E alua ion o u bulence- ela ed high- equency
idal cu en eloci y luc ua ion
P. Ga cia No o, Y. Kyozuka, M.J. Ginzo-Villamayo
Ve sion: Accep ed Manusc ip
HOW TO CITE
Ga cía No o, P., Kyozuka, Y., Ginzo-Villamayo , M.J. (2019). E alua ion o u bulence-
ela ed high- equency idal cu en eloci y luc ua ion Renewable Ene gy. 139. pp.
313-325.
FUNDING
The au ho s would like o hank he Minis y o En i onmen o Japan o pe mission o
publish o he da a used in his s udy, which we e ob ained h ough he p ojec o
P omo ion o Realiza ion o Tidal Cu en Powe Gene a ion suppo ed by he minis y
in 2014 and 2015.
© 2019 Else ie L d. All igh s ese ed. This manusc ip e sion is made a ailable
unde he CC-BY-NC-ND 4.0 license h p://c ea i ecommons.o g/licenses/by-nc-
nd/4.0/
Abs ac 1
Wi hin he de elopmen needed o economy iabili y o idal s eam ene gy,2
adap abili y o labo a o y con e e s o sea low condi ions is a miles one. The3
objec i e o his wo k is o in es iga e he high equency luc ua ions in cu enn 4
eloci y magni ude and di ec ion ela ed o he u bulen na u e o he low and5
p esen a new me hod o hei p edic ion. Wi h his pu pose, high equency da a6
measu ed by wo ADV (32 Hz) and wo ADCP (8 Hz) a ou di e en poin s in he7
sea a ea su ounding Go o Islands (Japan) a e analyzed. The da a we e di ided in8
sho - ime samples (3-minu es da a o ADV and 5-minu es da a o ADCP) and9
ea ed sepa a ely. Veloci y magni ude i s a no mal dis ibu ion, wi h p edic ion10
le els highe han 95% o a ma gin o e o o 0.25 m/s when compa ing di e en 11
pe cen iles be ween 0.1 and 99.9. Flow di ec ion is analyzed in e ms o opening12
angle be ween wo ep esen a i e pe cen iles equidis an om he median(99.9-0.1,13
95-5,. . . ), gi ing as a esul a lep oku ic dis ibu ion, mo e ou lie -p one han no -14
mal. Empi ically, o opening angles 99.9-0.1, 97.7-2.3 and 95-5, slopes o 6.79 (615
in no mal dis ibu ion), 4.17 (4) and 3.38 (3.29) we e ound, wi h esul s simila o16
a heo e ical no mal dis ibu ion o na owe angles. The new p edic ion me hod17
o high equency luc ua ions is based in his di ec co ela ion be ween eloci y18
magni ude and di ec ion luc ua ions wi h u bulence in ensi y and ans e se u -19
bulence in ensi y, espec i ely. These wo pa ame e s can be es ima ed indi ec ly20
by nume ical models, gi ing ise o a ool o he p edic ion o u bulence- ela ed21
high equency luc ua ion.22
Keywo ds— Tidal ene gy, Tu bulence, ADCP, ADV23
1
E alua ion o u bulence- ela ed high- equency idal24
cu en eloci y luc ua ion25
Pa xi Ga cia No o, Yusaku Kyozuka, Ma ia Jose Ginzo Villamayo 26
Janua y 21, 201927
1 In oduc ion28
Tidal s eam ene gy has been p esen ed as one o he mos p omising enewable ene gy29
op ions among o he easons due o he high p edic ion le el o a ailable esou ce. Tides30
can be de ined as he sum o cons i uen componen s as a esul o he in e ac ion31
be ween Ea h, Sun and Moon g a i a ional a ac ions, exp essed ma hema ically as32
[1]:33
ζ=
n
X
i=0
aicos(ωi +ϕi) (1)
being he ime; ai he angula equency dependen on he ela i e mo emen be ween34
Ea h, Sun and Moon; and ωiand ϕi he ampli ude and phase, espec i ely, o each35
ide cons i uen , which a ies acco ding o he geog aphical posi ion. This de ini ion has36
been a base o widely p o en ide le el p edic ion me hods [2, 3].37
Ha monic o cing simula ing ide condi ions has been also used o nume ical modelling-38
based idal s eam ene gy assessmen wo ks [4, 5, 6], wi h good ag eemen bo h in e ms39
o wa e le el [4] and idal eloci y [5, 6] when compa ing 3-minu es a e aged [6] mea-40
su ed da a wi h p edic ion esul s.41
Ne e heless, when hinking on ene gy ex ac ion, no only ides bu also cu en s42
mus be aken in o accoun . In his ega d, despi e he capabili y o ha monic analysis43
based app oaches o p edic a e aged idal cu en eloci ies [5, 6], he e a e ce ain44
cu en p ope ies ( h ee-dimensional na u e, e ec o local geomo phology and non-45
sinusoidal cha ac e is ics such as sub- idal a ia ions, sup a- idal a ia ions o u bu-46
lence) di e en iable om ides which limi hese me hods o cu en e alua ion. This47
issue was al eady poin ed a ew decades ago by Godin [7], who concluded ha cu en s48
canno be p edic ed wi h he same le el o p ecision as he ide. These a ia ions om49
he ha monic analysis-based es ima ion ha e meaning ul consequences in he u bine50
