1
E alua ion o Mock Quay Wall Dimensions o Tank Tes s
Based on Nume ical Analysis o Wall E ec s
Masa oshi Hi o a1*, Yasushi Ki agawa1, and Hi oshi Kobayashi1
1 Na ional Ma i ime Resea ch Ins i u e, Japan
Abs ac . This s udy p esen s nume ical analyses o wall e ec s du ing be hing and unbe hing maneu e s.
As a p elimina y s ep owa d u u e physical model expe imen s, i aims o p o ide insigh s in o he design o
a mock quay wall — a simpli ied e ical wall used o eplica e wall e ec s in ank es s. Nume ical analyses a e
conduc ed using a RANS-based nume ical analysis applied o he DTC benchma k hull o m unde deep-wa e
condi ions. Two ypes o maneu e s a e conside ed: (1) s aigh -ahead un pa allel o he quay wall and (2)
la e al be hing and unbe hing wi h he bow and s e n emaining pa allel o he quay wall. This s udy ocuses
on he e ec o mock quay wall geome y, pa icula ly i s dep h. When he hull mo es pa allel o he quay wall,
he hyd odynamic o ces ac ing on he hull a e a ec ed by he quay wall dep h. In con as , unde la e al mo ion,
he hyd odynamic o ces a e ound o be insensi i e o he mock quay wall dep h. Du ing la e al be hing and
unbe hing, oscilla o y ime his o ies o he la e al o ces on he hull a e obse ed, a ibu ed o ci cula ing lows
ha de elop a ound he bo om edge o he mock quay wall. Such oscilla o y ime his o ies a e no obse ed in
he deep ull dep h wall s uc u e wi hou open space. These esul s indica e ha he mock quay wall is no
capable o adequa ely ep oducing he wall e ec s.
Keywo ds: Nume ical analysis, Wall e ec , Po na iga ion.
1. In oduc ion
When a ship na iga es in he icini y o a quay wall, suc ion o ces owa d he wall and yaw momen s ac ing
on he hull a e known o occu [1]. These hyd odynamic in e ac ions a e collec i ely known as wall e ec s. Wall
e ec s induce non-negligible hyd odynamic o ces du ing be hing and unbe hing ope a ions and a e di ec ly
ela ed o ship maneu e abili y and sa e y. The e o e, accu a ely e alua ing he associa ed hyd odynamic
cha ac e is ics is essen ial o ensu ing sa e be hing and unbe hing ope a ions. To unde s and he in luence o
quay walls in es ic ed wa e s, nume ous expe imen al and nume ical s udies ha e been conduc ed unde
condi ions whe e bo h bank e ec s and shallow wa e e ec s a e simul aneously p esen . Expe imen al
in es iga ions ha e add essed wall o ces ac ing on he hull [2], hyd odynamic in e ac ions [3], and he e ec s o
wall geome y and wa e dep h [4]. On he nume ical analysis side, CFD simula ions [5], [6], [7] and as p edic ion
me hods using po en ial low heo y ha e been conduc ed [8].
This s udy aims o isola e and e alua e he wall e ec , ocusing speci ically on i s e ec s du ing be hing and
unbe hing maneu e s. Physical model es s conduc ed in expe imen al anks wi h e ical wall s uc u es
(he ea e e e ed o as mock quay wall) a e essen ial o e alua ing wall e ec s. Howe e , o app op ia ely
ep oduce wall-induced e ec s in such expe imen s, he dimensions and s uc u al con igu a ions o he mock
quay wall mus be ca e ully examined in ad ance.
In ou p e ious s udies, we conduc ed nume ical simula ions unde su icien ly deep-wa e condi ions o isola e
wall e ec s om shallow wa e e ec s. Two ypes o ship mo ion we e conside ed: (1) pa allel mo ion o he quay
wall [9], and (2) la e al be hing and unbe hing while main aining a pa allel heading o he wall [10].
Hyd odynamic o ces ac ing on bo h he hull and he mock quay wall we e analyzed, wi h a ocus on how he
dep h and leng h o he quay a ec ed he esul s. The simula ions e ealed ha du ing pa allel mo ion, he dep h
o he mock quay wall signi ican ly in luenced he hyd odynamic o ces ac ing on he hull. In con as , no
signi ican in luence o quay wall dep h on he o ces was obse ed du ing la e al mo ion.
