, Great Lakes Monitoring, http://www.epa.gov/glnpo/monitoring/great_minds_great_lakes/social_studies/acid_rain.html

[23] U.S. Energy Information Administration, http://www.eia.doe.gov/

[24] C.B. Vreugdenhil, Numerical Methods for Shallow Water Flow, Kluwer Academic Pub-lishers, Dordrecht, Germany, 1994.

[25] J. Wang, HG. Hu, D. Schwab, G. Leshkevich, D. Beletsky, N. Hawley, A. Clites, Devel-opment of the Great Lakes Ice-circulation Model (GLIM): Application to Lake Erie in2003-2004, Journal of Great Lakes Research, 36 (3), pp. 425–436, 2010.

[26] M. Zijlema, Computation of wind-wave spectra in coastal waters with SWAN on un-structured grids, Coastal Engineering, in press.

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