loads [8], making o his a key poin o idal s eam ene gy echnologies. A case ha 51
clea ly exempli ies his s a emen is he ailu e o an OpenHyd o u bine in he Bay o 52
Fundy in No embe 2009, due o idal lows ha we e wo and a hal imes s onge 53
han expec ed [9].54
2
Wi h he aim o ge ing a be e unde s anding o idal cu en s, Polagye e al [10]55
analyzed high equency eloci y da a measu ed in Puge Sound, obse ing wo kinds56
o a ia ions. Fi s , non-sinusoidal luc ua ions o e ime scales a ound 1 hou , which,57
al hough canno be es ima ed by ha monic analysis, exhibi a ce ain deg ee o pe i-58
odici y, allowing i s desc ip ion by si e-speci ic empi ical unc ions which mus include59
ebb and lood a ia ions o diu nal inequali y. Second, u bulence ela ed luc ua ion60
o e ime scales unde one minu e. This luc ua ion was ound mo e impo an han he61
i s one in e ms o magni ude (o e 0.5 m/s o peak cu en s) and i was conside ed62
unp edic able.63
Rega ding his second luc ua ion ype, al hough i s e ec on ene gy po en ial es i-64
ma ion is lowe , i s s udy is necessa y o u bine design conside a ions, such us blade65
loads, suppo s uc u es, seabed connec ions [11] o de ices s abiliza ion on he bo -66
om by he gene a ion o down o ce om he idal low [12]. Fo hese easons, se e al67
au ho s ha e ca ied ou u bulence s udies a po en ial idal s eam ene gy exploi a-68
ion si es based on eloci y measu emen . In hese s udies, besides he calcula ion o 69
ep esen a i e u bulen ela ed pa ame e s such as u bulence in ensi y, u bulen ki-70
ne ic ene gy o in eg al ime and leng h scales, whose cha ac e iza ion is also c ucial o 71
u bine design due o i s e ec on blade loads, powe and h us coe icien s o wake72
cha ac e is ics [13, 14, 15, 16], high equency eloci y luc ua ion was also analyzed. In73
his espec , eloci y luc ua ions wi hin a ange highe han 1 m/s du ing a 1-minu e74
pe iod o which a e aged alue was app oxima ely 2 m/s we e ound in he s eamwise75
signal o an ADV measu emen s in he Sound o Islay [17]. Also, in Kobe S ai [18],76
ins an aneous s eamwise eloci ies be ween 0.5 m/s and 2.5 m/s we e obse ed wi h an77
ADCP o a 5-minu e a e aged alue o 1.5 m/s.78
Recen ly, he e o s o idal ene gy esea che s ha e been ocused on he p edic ion o 79
u bulence condi ions a a gi en loca ion. On his poin , esul s om u bulence models80
simula ing cu en condi ions a idal s eam ene gy si es able o es ima e u bulen 81
kine ic ene gy ha e been ecen ly published [19]. In e ms o eloci y luc ua ion, Ha ding82
e al [11] p esen ed a long- e m p edic ion me hod o ex eme eloci ies (highe and83
lowe han he a e aged) based on 32 Hz and 2 Hz eloci y da a measu ed by an ADV and84
an ADCP, espec i ely, simul aneously and a he same poin in Puge Sound. Wi h one85
mon h da a, a 50-yea eloci y pe u ba ion om a 64s mean eloci y could be p edic ed.86
Howe e , he esul s show conside able disc epancies be ween he measu emen s o bo h87
de ices and “se e al yea s o da a is equi ed o pe o m he analysis o an accep able88
le el o con idence”.89
In his con ex , his s udy a emp s o seek a new me hod o p edic u bulence90
ela ed eloci y pe u ba ions bo h in e ms o magni ude and di ec ion, hus educing91
he need o in-si u measu emen , ollowing he Godin [7] sugges ion ha “ he s udy92
o cu en s is essen ially a esea ch p oblem and should no be conside ed a ma e o 93
ou ine da a p ocessing a he cle ical o echnical le el”. The p esen p oposal is based94
on he analysis o da a measu ed by wo 32 Hz ADVs (Acous ic Dopple Velocime e )95
and wo 8 Hz ADCPs (Acous ic Dopple Cu en P o ile ) a ou di e en poin s in96
Go o Islands, Japan.97
3
2 Ma e ials and Me hods98
2.1 Loca ion99
Loca ed in Nagasaki P e ec u e, sou hwes e n Japan, be ween he S ai o Ko ea and100
he Paci ic Ocean, Go o Islands is an a chipelago o med by 140 islands (see Fig.1). Fi e101
o hese islands o m ou main channels ( om wes o eas , Tanou a S ai , Na u S ai ,102
Takigawa a S ai , and Wakama su S ai ). The big amoun o wa e passing h ough103
hese channels gene a es s ong cu en s, making o his a ea a good loca ion o idal104
s eam ene gy exploi a ion. The e o e, wo o hese channels (Tanou a S ai and Na u105
S ai ) ha e been designa ed as a idal ene gy es si e by he Japanese go e nmen [20].106
A his a ea, he ide ype is ypically mixed mainly semidiu nal, being M2 he main107
idal cons i uen .
