I
n . J. Exe gy, Vol. x, No.
x
, xxxx 1
Copy igh © 200x Inde science En e p ises L d.
Quan i ica ion o he idal s eam exe gy in he
ía de Vigo (NW Spain)
Ma c Mes es*
In e na ional Cen e o Coas al Resou ces Resea ch (CIIRC),
c/ Jo di Gi ona 1-3, Mòdul D1,
Ba celona, 08034, Spain
and
Labo a o i d’Enginye ia Ma í ima (LIM-UPC),
Uni e si a Poli ècnica de Ca alunya-Ba celonaTech,
c/ Jo di Gi ona 1-3, Mòdul D1,
Ba celona, 08034, Spain
Fax: +34 934011861
Email: [email p o ec ed]
*Co esponding au ho
Ma ia G iñó
Labo a o i d’Enginye ia Ma í ima (LIM-UPC),
Uni e si a Poli ècnica de Ca alunya-Ba celonaTech,
c/ Jo di Gi ona 1-3, Mòdul D1,
08034 Ba celona, Spain
Email: m.g [email protected]
Joan Pau Sie a and Césa Mösso
In e na ional Cen e o Coas al Resou ces Resea ch (CIIRC),
c/ Jo di Gi ona 1-3, Mòdul D1,
Ba celona, 08034, Spain
and
Labo a o i d’Enginye ia Ma í ima (LIM-UPC),
Uni e si a Poli ècnica de Ca alunya-Ba celonaTech,
c/ Jo di Gi ona 1-3, Mòdul D1,
Ba celona, 08034, Spain
Email: joan.p[email p o ec ed]u
Email: [email p o ec ed]
Abs ac : The exe gy o he idal cu en s in he ía de Vigo a ea (NW Spain)
is quan i ied using he esul s o a 28-day long simula ion o he idal lows.
The esul s show ha he no he nmos s ai connec ing he ía wi h he
A lan ic Ocean is a p omising si e o idal ene gy apping, in con as wi h he
ene ge ically weake es ua y. On he basis o he a e age powe densi y (APD),
a 7.5 km2 egion is iden i ied in his s ai as he mos ad an ageous a ea
o ins all idal ene gy con e e s (TECs), wi h a o al annual exe gy o a ound
2
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3865 MWh/m2. Simila analyses using only 14-day simula ions change his
alue in 16%, depending on whe he he idal cycle conside ed is apogean o
pe igean. The s udy con ibu es o enla ge he in en o y o si es along he NW
Spanish coas a which idal s eam ene gy can be po en ially ex ac ed.
Keywo ds: ía de Vigo; idal cu en exe gy; meso idal es ua y; nume ical
modelling; ROMS_AGRIF.
Re e ence o his pape should be made as ollows: Mes es, M., G iñó, M.,
Sie a, J.P. and Mösso, C. (xxxx) ‘Quan i ica ion o he idal s eam exe gy in
he ía de Vigo (NW Spain)’, In . J. Exe gy, Vol. x, No. x, pp.xxx–xxx.
Biog aphical no es: Ma c Mes es is a Resea che wi h o e 20 yea s
expe ience in he Nume ical Modelling o Coas al Hyd odynamics and
Dispe sion. He holds a PhD in Physics (UPC, 2002), and has aken pa in
many publicly unded esea ch p ojec s. He has published o e 25 pape s
in pee - e iewed jou nals, mo e han 40 con ibu ions o scien i ic con e ences
and mee ings and 24 echnical and esea ch epo s.
Ma ia G iñó is a Ci il Enginee specialised in Wa e Enginee ing and
Renewable Ene gies. She ob ained he Mas e ’s deg ee a he Uni e si a
Poli ècnica de Ca alunya – Ba celonaTech in 2015, and is cu en ly a P ojec
Coo dina o a OCA Chile.
Joan Pau Sie a is a PhD in Ci il Enginee ing, and Full P o esso a he
Uni e si a Poli ècnica de Ca alunya (UPC). He de elops his esea ch ac i i y
in he ield o Coas al Enginee ing, in pa icula in he s udy o physical
p ocesses and nume ical modelling o hyd odynamics in coas al a eas.
He has published mo e han 60 esea ch pape s in SCI jou nals, mo e han
170 communica ions in con e ences and wo kshops and 120 echnical and
esea ch epo s. He has supe ised 12 PhD heses, six MSc heses and
60 g adua ion heses.