In his s udy, we u he in es iga e hese indings. In addi ion o analyzing hyd odynamic o ces du ing pa allel
mo ions, such as he p essu e dis ibu ion on he hull su ace and bow-ou momen s, we emphasize he oscilla ion
* Co espondence o: [email p o ec ed]
16 h In e na ional Symposium on P ac ical Design o Ships and O he Floa ing S uc u es PRADS 2025
Ann A bo , MI, USA, Oc obe 19 h – 23 d 2025
2
o he o ces du ing la e al mo ion. The analysis conside s he wo ypes o ship maneu e s: (1) pa allel mo ion o
he quay wall, and (2) la e al be hing and unbe hing while main aining a pa allel heading o he quay wall. Fo
each case, nume ical analyses based on RANS CFD models a e conduc ed unde wo condi ions: a mock quay
wall wi h an open space a he edge and a ull dep h wall con igu a ion wi h no openings. The mock quays a e also
simula ed a di e en dep hs. This s udy is a p elimina y nume ical in es iga ion o suppo he design and
in e p e a ion o u u e physical model es s. I s goal is o cla i y he e ec s o mock quay wall con igu a ions on
he hyd odynamic o ces ac ing on he hull.
2. Me hodology o CFD analysis
2.1. Nume ical schemes
2.1.1. O e se g id app oach
The nume ical analyses in his s udy a e pe o med using an o e se g id me hod. This me hod en ails he
u iliza ion o mul iple compu a ional g ids, including a hull, a quay, and a basin, which a e hen enclosed o
ep esen he compu a ional domain collec i ely and o e lap each o he wi hou equi ing ace- o- ace ma ching
be ween g ids. All compu a ional g ids a e gene a ed using he comme cial g id gene a ion so wa e, Poin wiseTM.
An in-house o e se assembling sys em called UP_GRID [11] compu es he domain connec i i y in o ma ion
(DCI) o he o e se g id me hod. UP_GRID is based on a s uc u ed g id DCI sys em and de eloped by Na ional
Ma i ime Resea ch Ins i u e (NMRI) o Japan.
2.1.2. Na ie -S okes Sol e
All simula ions a e ca ied ou by he in-house low sol e NAGISA [12], a 3D incomp essible Na ie -S okes
sol e de eloped by NMRI. Incomp essible Reynolds-a e aged Na ie –S okes equa ions a e sol ed o ob ain a
s eady solu ion by in oducing pseudo-comp essibili y o eloci y-p essu e coupling. Uns eady low can also be
simula ed by using a dual ime-s epping app oach. Spa ial disc e iza ion is based on a ini e- olume me hod, and
in iscid luxes a e e alua ed by he hi d-o de upwind scheme based on he lux-di e ence spli ing. The
e alua ion o iscous luxes is he second-o de cen e ed di e ence. The a i icial comp essibili y app oach is used
o eloci y-p essu e coupling. The single-phase le el-se me hod used in his s udy o cap u ing ee su ace.
Va ious u bulence models such as one-equa ion, wo-equa ion, and explici algeb aic s ess model(EASM [13])
a e implemen ed. The sol e is capable o he o e se g id me hod o complex geome y and can cope wi h
o e lapped g ids wi h DCI gene a ed by UP_GRID [11].
2.2. Ta ge Ship and Compu ed Cases
The geome y o he a ge ship is he Duisbu g Tes Case (DTC) [14], which is a pos -Panamax size con aine
ship. Table 1 shows he p incipal pa icula s o DTC, in which he alue o an ac ual ship and a model ship o
𝐿 = 3.740 m; he subsc ip 𝑀 is he model ship scale. The DTC wi hou bilge keels, udde , o o he appendages
is used in his s udy.
Table 1. P incipal pa icula s o he DTC.