Figu e 1: Tanou a S ai , Na u S ai and Kobe S ai in Go o Islands, Nagasaki P e-
ec u e, Japan
108
The a eas selec ed o measu ing de ices ins alla ion a e Na u S ai , Tanou a S ai 109
and Kobe S ai , a small semi-enclosed channel o med by an inne island in Wakama su110
S ai ( o a mo e de ailed desc ip ion o hese channels e e o [18, 21]). The impo ance111
o he i s wo channels lies in hei high idal s eam ene gy po en ial, as men ioned112
in he p e ious pa ag aph. Kobe S ai , due o i s lowe dep h and cu en eloci y,113
could be a conside able op ion o es ing low- eloci y con e e de ices o in an ea lie 114
de elopmen s age. A b ie desc ip ion o he ou measu ing loca ions o his s udy is115
4
p esen ed below.116
2.2 Da a measu emen 117
One No ek Vec o ADV was ope a ing du ing 8 days om No embe 17 h a 0:00h o118
No embe 24 h a 17:10h in 2014 in (32◦46’45.2”N, 128◦50’3.1”E; he ea e P1), Tanou a119
S ai , be ween Fukue Island and Hisaka Island. The dimensions o his channel a e 6120
km leng h and 2 km wid h, app oxima ely. Wa e lows in a SE-NW di ec ion du ing121
lood ide and ice e sa du ing ebb ide, wi h mino a ia ions due o e y local geomo -122
phologic cha ac e is ics. In he sou he n mou h, wa e mo e is a ec ed by Ta a ajima123
Island, di iding he low in o wo bi u ca ions. The sea bo om is mainly ocky. Focus-124
ing on he measu ing poin , i is loca ed a nea ly 200 m om Hisaka Island wes e n125
coas line, whe e he a e aged dep h du ing he da a collec ion pe iod was 26.1 m. The126
ADV ins alled a 3 me e om he sea bo om a his poin was se o measu e du ing127
he i s 3 minu es o e e y 10-minu e pe iod, ollowed by 7 minu es in s and-by. This128
de ice collec s high esolu ion eloci y, empe a u e and p essu e da a. The in e nal129
sampling a e is 250 Hz, while he sampling ou pu a e was se as 32 Hz, hus collec ing130
5760 da a o e e y 3-minu e measu ing pe iod. The sampling olume dimensions a e131
15 mm diame e and 5 mm heigh . I s eloci y measu emen accu acy is 0.5% o he132
measu ed alue ±1 mm/s.133
Simul aneously, in Na u S ai (32◦49’41.1”N, 128◦58’56.4”E; he ea e P2) a second134
No ek Vec o ADV, wi h he same cha ac e is ics abo e p esen ed, was ope a ing unde 135
analogous se up condi ions. Na u channel leng h and wid h a e app oxima ely 7 km136
and 2 km, espec i ely, wi h he excep ions o he na owing due o Kaga ibisaki cape137
and Sue sujima Island. As wi h Tanou a S ai , bo om is mainly ocky and he main138
axis o ien a ion is NW-SE. The a e aged dep h du ing he 8-days pe iod a he ADV139
measu ing poin , nea ly 300 m eas o Wa abikojima Island, was 24.6 m. A his same140
channel, a app oxima ely 200 m eas om he ADV measu ing poin (32◦49’38.8”N,141
128◦54’3.7”E; he ea e P3), one No ek Signa u e 1000 AD2CP was ope a ional om142
Ap il 14 h un il May 24 h, 2016. Ne e heless, i mus be said ha quali y o da a143
collec ed du ing he las 15 days is no good enough o gua an ee eliable esul s, so144
hey we e emo ed o u he analysis. This de ice beam equency and wid h a e 1145
MHz and 2.9◦, espec i ely. The measu ing sampling olume o each beam and laye is146
de ined by a polyhed on o 142 mm heigh and 212 mm leng h, i s minimum accu acy is147
a 0.3% o he measu ed alue and he eloci y esolu ion is 0.1 cm/s. This AD2CP was148
se o cyclically measu e wi h an 8Hz sampling ou pu a e du ing 5 minu es ollowed149
by 15 minu es in s andby. The numbe o e ical laye s is 22, 1 m wid h each one, wi h150
a blanking dis ance o 1 m. Since he ime a e aged dep h du ing he measu ing pe iod151
was 35.0 m, app oxima ely wo- hi ds o he wa e column we e co e ed.152
The same AD2CP had been ope a ional om Feb ua y 27 h o Ma ch 14 h, 2014,153
a (32◦52’40.81”N, 129◦01’46.79”E; he ea e P4) in Kobe S ai . A his poin , whe e154
he ime a e aged dep h du ing his 15-day pe iod was 18.0 m, 36 e ical laye s (0.5 m155