Césa Mösso ecei ed his PhD in Ma ine Sciences a Uni e si a Poli ècnica de
Ca alunya (UPC), and is an Associa e P o esso in he Depa men o Ci il and
En i onmen al Enginee ing (DECA). His esea ch is ocused essen ially on he
ield o ma i ime enginee ing, and his cu en ac i i y is cen ed on he da a
analysis o coas al and ha bou hyd odynamics, and issues ela ed o clima e
change and he ela ed impac s in he coas al zone.
1 In oduc ion
Wi hin he global con ex o g owing ene gy demand, dec easing ese oi s o
con en ional ossil uels and ising en i onmen al awa eness, ocus has shi ed owa ds
he p oduc ion o sus ainable ene gy. Nume ous s udies ha e been de o ed in he las
wo decades o assess he exe gy o di e en po en ial sou ces o ene gy, such as sola
adia ion (Edala i e al., 2016; Ku goz and Deniz, 2016), wind (Öz ü k, 2011) o he
a ious ma ine op ions (B yden e al., 2007; Miguel and Aydin, 2012; Libe i e al.,
2013). In his sense, idal cu en s appea o be one o he mos p omising sou ces o
g een ene gy (O’Rou ke e al., 2010). Al hough he p inciples behind wind and idal
powe ex ac ion a e essen ially he same, he e a e some ac o s ha a ou he la e ,
Quan i ica ion o he idal s eam exe gy in he ía de Vigo (NW Spain) 3
among hem he high p edic abili y o idal cu en s as compa ed o a mosphe ic lows,
o he minimum en i onmen al impac associa ed o idal ene gy-ex ac ing acili ies
(Iglesias e al., 2012). In addi ion, he highe densi y o seawa e (o e 800 imes ha
o ai ) gua an ees ha , o ypical luid speeds and unde equal ex ac ing condi ions
(i.e., c oss-sec ional a ea), he powe gene a ed by a idal ene gy con e e (TEC) will be
compa able o ha gene a ed by a wind ene gy con e e .
Recen ly, idal exe gy has been e alua ed a di e en coas al egions, using ei he
ex ensi e ield campaigns o nume ical modelling, as a i s s ep owa ds iden i ying
sui able loca ions o idal s eam exploi a ion and o quan i y he le el o ene gy ha can
be ex ac ed. Some examples include he UK (D ape e al., 2014; Xia e al., 2010),
he USA (B ooks, 2011), Canada (Ka s en e al., 2008) o No way (G abbe e al., 2009),
bu also he coas s o de eloping coun ies such as I an (Rashid, 2012) o China (Li e al.,
2010).
In he pa icula case o Spain, enewable sou ces p o ide 14.4% o he p ima y
ene gy ha is used (APPA, 2015), and one- hi d o he elec ici y p oduced (APPA,
2016). O he la e , 90% is p o ided by wind, hyd aulic and sola sou ces (MINETUR,
2014). Ne e heless, in he las ew yea s he in e es in ma ine sou ces o ene gy has
inc eased conside ably. Mos o i has been ocused on wa e exe gy (e.g., Iglesias and
Ca ballo, 2005; Sie a e al., 2013), bu idal ene gy esou ces ha e also been e alua ed a
se e al si es along he Spanish coas (Ca ballo e al., 2009; Mösso e al., 2015).
Wi h he goal o con ibu ing o he map o si es o po en ially exploi able idal
cu en ene gy, in his pape we assess he exe ge ic po en ial o he idal s eam in he
ía de Vigo a ea, in he No hwes Spanish A lan ic coas . Fo his, we use he esul s o a
28-day nume ical simula ion employing a p e iously alida ed 3D hyd odynamic model.
The analysis allows iden i ying he a ea in which he a ailable idal exe gy is he la ges
and is, hus, he mos app op ia e heo e ical loca ion o he de elopmen o a TEC plan .
2 S udy a ea
The ía de Vigo (Figu e 1) is he sou he nmos o he ou ías Baixas, loca ed in he
No hwes e n Spanish A lan ic coas . I s e ches app oxima ely 32 km in a ough
NE-SW di ec ion, wi h an ex e nal wid h o 10 km and a dep h in i s cen al pa o abou
26 m, which dec eases apidly owa ds he banks (Ma ín, 2003). This ía co e s an a ea
o abou 185 km2, and has a olume capaci y sligh ly la ge han 3250 Hm3, yielding a
su ace/ olume a io o 0.05, ypical o V-shaped es ua ies (Noguei a e al., 1997).