Ac ual Model
Leng h be ween pe pendicula s:
𝐿
[m]
355.0
3.740
B ead h:
𝐵
[m] 51.0 0.537
D a :
𝑑
[m] 14.5 0.153
Block Coe icien :
𝐶
0.661
Design Speed:
𝑉
[kno ] 25.0 -
This s udy aims o in es iga e he speci ica ions o he mock quay wall o ank es s h ough nume ical
analyses, wi h he objec i e o e alua ing he wall e ec s in he Ac ual-sea Model Basin (AMB; 80 m (leng h) x
40 m (wid h) x 4.5 m (dep h)) o he NMRI. A wa e dep h o 7.48 m is equi alen o wice he 𝐿 o he model
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ship, is selec ed as su icien ly deep. When a hull na iga es nea a quay wall, hyd odynamic in e ac ion be ween
he hull and he quay wall occu s, and his in e e ence is expec ed o depend on he dimensions o he quay wall.
The e o e, nume ical analyses a e conduc ed unde he condi ions shown in Table 2 o e alua e he e ec o quay
wall dimensions on he wall e ec . In Table 2, he o e all quay leng h indica es he o al leng h o he mock quay,
which is he same as he ull longi udinal ex en o he compu a ional domain. Figu e 1 shows wo ypes o hull
mo ions conside ed in his s udy. The le diag am ep esen s s aigh -ahead un pa allel o he quay wall, while
he igh diag am shows be hing and unbe hing ope a ions by la e al mo ion wi h he heading angle main ained
pa allel o he quay wall. This s udy e alua es he wall e ec s unde hese mo ion condi ions using nume ical
analysis.
Table 2. Compu ed cases.
Case
Di ec ion o
hull
mo ion
Wa e dep h
([m])
Quay ype Quay
d
ep h
[m]
Quay
leng h
[m]
Rema ks
1
-
1
Pa allel
mo ion o
he quay
wall
Deep (7.48)
w/o wall
-
-
Baseline w/o quay
1-2
Deep (7.48) Full dep h wall
7.48 O e all Re e ence
1-3
AMB (4.5) Mock 1.0 O e all MQ dep h a ia ions
1-4
AMB (4.5) Mock 3.0 O e all MQ dep h a ia ions
1-5
AMB (4.5) Mock 2.0 20.0 Close o he expe imen
2-1
Be hing and
Unbe hing
wi h la e al
mo ion
AMB (4.5) w/o - - Baseline w/o quay
2-2
AMB (4.5) Full dep h wall
4.5 O e all Re e ence
2-3
AMB (4.5) Mock 1.0 20.0 MQ dep h a ia ions
2-4
AMB (4.5) Mock 3.0 20.0 MQ dep h a ia ions
MQ: Mock quay
Figu e 1. Hull mo ions nea a quay wall, s aigh -ahead un pa allel o he quay wall (le ), la e al mo ion while main aining
he hull pa allel o he quay wall ( igh ).
2.3. Compu a ional se up
All nume ical analyses a e ca ied ou on a model scale, dimensioned by 𝐿 = 3.740 [m]. The kinema ic
iscosi y and he densi y o wa e a e se o 𝜈 = 1.1386 × 10−6 [m2/s] and 𝜌 = 999.1026 [kg/m3], espec i ely, om
ITTC Recommended P ocedu es [15]. Fo a u bulence model, EASM [13] model wi h wall unc ions is applied.
The e o e, he minimum g id spacings on he su ace o a hull, a quay wall and basin walls a e se o 0.187 × 10−2
which sa is ies 𝑦≅ 100 o he wall unc ion bounda y condi ion. The ee su ace is ea ed using a single-phase
le el se me hod, and he g id spacings in he e ical di ec ion a e clus e ed nea he wa e su ace. Nume ical
analyses a e ca ied ou using an uns eady condi ion wi h a ime inc emen o ∆𝑡 = 0.05 [s].
To accu a ely e alua es he wall e ec s, he ship speed and he dis ance o he quay wall a e se o s ingen
condi ions such as be hing o unbe hing ope a ions. In he nume ical analyses o he ship mo ing pa allel o he
quay wall, he ship speed is se o 0.333 [m/s], which is equi alen o 25% o he design speed in model scale. Fo
la e al unbe hing and be hing wi h he bow and s e n pa allel o he quay wall, he maximum unbe hing and
be hing speed is se o 0.133 [m/s], which is 10% o he design speed in model scale. Du ing unbe hing, he ship
accele a es om a s a iona y posi ion o i s maximum eloci y in 10 seconds. The ship speed inc eases, and he
ship lea es om he quay. Simila ly, du ing be hing, he ship accele a es om es o i s maximum speed in 10
seconds and mo es. The ship slows down om i s maximum speed in 10 seconds and s ops nea he quay wall.