hickness) we e measu ed wi h he same iming and equency measu ing se up (8 Hz,156
5-minu e on, 15-minu e o ) as p e iously p esen ed o P3. The blanking dis ance was157
5
se as 0.1 m. Due o he wa e column wid h limi a ions, da a measu ed o he se en158
las e ical laye s coun ing om he bo om (29 o 36) a e un eal and no conside ed o 159
he wa e low analysis. Likewise, due o bo om in e ac ion, an accu a e measu emen 160
canno be gua an eed in he deepes laye , so i is disca ded.161
2.3 Da a ea men 162
2.3.1 Signal p e ea men 163
P e ious o he eloci y luc ua ion and u bulence analysis, a da a quali y p e ea men 164
is necessa y. In he ou cases, his p e ea men consis ed o wo s eps: denoising and165
despiking. Noise was elimina ed ollowing he manu ac u e ecommenda ions, eplacing166
poin s o which co ela ion is unde 70% o he ADV signals [22] and unde 50% o 167
he AD2CP signals [23] by he linea ly in e pola ed alues. The al eady denoised signal168
was ea ed wi h a Ke nel Densi y based algo i hm de eloped by Islam and Zhu [24] and169
es ed in his kind o da a despiking. A e noise elimina ion, 5-minu e (ADCP) and 3-170
minu e (ADV) a e aged alues o he h ee signals, one o each componen o eloci y,171
we e calcula ed. Based on hese a e aged alues and using a leas squa e me hod which172
gua an ees ha he mean alue o all he 5-minu e o 3-minu e a e aged ans e se173
eloci ies du ing he measu ing pe iod is null, a o a ion angle is calcula ed o con e 174
he o iginal da a o a s eamwise (pa allel o N-S axis), ans e se (pe pendicula o175
N-S axis) and e ical coo dina e sys em. Ro a ion angles we e calcula ed sepa a ely176
o lood and ebb ide and o each measu ing poin and e ical laye (in he case o 177
ADCP). This da a o a ion allows a clea e analysis o he low cha ac e is ics.178
2.3.2 Veloci y magni ude luc ua ion179
In o de o analyze only u bulence- ela ed a ia ions and minimize he in luence o 180
o he luc ua ion gene a o ac o s, e e y da a block co esponding o a 3-minu e mea-181
su ing pe iod o ADV da a and 5-minu e measu ing pe iod o ADCP da a was ea ed182
sepa a ely. The eloci y magni ude luc ua ions a e pa ame e ized by pe cen iles. Fo 183
each da a block, pe cen iles o each mul iple o i e om 5 o 95, as well as hose pe -184
cen iles co esponding wi h sigma in ege mul iplying ac o s o a heo e ical no mal185
dis ibu ion (0.1, 2.3, 15.9, 84.1, 97.7, 99.9), a e ex ac ed.186
2.3.3 Cu en di ec ion luc ua ion187
The analysis in he cu en di ec ion luc ua ion is analogous o he p esen ed o eloci y188
magni ude. Conside ing 0◦ o Eas and 90◦ o No h, a nume ical alue is gi en o he189
di ec ion obse ed o each 8 Hz (ADCP) o 32 Hz (ADV) measu emen . Wi h hese190
alues, he same pe cen iles p esen ed in 2.1.2 a e ex ac ed om each 5-minu e o 3-191
minu e da a block. Finally, assuming symme y in sho ime pe iod da a, he luc ua ion192
in he cu en di ec ion is pa ame e ized by opening angles be ween wo pe cen iles193
equidis an om he median alue (99.9-0.1, 97.7-2.3, 95-5,. . . ). In his case, mos o 194
he 5-minu e o 3-minu e da a blocks a e “con amina ed” wi h he cu en di ec ions195
6
collec ed om e y low eloci y magni ude poin s, esul ing on opening angles much196
wide han hose o be conside ed o idal u bine designing pu poses. In o de o a oid197
his kind o con amina ion in he samples, ins an aneous low di ec ions co esponding198
wi h eloci y magni udes lowe han 0.5 m/s a e excluded o he cu en di ec ion199
analysis. A g aphic summa y o he p ocedu e o he ex ac ion o opening angles is200
p esen ed in Fig 2, showing he opening angles be ween pe cen iles 99.9 and 0.1 and201
be ween pe cen iles 70 and 30.202
Figu e 2: G aphic ep esen a ion o opening angles ex ac ion wi h pc 99.9 - pc 0.1
opening angle (blue), pc 70 - pc 30 opening angle (g een) and 0.5 m/s h eshold ( ed)