The wa e body is connec ed o he A lan ic Ocean h ough h ee channels de ined by he
p esence o he Cíes Islands a he es ua y mou h. The no he n channel is a ound 2.5 km
wide, wi h a maximum dep h o 23 m, while he sou he n mou h is wide and deepe
(5 km and 52 m, espec i ely), and he cen al channel, sepa a ing bo h islands,
is na owe and shallow (Mon e o, 1999).
As onomical ides cons i u e he p incipal con ibu ion o he sea le el a ia ions in
his a ea. The idal wa e p opaga ion along he ía is synch onic, a leas downs eam
om he Rande S ai , showing no signi ican g adien s nei he in ampli ude no in phase.
The idal ange a ies be ween 0.82 m and 4.21 m, wi h a mean alue o 2.4 m. Sea le el
a ia ions associa ed o s o m su ge a e ypically much smalle , al hough alues o
1.08 and 0.69 m ha e been obse ed du ing he 1992–2009 pe iod (Ál a ez e al.,
2005).
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Figu e 1 Map o he s udy a ea, and i s loca ion in he NW Spanish coas . The dashed line shows
he local compu a ional domain used o he analyses in his s udy (see online e sion
o colou s)
The semidiu nal meso ides also condi ion he ci cula ion pa e ns in he es ua y
(Mes es and Sie a, 2011), oge he wi h he wind egimes on he con inen al shel and in
he ía i sel , and he eshwa e discha ge o he Oi abén-Ve dugo i e sys em.
The la e , howe e , is ela i ely low, wi h a mean annual discha ge o 11 m3/s (Ma ín,
2003), and maximum mon hly mean alues anging be ween 56 m3/s and 12.5 m3/s. The
esidual ci cula ion is also a ec ed, mainly du ing he summe , by equen upwelling
e en s (Ma ín, 2003). The ela i e combina ion o he a ious o cing mechanisms
allows o de ine h ee di e en egions om a hyd odynamic poin o iew. The shallow
and wide basin a he es ua y head is domina ed by i e ine ou pu and cu en s induced
bo h by he ide and he local wind. The a ea closes o he mou h (be ween he Cíes
Islands and he line joining Ma Cape and Bo nei a Tip) is in luenced mos ly by idal
cu en s and lows d i en by he wind blowing o e he con inen al shel , whe eas he
cu en s in he cen al s e ch migh be d i en by any o all o he a o emen ioned
o cings. Obse a ions in he ía show ha he ide is he main d i e o wa e cu en s,
pa icula ly in he deepe laye s in which he in luence o he wind is no so impo an
(Ma ín, 2003). Nea he su ace, he e ec o he local wind becomes signi ican ,
accoun ing o up o 94% o he cu en a iabili y. Su ace lows measu ed in he ía a e
ypically be ween 0.3 and 0.8 m/s, bu can locally exceed 1.25 m/s; in he bo om laye s,
hese cu en s a e weake , anging om 0.06 m/s o 0.15 m/s (Ma ín, 2003).
3 Me hodology
The idal s eam exe gy o he ía de Vigo has been es ima ed om he esul s o a
28-day nume ical simula ion using a 3D hyd odynamic model o ced a he bounda ies
exclusi ely by idal sea le els and cu en s. The e ically in eg a ed eloci y hus
ob ained has hen been used o assess he powe densi ies using he equa ions desc ibed
below. Whe eas p e ious nume ical s udies ha e ypically used a ep esen a i e
sp ing-neap idal cycle (i.e., 14 days) o accoun o he co esponding idal cu en
Quan i ica ion o he idal s eam exe gy in he ía de Vigo (NW Spain) 5
a ia ion, Byun e al. (2013) poin ou ha a leas a luna mon h (28 days) should be
conside ed o a oid mises ima ing he mean annual ene gy by neglec ing he e ec s o
he changes in he Ea h–Moon dis ance. In hei s udy o idal ene gy esou ces in Ko ea,
hey ound ha he annual ene gy po en ial could be unde - o o e es ima ed by as much
as 12%, depending on whe he he selec ed 14-day cycle ep esen ed an apogean o
pe igean ide.