The dynamic o e se g id me hod [11] is applied o upda e DCI a each compu a ional s ep. In nume ical analyses,
he mo ion o he hull is p esc ibed in he su ge di ec ion o pa allel mo ion cases, and in he sway di ec ion o
la e al mo ion cases. Du ing he nume ical analysis, all deg ees o eedom excep o he p esc ibed mo ion a e
ixed, as he induced mo ions a e expec ed o be negligible unde he low-speed condi ion.
4
The minimum dis ance be ween he ship and he quay wall Δ𝑏 is 1.2. Δ𝑏 is calcula ed by Δ𝑏 = 𝑏/(0.5𝐵),
based on he a io o he dis ance be ween he ship cen e line and he quay wall, 𝑏. Figu e 2 shows he posi ion o
he hull and quay wall. The dis ance be ween he quay wall su ace and he po side su ace o he hull is 0.054
[m] in model scale, and 5.1 [m] in ac ual scale. In he case o pa allel, Δ𝑏 emains cons an . Fo la e al mo ion, Δ𝑏
is he minimum alue a he poin o he closes app oach o he quay wall.
Figu e 3 shows he CFD coo dina e and he di ec ion o he o ces and momen s. The CFD coo dina es a e
igh handed, wi h coo dina e X posi i e om bow o s e n and coo dina e Z posi i e upwa d. The o igin is loca ed
a midship on he s ill wa e line. The longi udinal o ce is deno ed as FX, he la e al o ce is deno ed as FY, and
he yaw momen is deno ed as MZ. The yaw momen is calcula ed a ound he midship.
The hull g id is gene a ed o bo h sides. This hull g id is used in all simula ions. Figu e 4 shows he
compu a ional g id and bounda y condi ions o cases 1-1, 1-2, 1-3, and 1-5 in Table 2. The compu a ional domain
o case 1-2 is he y > 0 pa o case 1-1. In case 1-2, he posi ion o he minimum y in he basin g id co esponds
o he quay wall su ace ( ull dep h wall). In cases 1-1 h ough 1-4, he hull g id is ixed, and a uni o m low
eloci y is gi en. Acco dingly, a mo ing wall condi ion is applied as a bounda y condi ion on he su ace o he
quay wall in cases 1-2, 1-3 and 1-4. In case 1-3 and 1-4, a pa o walls and bo om o he expe imen al ank, AMB
is ep oduced in he compu a ional g id. In case1-5, a sec ion o he AMB is ep oduced on he compu a ional g id
and he hull is na iga ed along he mock quay wall in an AMB. Figu e 5 shows he compu a ional g ids and
bounda y condi ions o cases 2-1, 2-2, and 2-4. The AMB g ids o case 2-1, 2-3 and 2-4 a e he same as in case
1-5. In case 2-2, he basin g id o case 1-2 is ex ended in o he AMB shape o c ea e DCI in he hull and basin
g ids. Figu e 6 shows he enla ged iew o he g ids a ound he hull. In case 2-2, he numbe o g id poin s is
inc eased a ound he hull in he basin g id om case 1-2. Table 3 shows he g id size and he cell numbe o each
g id, and Table 4 shows he g id combina ions o each calcula ion case.
The pu pose o hese compu a ions is o p elimina ily in es iga e he o e iew o he o ces and he low ield
a ound he mock quay p io o i s cons uc ion. Since i is no necessa y o e i y he accu acy o es ima ing he
pe o mance o he ship, he e i ica ion o g id dependency is no ca ied ou . The g id dimension and numbe o
g id poin s a e de e mined by e e ing o he p eceding o e se compu a ions [16].
Figu e 2. Posi ion o he hull and quay wall.