7
2.3.4 Tu bulence in ensi y and p edic ion o eloci y magni ude luc ua ion203
Labo a o y es s ha e demons a ed he in luence o u bulence in ensi y (TI) condi ions204
o he con e e de ices in e ms o a igue [13]. Fu he mo e, highe u bulence in ensi y205
alues lead o a educ ion in he eloci y de ici downs eam, wi h he maximum de ici 206
poin close o he con e e [14]; and a small educ ion in he a e aged lapwise and207
edgewise blade oo bending momen s, hough luc ua ions inc ease [15]. Fo his eason,208
u bulence in ensi y is a key pa ame e o idal s eam ene gy con e e s design.209
Tu bulence in ensi y is de ined o a gi en pe iod o ime as he a io o s anda d de i-210
a ion o a e aged eloci y magni ude (see Eq 2). Thus, when cu en eloci y app oaches211
ze o, e y high and un ep esen a i e alues a e ob ained o u bulence in ensi y. This212
e ec was obse ed and analyzed in p e ious simila s udies, neglec ing u bulence in-213
ensi y esul s o de ined “slack condi ions” ange o which idal ene gy ex ac ion is214
expec ed o be null [25]. In he p esen s udy, he uppe limi o his ange can be se 215
a 0.7 m/s, a ypical cu -in speed o idal s eam ene gy u bines [26], disca ding all216
he 3-minu e o 5-minu e da a blocks o which mean eloci y is lowe .217
TI =σV
¯
V(2)
Besides i s e ec on he con e e beha io , summa ized in he i s pa ag aph in Sec-218
ion 2.3.4, in he p esen s udy u bulence in ensi y is used as a means o he p edic ion219
o he di e en pe cen iles o eloci y magni ude. The elec ion o u bulence in ensi y220
as he pa ame e used o his pu pose is based on wo easons. Fi s , he dimension-221
less na u e o u bulence in ensi y, which makes he di ec compa ison wi h eloci ies222
possible. Second, he capabili y o nume ical me hods o i s p edic ion. Tu bulence223
in ensi y can be es ima ed om nume ical model esul s o u bulen kine ic ene gy by224
ke =3
2(Ua g ·T I)2[19]. Fo a sho pe iod o ime, in his case 5 (ADCP) o 3 (ADV)225
minu es, he di ec co ela ion be ween a ce ain pe cen ile αo eloci y magni ude and226
u bulence in ensi y p oposed in he p esen s udy is de ined by Eq 3:227
Vpα= (MFM·TI + 1) ·¯
V(3)
Whe e Vpαis he eloci y magni ude alue o a ce ain pe cen ile, MFMis a mul-228
iplie ac o o ha eloci y magni ude pe cen ile, and TI and ¯
Va e he u bulence229
in ensi y and a e aged eloci y magni ude, espec i ely, o a 3-minu e o 5-minu e pe-230
iod. Physically, in a low wi h no u bulence, eloci y luc ua ion is null. This is231
ep esen ed in he equa ion wi h he “+1” e m.232
The me hod o es ablish he MFM o each pe cen ile s a s assuming and e alua -233
ing a heo e ical no mal dis ibu ion. I his does no i he measu ed da a, al e na i e234
alues a e calcula ed empi ically. The p ocedu e is as ollows. F om a i s lineal ap-235
p oach, o which all he 3-minu e (ADV) o 5-minu e (ADCP) samples wi h mean236
eloci y highe han 0.7 m/s a e used, he 1% a hes poins a e disca ded in o de o237
a oid ou lie s, calcula ing he inal equa ions wi h he lineal eg ession o he emaining238
99% poin s. The esul ing 52 app oaches (P1, P2, 22 laye s in P3 and 28 laye s in P4)239
a e e alua ed indi idually compa ing hem wi h he measu ed da a a i s co esponding240
8
Figu e 9: Median alue o he 52 p edic ion le els (Median PL) o ma gins o e o o
0.1 m/s, 0.15 m/s and 0.25 m/s conside ing a no mal dis ibu ion o eloci y magni ude
luc ua ion and minimum p edic ion le els (Min PL) o a ma gin o e o o 0.15 m/s
using ADCP and ADV
o unde es ima ion o pe cen ile 99.9 and pe cen ile 0.1 (and by ex ension o he o he 360
pe cen iles) assuming a no mal dis ibu ion can be disca ded.361
Figu e 10: Absolu e e o s box plo o pe cen iles 99.9 (pc 99.9) and 0.1 (pc 0.1) o
eloci y magni ude wi h he no mal dis ibu ion assump ion
15
3.3 P edic ion o cu en di ec ion luc ua ion362