3.1 The nume ical model
The simula ion o he idally-induced cu en s a he ía de Vigo was ca ied ou using he
AGRIF e sion o he ROMS sys em (Regional Ocean Modelling Sys em). I is a 3D,
ee-su ace, e ain- ollowing nume ical model ha sol es he Reynolds-a e aged
Na ie –S okes equa ions using he hyd os a ic and Boussinesq assump ions (Shchepe kin
and McWilliams, 2005). ROMS uses he A akawa-C di e encing scheme o disc e ise
he ho izon al g id in cu ilinea o hogonal coo dina es, and ini e di e ence
app oxima ions on e ical s e ched coo dina es (Haid ogel e al., 2008). The model
ollows a spli -explici app oach in which he e olu ion o he ba o opic (i.e., ee
su ace and 2DH eloci ies) and ba oclinic ( empe a u e, salini y and 3D momen um)
e ms a e sol ed sepa a ely, using di e en ime s eps. This echnique conside ably
educes he du a ion o he simula ions, wi hou a ec ing he alidi y o he solu ions.
The nume ical de ails o ROMS a e desc ibed ex ensi ely in Shchepe kin and
McWilliams (2005).
The AGRIF e sion o ROMS (Pen en e al., 2006) was chosen o ake ad an age o
he se o p e- and pos -p ocessing ou ines, con ained in he ROMS_TOOLS package
(Pen en e al., 2007), which acili a es he p epa a ion o he inpu iles. Bo h he ROMS
and ROMS_AGRIF models ha e been success ully applied in a a ie y o di e en
scena ios wi h a ying spa ial scales (Kim and Lim, 2009; Mes es e al., 2010, 2014;
Wa ne e al., 2005).
Ce albo e al. (2013) implemen ed he ROMS_AGRIF model in he domain
ma ked in Figu e 1 using a 176 u 153 mesh, wi h a ho izon al esolu ion o 150 m and
10 sigma-laye s in he e ical di ec ion. They nes ed his local domain in a la ge mesh
wi h hyd odynamic da a ob ained by he Galician Me eo ological Se ice (Me eogalicia)
using he MOHID model. Fla he and O lanski condi ions we e p esc ibed o he 2D
and 3D a iables, espec i ely, a he open bounda ies. The ho izon al di usion was
eplica ed using he Laplacian scheme desc ibed in Song and Haid ogel (1994), while he
LMD-KPP closu e scheme was used o e ical mixing (La ge e al., 1994).
This implemen a ion was alida ed using idal gauge da a, cu en s om a HF-Rada
and a Ho izon al Acous ic Dopple Cu en P o ile , and se e al CTD p o iles wi hin he
es ua y. These au ho s ound ha he model ep oduced accep ably well he obse ed sea
le el a ia ions and he su ace cu en s (wi h oo -mean-squa e e o s be ween 0.07 and
0.13 m o he o me , and a ound 0.07 m/s o he la e ), whe eas i showed some la ge
e o s o he salini y p o iles, which hey associa ed o inaccu acies in he eshwa e
inpu s. O e all, hey concluded ha hei implemen a ion eplica ed he hyd odynamic
beha iou in he ía de Vigo o an accep able deg ee.
Fo he pu pose o his s udy, some simpli ica ions ha e been in oduced in Ce albo
e al.’s (2013) app oach. Densi y-d i en lows ha e been dis ega ded by conside ing a
cons an and uni o m wa e densi y o 1025 kg/m3, ob ained om ypical obse a ional
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alues, and supp essing i e discha ges a he head o he es ua y. Wind-induced e ec s
ha e also been igno ed, se ing a ze o wind speed h oughou he simula ed pe iod.
The model is hen o ced exclusi ely by idal ele a ions and cu en s, ob ained om
he TPXO7.2 global model da abase (Egbe and E o ee a, 2002). Compa ison o he
TPXO7.2 idal pa ame e s wi h hose om o he da abases such as he LEGOS FES2004
(Le e e e al., 2002) o he No h A lan ic (AO) OTIS egional model, shows e o s o
he o de o 1%, mos ly in he mino idal cons i uen s, indica ing ha he idal o cing is
well speci ied. The code has been un o a comple e 28-day idal mon h, using ba o opic
and ba oclinic imes eps o 2 and 18 s, espec i ely, and p o iding hou ly in o ma ion on
he sea le el and he 2DH and 3D cu en eloci ies inside he domain.
3.2 Es ima ion o he po en ial idal s eam exe gy
The exe gy o a low o ma e (ai o wa e , o ins ance) can be de ined as he maximum
wo k ha can be acqui ed when he ma e lows om i s o iginal s a e o ha o he
ambien (Sahin e al., 2006). This is equi alen o he ene gy esou ce, i.e., he amoun o
ene gy ( heo e ically) a ailable o be exploi ed (Dince and Rosen, 2007). In he
pa icula case o u bines placed in a low, he ene gy ha can be ac ually ex ac ed will
depend essen ially on he kine ic ene gy o he low and on he o e all pe o mance o he
u bine. The la e a iable is a measu e o he exe gy ha is los du ing he ene gy
con e sion p ocess due o, among o he s, he mechanical unc ioning o he de ice.