Figu e 3. The CFD coo dina es and he di ec ion o he o ce and momen . The longi udinal o ce is deno ed as FX, he la e al
o ce as FY, and he yaw momen as MZ.
5
Figu e 4. Schema ic iew o he compu a ional g ids and bounda y condi ions o cases 1-1( op le ), 1-2( op igh ), 1-3(bo om
le ) and 1-5(bo om igh ).
Figu e 5. Schema ic iew o he compu a ional g ids and bounda y condi ions o cases 2-1( op le ), 2-2( op igh ) and 2-
4(bo om) in he unbe hing condi ion.
X[m]
-20
-15
-10
-5
0
5
10
15
20
Y[m]
0
5
10
15
Z [m]
-4
-2
0
XY
Z
X[m]
-20
-15
-10
-5
0
5
10
15
20
Y[m]
0
5
10
15
Z [m]
-4
-2
0
XY
Z
2-1 2-2
X[m]
-20
-15
-10
-5
0
5
10
15
20
Y[m]
0
5
10
15
Z [m]
-4
-2
0
XY
Z
2-4
Wall o mock quay
Wall o AMB
Wall o hull
Z symme y
Fa ield
Wall o AMBWall o AMB
Wall o hull Wall o hull
Z symme y Z symme y
Fa ield Fa ield
6
Figu e 6. Enla ged iew o he compu a ional g ids and bounda y condi ions a ound he hull o cases 2-1( op), 2-2(bo om)
in he unbe hing condi ion.
Table 3. G id size and numbe o cells.
G id G id size [m] Numbe o cells
Hull -3.74
≤
x
≤
3.74, -1.65
≤
y
≤
1.65,
-
1.65
≤
z
≤
0.374
1,032,192
Basin -7.48
≤
x
≤
11.22, -11.22
≤
y
≤
11.22,
-
7.48
≤
z
≤
0.374
1,277,952
Basin wi h quay -7.48
≤
x
≤
11.22, 0.00
≤
y
≤
11.22,
-
7.48
≤
z
≤
0.374
638,976
A pa o AMB -10.0
≤
x
≤
10.0, 0.0
≤
y
≤
18.7,
-
4.50
≤
z
≤
0.374
182,784
A sec ion o AMB
-20.0
≤
x
≤
20.0, 0.0
≤
y
≤
18.7,
-4.50
≤
z
≤
0.374
(*case2
-
2,
4.0
≤
y
≤
18.7
)
1,204,224
(*case2-2, 442,368)
MQ, L=o e all, d= 1.0m -10.0
≤
x
≤
10.0, 0.11
≤
y
≤
7.74,
-
4.74
≤
z
≤
0.374
1,240,320
MQ, L=o e all, d= 3.0m -10.0
≤
x
≤
10.0, 0.11
≤
y
≤
7.74,
-
6.74
≤
z
≤
0.374
1,969,920
MQ, L=20.0m, d= 1.0m -13.8
≤
x
≤
13.8, 0.11
≤
y
≤
7.74,
-
4.74
≤
z
≤
0.374
1,452,480
MQ, L=20.0m, d= 2.0m -13.8
≤
x
≤
13.8, 0.11
≤
y
≤
7.74,
-
5.74
≤
z
≤
0.374
1,875,456
MQ, L=20.0m, d= 3.0m -13.8
≤
x
≤
13.8, 0.11
≤
y
≤
7.74,
-
6.74
≤
z
≤
0.374
2,301,696
MQ: Mock quay
XY
Z
2-1
Wall o hull
Wall o AMB
Z symme y
XY
Z
2-2
Wall o hull
Wall o AMB
Z symme y
7
Table 4. G id combina ions o each calcula ion case.
G id
Case
1
-
1
1
-
2
1
-
3
1
-
4
1
-
5
2
-
1
2
-
2
2
-
3
2
-
4
Hull ✓
✓
✓
✓
✓
✓
✓
✓
✓
Basin ✓
Basin wi h quay ✓
A pa o AMB ✓
✓
A sec ion o AMB ✓
✓
✓*
✓
✓
MQ, L=o e all, d= 1.0m
✓
MQ, L=o e all, d= 3.0m
✓
MQ, L=20.0, d= 1.0m ✓
MQ, L=20.0, d= 2.0m ✓
MQ, L=20.0, d= 3.0m ✓
MQ: Mock quay
*In case 2-2, AMB g id is modi ied o gene a ing DCI.