Time his o y o he same pe iod as o u bulence in ensi y in Fig 6 is p esen ed in363
Fig 11 o ans e se u bulence in ensi y. Excep o he mo e p onounced di e ence364
be ween ebb and lood ide condi ions in P3 a 3 me e om he bo om o in P4 a bo h365
ep esen a i e dep hs, esul s a e e y simila o hose p esen ed in Fig 6. Rega ding he366
e ical p o iles, shown in Fig 4 and Fig 5, TTI cu es o ebb and lood in P3 a e simila ,367
dec easing om he bo om o app oxima ely 12 m om he seabed and emaining almos 368
cons an o uppe laye s. In P4, du ing lood ide TTI g adually dec eases om he369
bo om o he su ace, while o ebb ide i is cons an h oughou he whole wa e 370
column. The same cha ac e is ics we e obse ed o he a ia ions in cu en di ec ion371
o a 3-minu e o 5-minu e pe iod (Fig 4 and Fig 5), con i ming he expec ed ela ion372
be ween ans e se u bulence in ensi y and cu en di ec ion luc ua ion.373
Figu e 11: T ans e se u bulence in ensi y ime his o y o a idal cycle in P1 (3m), P2
(3m), P3 (3m, 15m) and P4 (3m, 15m)
As o eloci y magni ude, he adap abili y o cu en di ec ion luc ua ion in a sho 374
pe iod o ime o a no mal dis ibu ion is e alua ed wi h skewness and ku osis analysis.375
Resul s ob ained o skewness e alua ion a e shown in Fig 12, wi h coe icien s sligh ly376
de ia ioed om ze o o all he cases (|S|<0.05), and wi hou a uni o m endency (pos-377
i i e skew in P4 and he lowe laye s in P3 and nega i e skew in he uppe laye s in P3,378
P1 and P2). In addi ion o he e alua ion o he adap abili y o a no mal dis ibu ion,379
his also con i ms symme y in cu en di ec ion luc ua ion o a sho pe iod da a and380
alida es he assump ion es ablished in Sec ion 2.3.3.381
Rega ding ku osis, Fig 13 shows alues clea ly highe han 3 o all he 52 cases,382
based on which a lep oku ic dis ibu ion mo e ou lie -p one han no mal can be con-383
cluded. Subs i u ing MFDin Eq 5 by he heo e ical σmul iplie ac o in a no mal384
dis ibu ion o e e y analyzed opening angle, despi e he good adap abili y o cen al385
16
Figu e 12: G oeneweld and Meeden skewness ac o box plo o eloci y di ec ion sho
samples measu ed in P1, P2, P3 and P4
angles (55-45 o 90-10), low di ec ion luc ua ion does no i well wi h a no mal dis i-386
bu ion o he wides angles (see Fig 14). Thus, al e na i e MFDmus be ound o he387
co ela ion be ween ans e se u bulence in ensi y and opening angle. The p o a ed388
alues ob ained empi ically o each opening angle ollowing he p ocedu e desc ibed in389
Sec ion 2.3.4 and Sec ion 2.3.5 a e p esen ed in Table 2.390
Figu e 13: Ku osis ac o box plo o eloci y di ec ion sho samples measu ed in P1,
P2, P3 and P4
The mul iplie ac o s o he di e en angles a e consis en wi h he lep oku ic391
dis ibu ion concluded om he ku osis analysis, wi h MFDhighe han hose in a392
no mal dis ibu ion o he h ee wides angles. This app oxima ion i s mo e han 75%393
o 3-minu es o 5-minu es samples wi h a ma gin o e o o 15% and mo e han 92% i 394
we conside a ma gin o 25% om he measu ed alue o he 0.1-99.9 angle. Conside ing395
absolu e e o , esul s a e also clea ly be e han hose obse ed when compa ed wi h396
he no mal dis ibu ion, inc easing he median o p edic ion le els o 1◦, 2◦and 5◦in 14,397
18 and 21 pe cen age poin s. Fo he 2.3-97.7 angle, he p oposed app oxima ion i s398
mo e han 77% o samples wi h a 5% ma gin o e o , inc easing o almos 100% o 399
highe ma gins, as shown in Table 2. Fo na owe opening angles, wi h empi ical MFD
400
e y close o a no mal dis ibu ion, e o conclusions a e simila o hose p esen ed in401
17
Figu e 14: Median alue o he 52 p edic ion le els o ma gins o e o o 1◦, 2◦and
5◦conside ing a no mal dis ibu ion o eloci y di ec ion luc ua ion and minimum p e-
dic ion le els o a ma gin o e o o 2◦using ADCP and ADV
Table 2: Mul iplying ac o , absolu e and ela i e p edic ion le els o he di e en