The exe ge ic balance du ing he ull ans o ma ion p ocess is gi en by
Ex K H S' ''' (1)
whe e 'K, 'H and 'S a e he changes in he sys em’s kine ic ene gy, en halpy and
en opy, espec i ely. Thei de ailed exp essions depend on he di e ence in magni ude
o some low pa ame e s ( low speed, empe a u e and p essu e) up- and downs eam
om he u bine, and can be ound in Sahin e al. (2006) o Hoge waa d and Dince
(2014).
Since he goal o his s udy is o e alua e he po en ially exploi able idal s eam
esou ce, i is assumed he eina e ha he e a e no exe ge ic losses du ing he ene gy
ans o ma ion p ocess. A u he analysis conside ing he e ec s o se e al ac o s, such
as u bine pe o mance, on he powe ou pu om a se ies o u bines is p esen ed in
Mes es e al. (2016).
Acco ding o Hoge waa d and Dince (2014, ci ed in Mousa i, 2012), he op imum
powe ou pu o a u bine can be de ined as he kine ic ene gy o a luid in a s eam ube
wi h a diame e equal o ha o he u bine o o , i.e.,
3
1
2
p
PC AV
U
(2)
whe e P is he o al powe ou pu om he TEC (W), ȡ (kg/m3) is he densi y o he luid,
A (m2) is he c oss-sec ional a ea o he TEC’s o o blades and V (m/s) is he low
eloci y a e aged o e his a ea. The powe coe icien Cp is in oduced o accoun o
he loss in gene a ed powe ela i e o he heo e ically a ailable powe due o se e al
ac o s. These migh include u bine speci ics (i.e., e ical o ho izon al axis u bine,
pe o mance), he pi ch angle o he blades o he u bine (Bahaj e al., 2007), he ela i e
Quan i ica ion o he idal s eam exe gy in he ía de Vigo (NW Spain) 7
posi ion o he u bine wi hin an a ay plan deploymen (Blunden and Bahaj, 2007) o
he a iabili y o he inciden low speed. Al hough he maximum heo e ical alue o Cp
is gi en by Be z’s limi (0.59 – which can ne e heless be exceeded unde ce ain
condi ions; Vennell, 2013), in p ac ice he accep ed alues o idal s eam u bines ange
be ween 0.3 and 0.5 (Ba en e al., 2007; Vennell, 2013).
F om his equa ion, he powe po en ially accessible o a TEC can be ob ained by
se ing Cp = 1. Thus,
3
1
2
PAV
U
(3)
Fo TECs, he a e age powe densi y (APD) du ing one idal cycle, in W/m2 can be
ob ained using he ou pu om a hyd odynamic nume ical simula ion, as
3
1
11
APD 2
N
i
i
V
N
U
¦ (4)
whe e Vi (i = 1, …, N) is he eloci y a ime i o he modelled ime se ies, and N is he
numbe o da a alues.
4 Resul s and discussion
Because o he simpli ica ions in oduced in o he model (no wind o cing, no densi y
cu en s) a di ec alida ion o he simula ion esul s wi h obse a ional da a is no
easible. Howe e , as men ioned be o e, he implemen a ion used he ein has been
accep ably alida ed by Ce albo e al. (2013), and he esul s ob ained show an
accep able ag eemen (in bo h ci cula ion pa e ns and magni udes) wi h o he s udies
a ound he same a ea published in he li e a u e (e.g., Mon e o, 1999). As an example, he
mean alues o he cu en s ob ained in his wo k a e o he same o de (60–70 cm/s) as
he su ace cu en s measu ed by a high- equency ada and used in Pied acoba e al.
(2016). This allows placing some con idence on he eliabili y o he ob ained nume ical
esul s.
The ou pu om he ROMS_AGRIF model shows ha , in gene al, he highes
eloci ies in he domain a e no ound wi hin he es ua y, bu a he in he no he n
channel sepa a ing he es ua y om he A lan ic Ocean (Figu e 2), be ween he la ges o
he Cíes islands (Mon eagudo o Illa No e) and he mainland. In his sec ion, he idal
low becomes accele a ed due o he na owing o he basin, du ing bo h he lood and
ebb phases o he ide. Inside he ía, maximum low eloci ies a e o he o de o 1 m/s,
ba ely exceeding he h eshold abo e which he cu en s con ain enough ene gy o
p ac ical ex ac ion (Mye s and Bahaj, 2005).