3. Resul s and Discussions
3.1. Pa allel mo ion o he quay wall
Nume ical analyses a e pe o med o in es iga e he in luence o he wall e ec on he hyd odynamic o ces
ac ing on a hull ad ancing along a s aigh pa h pa allel o he quay wall. The analyses ocused on h ee condi ions:
wi hou a quay wall (case 1-1), wi h a quay wall (case 1-2), and wi h mock quay walls o a ying subme ged
dep hs (cases 1-3 o 1-5). A compa ison be ween case 1-1 and case 1-2 (Table 5) e ealed ha he p esence o he
quay wall inc eases he longi udinal o ce (FX), la e al o ce (FY), and yaw momen (MZ). This phenomenon can
be a ibu ed o he wall e ec , whe ein he p oximi y o he hull o he wall gene a es asymme ic p essu e ields
a ound he hull. The di ec ion o he o ces ag ees wi h p e ious expe imen al and heo e ical indings: a la e al
o ce ac ing owa d he quay and a yaw momen ha causes he bow o u n ou wa d (bow-ou momen ), bo h o
which a e ep oduced by nume ical analysis. Figu e 7 shows he hull su ace p essu e dis ibu ions di ided by
densi y. o case1-1 and case1-2. The esul s o case 1-2 show ha a la ge nega i e p essu e a ea is gene a ed on
he po side.
Table 5. Compa ison o hyd odynamic o ces ac ing on he hull.
Case
F
X
[N]
F
Y
[N]
M
Z
[Nm]
1
-
1
0.6
38
0.0
0
0
0.00
0
1
-
2
0.6
66
-
0.53
3
-
0.27
2
Figu e 7. Compa ison o hull su ace p essu e dis ibu ion di ided by densi y o cases 1-1 and 1-2, po side( op) and s a boa d
side(bo om).
8
To u he examine he ole o wall dep h, addi ional simula ions a e conduc ed wi h a ying dep hs o he quay
wall. Table 6 shows he ela i e magni udes o he hyd odynamic o ces wi h espec o case 1-2. Case 1-5 is he
a e age o he compu ed alues in a s able ange, abou 30 seconds in eal ime. Comp ehensi e esul s o
addi ional quay dep h con igu a ions can be ound in [9].
In case 1-3, whe e he wall dep h is shallow, FY and MZ dec ease. In con as , cases 1-4 and 1-5 exhibi
hyd odynamic o ces nea ly equi alen o hose in case 1-2, indica ing ha he e ec o he wall pe sis s when he
subme ged dep h is su icien . Figu e 8 shows he p essu e dis ibu ion di ided by densi y on he XY c oss-sec ion
a he midship posi ion o case 1-2, 1-3 and 1-4. In case 1-3, he p essu e dis ibu ion ex ends down o he bo om
edge o he mock quay wall, and he pa e n a ound he hull di e s signi ican ly om hose obse ed in o he cases.
This de ia ion is conside ed o be he p ima y eason why FY in case 1-3 is smalle han in he o he cases. In
con as , he p essu e dis ibu ion in case 1-4 is simila o case 1-2, including nea he hull and a ound he mock
quay.
These esul s sugges ha nume ical analyses a e capable o quali a i ely cap u ing he wall e ec and he
associa ed hyd odynamic o ces ac ing on a hull na iga ing nea a quay wall. The magni ude o hese o ces
appea s o be sensi i e o he quay wall dep h, which a ec s he deg ee o low blockage and he esul ing
asymme y in he p essu e dis ibu ion a ound he hull.
Table 6. Compa ison o he a io o hyd odynamic o ces ac ing on he hull o case 1-2.
Ra io o
c
ase 1
-
2
Case
F
X
F
Y
M
Z
1
-
3
0.997
0.978
0.979
1
-
4
1.001
0.993
0.997
1
-
5
*
0.999
0.994
1.003
*A e age o abou 30 seconds o s able ange
Figu e 8. Compa ison o he p essu e dis ibu ion di ided by densi y a ound he hull and he mock quay a midship o cases
1-2, 1-3 and 1-4 (Δ𝑝/𝜌 = -0.0005).