analyzed opening angles
Angle MFD(Theo. No mal Dis ibu ion) PL abs 5◦(min-max) PL abs 10◦(min-max) PL el 15% (min-max) PL el 15% (min-max)
99.9-0.1 6.79 (6.00) 0.55-0.89 0.82-0.98 0.75-0.97 0.92-0.99
97.7-2.3 4.17 (4.00) 0.93-1.00 0.98-1.00 0.98-1.00 0.99-1.00
95-5 3.38 (3.29) 0.97-1.00 0.99-1.00 0.99-1.00 0.99-1.00
90-10 2.60 (2.56) 0.99-1.00 0.99-1.00 0.98-1.00 0.99-1.00
85-15 2.08 (2.07) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00
84.1-15.9 2.01 (2.00) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00
80-20 1.68 (1.68) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00
75-25 1.37 (1.35) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00
70-30 1.08 (1.05) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00
65-35 0.81 (0.77) 0.99-1.00 1.00-1.00 0.97-1.00 0.98-1.00
60-40 0.54 (0.51) 0.99-1.00 1.00-1.00 0.97-1.00 0.98-1.00
55-45 0.27 (0.25) 1.00-1.00 1.00-1.00 0.98-1.00 0.99-1.00
Fig 14. Focusing in he wides angle, o which he highes di e ence wi h he measu ed402
da a is ound, a deepe e o analysis is p esen ed in Fig 15. Fo all he 52 cases, median403
alues a e close o ze o, wi h a highes median ela i e e o o 4.82% in he eigh h laye 404
in P3 and a lowe o -4.97% in P2. Thus, as o he eloci y magni ude luc ua ion405
p edic ion me hod, o e es ima ion o unde es ima ion can be disca ded.406
4 Discussion407
The new me hods a e e alua ed by compa ing he esul s om he es ima ion by Eq408
3 and Eq 5 wi h measu ed da a o eloci y magni ude pe cen iles and opening angles,409
espec i ely.410
Rega ding eloci y magni ude luc ua ion, Fig 16 shows a compa ison o eloci y411
magni ude measu ed and es ima ed alues o he 0.1 and 99.9 pe cen iles du ing he412
18
Figu e 15: Absolu e and ela i e e o s box plo o pc 99.9 - pc 0.1 opening angle
es ima ion wi h he empi ical mul iplying ac o
measu ing pe iod in P2. E en in he wo s scena io (pe cen iles wi h he lowe p edic ion413
le els and he measu ing poin wi h he highes median e o ), ed line shows a e y good414
ag eemen wi h measu ed da a, gi ing an idea o he high accu acy o his es ima ion415
me hod. In Fig 16, i is also no able he impo an di e ence be ween lood and ebb,416
wi h good esul s o bo h ide di ec ions, which shows he capabili y o his me hod o 417
di e se low condi ions.418
Simila ly, a compa ison o measu ed and es ima ed alues o he h ee wides angles419
in P2 is shown in Fig 17, o which alues co esponding wi h 3-minu e a e aged eloci y420
lowe han 0.7 m/s a e disca ded. As in Fig 16, he di e ence be ween ebb and lood421
ides is no able, ge ing a e y good co ela ion o bo h low condi ions. Since hese422
h ee opening angles show he lowes p edic ion le els acco ding o in o ma ion p o ided423
in Table 2, a be e ag eemen is expec ed o na owe angles and o he spa ial cases.424
Fo cu en di ec ion luc ua ion p edic ion by nume ical modelling, a u bulence425
aniso opic a io (σs:σ :σ ) needs o be assumed. As p esen ed in Sec ion 2.3.5, Nezu426
and Nakagawa [27], based on an expe imen al s udy wi h wo-dimensional channel lows427
a ela i ely low Reynolds numbe s, p oposed he a ios 1:0.71:0.55. Rega ding da a428
measu ed in s ong idal channels, Milne e al [8] obse ed 1:0.75:0.56 a ios o cu en 429
eloci ies a ound 2 m/s. The a ios calcula ed om he da a measu ed o he p esen 430
s udy o he 3-minu e da a blocks ep esen a i e o lood condi ions a 1 m/s shown431
in Table 1 a e 1:0.85:0.45 o P1 and 1:0.78:0.58 o P2. Conce ning he da a measu ed432
by ADCP, e ical a e aged a ios a e 1:0.79:0.40 o P3 and 1:0.98:0.41 o P4. Excep 433
o P4, bo h he a ios shown in [8] and measu ed in he p esen s udy ag ee ela i ely434
19
Figu e 16: Compa ison o measu ed (blue) da a and es ima ion ( ed) alues o pe -
cen iles 99.9 (pc 99.9) and 0.1 (pc 0.1) o eloci y magni ude
Figu e 17: Compa ison o measu ed (blue) da a and es ima ion ( ed) alues o opening