On he o he hand, he maximum low speeds in he no he n channel a e much la ge .
A mid- lood du ing he sp ing ide, cu en s nea he ip o he peninsula a e close o
2.5 m/s, and a e sligh ly weake a mid-ebb (2.2 m/s), indica ing a lood-domina ed
ebb- lood asymme y in he idal low. No e ha he posi ions a which he maximum
alues o he cu en a e a ained a mid- lood and mid-ebb (PF and PE in Figu e 2) a e
no he same, bu a e sepa a ed by abou 1 km in he la i udinal di ec ion.
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Figu e 2 Ba o opic cu en s in he domain a mid- lood ( op) and mid-ebb (bo om) du ing a
sp ing ide. PF and PE show he posi ions a which he cu en speed is maximum a
mid- lood and mid-ebb, espec i ely (see online e sion o colou s)
Figu e 3 ( op) shows he modelled ime se ies o dep h-a e aged cu en eloci y a bo h
posi ions, du ing he comple e 28-day cycle. Fo bo h cases, he maximum modelled
eloci ies a e la ge han he limi o 1.5–2 m/s o he mean sp ing peak idal cu en
p oposed by Xia e al. (2010) o he idal s eam powe o be wo h exploi ing.
Acco ding o he eloci y dis ibu ions in Figu e 3 (bo om) a bo h loca ions he cu en
exceeds 1 m/s jus o e one hi d o he ime (35% and 34%, espec i ely). Using hese
eloci y alues, he powe densi y o bo h semidiu nal cycles (mid- lood and mid-ebb o
a mean sp ing ide) can be calcula ed using equa ion (3), yielding a maximum peak alue
o 7.5 kW/m2 du ing he lood and 5.6 kW/m2 du ing he ebb (Figu e 4).
The APD du ing he ull simula ed pe iod can be calcula ed om equa ion (4)
using he low speed ime se ies a each compu a ional node. The esul ing dis ibu ion
(Figu e 5) e eals ha , al hough he la ges alues o APD a e again ound in he no he n
channel, he highes APD does no co espond o nei he o he nodes wi h highe peak
Quan i ica ion o he idal s eam exe gy in he ía de Vigo (NW Spain) 9
cu en s (PF and PE), bu o a posi ion sligh ly o he wes o PF (PM in Figu e 5). A his
poin , he APD is 1.67 kW/m2, which is signi ican ly la ge han he alues es ima ed a
PF (0.96 kW/m2) and PE (0.71 kW/m2). The ime a ia ion o he powe densi y a PF
and PE, calcula ed using he cu en se ies gi en in Figu e 3 ( op), is shown in Figu e 6.
The o al ene gy a ailable o ex ac ion a hese poin s du ing bo h modelled idal cycles
is he a ea unde he cu es. The es ima ed ene gy densi ies o he simula ed pe iod a PF
and PE a e 647.63 kWh/m2 and 478.71 kWh/m2, espec i ely, which co espond o an
annual ene gy densi y o 8.44 MWh/m2 and 6.24 MWh/m2. A simila in eg a ion a PM
yields conside ably highe ene gy densi ies, abou 1122.24 kWh/m2 o he simula ed
pe iod and a ound 14.64 MWh/m2 o an en i e yea . A all h ee poin s, he a ailable
ene gy associa ed o he idal s eam is la ge han he maximum alue ound by Ca ballo
e al. (2009) in he nea by ía de Mu os (5.3 MWh/m2).
Figu e 3 (Top) Cu en speed modelled a posi ions PF (a) and PE (b) du ing he idal mon h.
(Bo om) His og am o modelled eloci y dis ibu ion a PF (le ) and PE ( igh )
(see online e sion o colou s)
By subs i u ing V in equa ion (3) wi h he cu en speed limi o 1 m/s gi en by Mye s
and Bahaj (2005), he minimum a ailable APD ha allows a si e o be wo h exploi ing
om an ene ge ic poin o iew can be de ined. In he ía de Vigo egion, his h eshold
is exceeded in an a ea ex ending o e 7.5 km2, in he no he n channel (Figu e 7).
The e o e, om an exe ge ic pe spec i e, his en i e egion is a po en ially sui able si e
16
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