3.2. Be hing and unbe hing wi h la e al mo ion while main aining he hull pa allel o he quay wall
In o de o in es iga e he wall e ec s on he na iga ion o he hull di e en om he subsec ion 3.1, nume ical
analyses wi h la e al mo ion o he hull a e pe o med wi h no quay (case 2-1), wi h a deep ull dep h wall quay
(case 2-2) and wi h di e en mock quay dep hs (cases 2-3 and 2-4). Figu e 9 and Figu e 10 show he posi ion o
he hull and he his o ies o FY and MZ ac ing on he hull. Figu e 9 shows he esul in unbe hing condi ions, and
Figu e 10 shows he esul in be hing condi ions.
Figu e 9 shows ha in he p esence o he quay wall (case 2-2 o 2-4), he la e al o ce ac ing on he hull is
la ge , and he yaw momen has a smalle ini ial peak han wi hou he quay wall (case 2-1). This is due o he wall
e ec . The FY is la ge due o he mu ual in e e ence be ween he hull and he wall. In con as , he u ning momen
9
is smalle due o he la e al o ce. On he o he hand, in he case wi hou he quay wall, he yaw momen ac s in
he di ec ion o u ning he bow o po . When he quay wall is p esen , howe e , he yaw momen becomes smalle ,
p ima ily due o he in luence o he inc eased la e al o ce and he induced bow-ou momen , esul ing om he
in e ac ion be ween he hull and he quay wall. A simila phenomenon is obse ed du ing be hing in Figu e 10.
Also, he hyd odynamic o ces ac ing on he hull a e la ge when he hull is unbe hing han when i is be hing
o he quay. This can be a ibu ed o wo ac o s. Fi s , he highe ela i e eloci y be ween he hull and he ini ially
s a iona y luid. Secondly, he gene a ion o s onge added mass e ec s du ing accele a ion. Con e sely, du ing
he be hing p ocess, he luid a ound he ship is al eady in mo ion, and decele a ion g adually educes hese e ec s,
esul ing in lowe hyd odynamic o ces. Fo he mock quays (case 2-3, 2-4), he la e al o ce and yaw momen
ac ing on he hull a e nea ly iden ical unde bo h be hing and unbe hing condi ions. Addi ional a ia ions o quay
dep h, along wi h he co esponding esul s, a e p o ided in de ail in [10].
Compa ed o he case2-2, wi h a su icien ly deep ull dep h wall quay, case 2-3 and 2-4 show he la ge FY,
and he oscilla o y ime his o ies. The p esen s udy u he in es iga es he ampli ica ion o hese o ces and
elucida es he mechanisms esponsible o he obse ed oscilla ions.
Figu e 9. Posi ion o he hull( op) and he ime his o ies o Y-di ec ion(cen e ), la e al o ce FY(bo om le ) and yaw momen
MZ(bo om igh ) du ing unbe hing o cases 2-1 o 2-4.
X
Y
Z
Quay wall
= 8.0
= 6.0
= 4.0
= 2.0
= 10.0
= 0.0
Time: [s]
/ /// /// /////////
ime[s]
Po -side clea ance [m]
0 1 2 3 4 5 6 7 8 9 10 11 12
0.0 0.0
0.1 0.1
0.2 0.2
0.3 0.3
0.4 0.4
0.5 0.5
0.6 0.6
0.7 0.7
0.8 0.8
0.9 0.9
1.0 1.0
ime[s]
F
Y
[N]
0 1 2 3 4 5 6 7 8 9 10 11 12
-7.0 -7.0
-6.0 -6.0
-5.0 -5.0
-4.0 -4.0
-3.0 -3.0
-2.0 -2.0
-1.0 -1.0
0.0 0.0
2-1
2-2
2-3
2-4
ime[s]
M
Z
[Nm]
0 1 2 3 4 5 6 7 8 9 10 11 12
0.0 0.0
1.0 1.0
2.0 2.0
2-1
2-2
2-3
2-4
16
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