angles 99.9-0.1, 97.7-2.3 and 95-5
well wi h hose p oposed by Nezu and Nakagawa [27], wi h he expec ed de ia ions om435
he heo e ical a ios due o he di e ences in ba hyme y and Reynolds numbe s. In436
he case o P4, due o he shallowe and na owe na u e o he channel, he i egula 437
shape o he coas line (mul iple small capes and gul s) and he a iable dep h (hills and438
alleys in a ious di ec ions), he luc ua ion in he ans e se componen o eloci y439
20
becomes mo e impo an . These di e ences in he u bulence aniso opic a ios mus be440
conside ed when applying his me hod o he p edic ion o cu en di ec ion luc ua ion441
by nume ical modelling.442
5 Conclusions443
Wi hin he jou ney owa ds idal ene gy s eam comme cial exploi a ion, one o he main444
opics is he adap abili y o labo a o y de ices o sea wa e and low condi ions. In his445
ega d, some con e e s ha e had o ace issues ela ed o bio ouling, ma ine co osion446
o u bulence condi ions. Conce ning his las opic, no able u bulence- ela ed high447
equency luc ua ions in eloci y magni ude and di ec ion ha e been obse ed by in-448
si u measu emen s. The p esen pape analyzes his luc ua ion and in oduces a new449
me hod o i s es ima ion based on sho da a samples measu ed by wo ADVs and wo450
ADCPs a 4 di e en loca ions wi h di e se low condi ions in he wa e s o Go o Islands,451
Japan.452
Di iding measu ed da a in o 3-minu es (ADV) and 5-minu es (ADCP) samples, mag-453
ni ude luc ua ion is well adap ed o a heo e ical no mal dis ibu ion. Wi h his as-454
sump ion, mo e han 80% pe cen iles 0.1 and 99.9 can be p edic ed wi hin a ma gin455
o e o o 0.15 m/s. This pe cen age inc eases o alues e y close o 100% o mo e456
cen e ed pe cen iles (2.3, 97.7, 5, 95,. . . ). Fo di ec ion luc ua ion, da a samples show457
a lep oku ic dis ibu ion, which implies a g ea e impo ance o ou lie s. Thus, he458
no mal dis ibu ion assump ion showed good esul s o cen al opening angles ( om459
pe cen iles 45-55 o pe cen iles 10-90), whils o wide angles he e is an unde es ima-460
ion p oblem. The h ee wides angles (5-95, 2.3-97.7, 0.1-99.9) we e ea ed empi ically,461
ob aining slope ends o 3.38, 4.17 and 6.79, espec i ely, ins ead o 3.29, 4 and 6 o he462
heo e ical no mal dis ibu ion. Wi h hese new ac o s, mo e han 75% o he 99.9-0.1463
and mo e han 98% o 97.7-2.3 opening angles can be es ima ed wi h a 15% ma gin464
o e o . These esul s demons a e he alidi y o his me hod o he es ima ion o 465
his kind o luc ua ion, ega dless o measu ing de ice, equency sampling, loca ion o 466
dep h.467
The impo ance o his wo k lies no only in he unde s anding o his kind o luc-468
ua ions, bu also in he ela ion o hese wi h u bulence in ensi y o magni ude and469
ans e se u bulence in ensi y o di ec ion. Since bo h pa ame e s can be calcula ed470
indi ec ly by nume ical models, he conclusions ex ac ed om his pape ep esen a471
signi ican s ep owa ds idal s eam ene gy comme cializa ion. Reducing he need o 472
in-si u measu emen s, his new p edic ion me hod allows a highe accu acy in ene gy473
esou ce p edic ion ( esiduals om ha monic analysis up o 5 kW/m2ha e been ob-474
se ed in a idal si e wi h maximum eloci y o 3 m/s [10]) and an impo an ad ance475
conce ning con e e s design, since high equency luc ua ions in eloci y ha e an im-476
po an e ec on he de ice s abiliza ion [12] and on he dynamic loading condi ions on477
he blades, suppo s uc u es and seabed connec ions [11].478
21
Acknowledgemen s479
The au ho s would like o hank he Minis y o En i onmen o Japan o pe mission480
o publish o he da a used in his s udy, which we e ob ained h ough he p ojec o 481
P omo ion o Realiza ion o Tidal Cu en Powe Gene a ion suppo ed by he minis y482
in 2014 and 2015.483
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