tranquility

Construction of Ship Repair Yard and

Dry Dock Complex at Duqm Port

Directorate General of Ports and Maritime Affairs,

Ministry of Transport and Communications

PRINCIPAL :

DIRECTORATE GENERAL OF PORTS ANDMARITIME AFFAIRS, MINISTRY OFTRANSPORT AND COMMUNICATIONSSULTANATE OF OMAN

ENGINEER :

DAEWOO SHIPBUILDING & MARINE ENGINEERING

CONTRACTOR :

DAEWOO–GALFAR CONSORTIUM

PROJECT NAME : CONSTRUCTION OF SHIP REPAIR YARD ANDDRYDOCK COMPLEX AT DUQM PORT

DOCUMENT TITLE :

NUMERICAL EXPERIMENT OF HARBOUR TRANQUILITY

Document No:Prepared by: Design Team of Daewoo E&CSubmitted by: Daewoo – Galfar Consortium Member

01 04/02/09 Issued for Review J.H.Kim K.S.Cho H.J.Sung

Rev. DateDescription of

Revision

Prepared

CheckedSubmitt

edApprove

d

CONTRACTOR ENGINE

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ER

Numerical Experiment of Harbor Tranquility

1. Summary

1.1 Object

◦ The object of this numerical experiment is to evaluate the harbour tranquility of the Duqm New Port in OMAN using SWAN wave model for the two different port layouts designed with three cross-sections of the Duqm New Port.

1.2 Contents

The numerical experiments were conducted with the wave direction, N60°E which is the most effective waves causing the harbour tranquility of Duqm New Port.

◦ Three different incident wave conditions were used for the numerical experiments ie, the 100 years return period of the deep water wave and the design waves used as Duqm New Port Design Criteria(Ministry of Transport and Communication in Oman, 2005. 10).

◦ The harbour tranquility criterion was used "Target Wave Heights at Berthing Facilities" suggested by the Duqm New Port Design Criteria. The wave height criterion for harbor tranquility was determined as 1.0m which was required for ship repair facility and floating docks(<Table 1.1>).

◦ Goda's reflection rates for coastal structure were used for the numerical experiments(<Table 1.2>).

◦ The numerical experiments were carried out for the six different cases of port design layouts shown in <Table 1.3> which include the two construction cases of main breakwater and lee breakwater with three cross-secton forms by changing reflection coefficients at Q1(Quay No. 1) section.

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【 Target Wave Heights 】

<Table 1.1>

Type of Facility Target Wave Height (Hs m)

Ship repair, floating docks 1.00

Main commercial quays 1.00

Naval Craft 0.75

International Fishing Craft 0.75

Small Craft berths 0.50

Pontoon Locations 0.25

【Goda's Reflection rates for costal structure】

<Table 1.2>

Structure form

Reflection

Coefficient

Structure formReflection

Coefficient

Vertical wall 0.7∼1.0Deformed armour unit

0.3∼0.5

Vertical wall(submerged)

0.5∼0.7Vertical wave-absorbing structure

0.3∼0.8

Rubble mound

(1:2∼3 slope)0.3∼0.6 Coast line 0.05∼0.2

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【Test plan】<Table 1.3>

CaseA-0 CaseB-0

▪Plan arrangement CaseA▪Quay section reflection no consideration

▪Plan arrangement CaseB▪Quay section reflection no consideration

CaseA-1 CaseA-2 CaseA-3

▪Plan arrangement CaseA▪Q1 : Igloo Block

▪Plan arrangement CaseA▪Q1 : Con'c Block

▪Plan arrangement CaseA▪Q1 : Igloo + Con'c Block

CaseB-1 CaseB-2 CaseB-3

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▪Plan arrangement CaseB▪Q1 : Igloo Block

▪Plan arrangement CaseB▪Q1 : Con'c Block

▪Plan arrangement CaseB▪Q1 : Igloo + Con'c Block

2. Model description (SWAN model)

2.1 Governing equation

◦ In SWAN the waves are described with the two-dimensional wave action density spectrum, even when nonlinear phenomena dominate(e.g., in the surf zone). The rationale for using the spectrum in such highly nonlinear conditions is that, even in such conditions it seems possible to predict with reasonable accuracy this spectral distribution of the second order moment of the waves(although it may not be sufficient to fully describe the waves statistically). The spectrum that is considered in SWAN is the action density spectrum rather than the energy density spectrum since in the presence of currents, action density is conserved whereas energy density is not(e.g., Whitham, 1974). The independent variables are the relative frequency (as observed in a frame of reference moving with current velocity) and the wave direction (the direction normal to the wave crest of each spectral component). The action density is equal to the energy density divided by the relative frequency: . In SWAN this spectrum may vary in time and space.

◦ In SWAN the evolution of the wave spectrum is described by the spectral action balance equation which for Cartesian coordinates is(e.g., Hasselmann et al., 1973):

◦ The first term in the left-hand side of this equation represents the local rate of change of action density in time, the second and third term represent propagation of action in geographical space(with propagation velocities and

in x- and y-space, respectively). The fourth term represents shifting of the relative frequency due to variations in depths and currents(with propagation velocity in -space). The fifth term represents depth-induced and current-induced refraction(with propagation velocity in -space). The expressions for these propagation speeds are taken from linear wave theory(e.g., Whitham, 1974; Mei, 1983; Dingemans, 1997). The term ( ) at the right hand side of the action balance equation is the source term in terms of energy

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density representing the effects of generation( ), dissipation( ) and nonlinear wave-wave interactions( ).

◦ The integration in time is a simple backward finite difference, so that the discretization of the action balance equation is(for positive propagation speeds , > 0, including the computation of the source terms but ignoring their discretization):

- Propagation term for the topography space

- Propagation term for the spectrum space

- Propagation term for the direction space

there,

2.2 Wind input

◦ Transfer of wind energy to the waves is described in SWAN with a resonance mechanism(Phillips, 1957) and a feed-back mechanism(Miles,

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1957). The corresponding source term for these mechanisms is commonly described as the sum of linear and exponential growth:

in which A describes linear growth and BE exponential growth.

◦ For the linear growth term A, the expression due to Cavaleri and Malanotte-Rizzoli(1981) is used with a filter to eliminate wave growth at frequencies lower than the Pierson-Moskowitz frequency(Tolman, 1992a):

, 7

in which is the wind direction, is the filter and is the peak frequency of the fully developed sea state according to Pierson and Moskowitz(1964; reformulated in terms of friction velocity).

◦ It should be noted that the SWAN model is driven by the wind speed at 10 m elevation whereas the computations use the friction velocity . For the WAM Cycle 3 formulation the transformation from to is obtained with

in which is the drag coefficient from Wu(1982):

For the WAM Cycle 4 formulations, the computation of is an integral part of the source term.

◦ Two expressions for exponential growth by wind are optionally available in the SWAN model. The first expression is due to Komen et al.(1984). Their

expression is a function of :

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in which is the phase speed and and are the density of air and water, respectively. This cph expression is also used in WAM Cycle 3(the WAMDI group, 1988). The second expression is due to Janssen(1989,1991). It is based on a quasi-linear wind-wave theory and is given by:

where is the Miles "constant". In the theory of Janssen(1991), this Miles "constant" is estimated from the non-dimensional critical height:

,

where is the Von Karman constant, equal to 0.41 and is the effective surface roughness. If the non-dimensional critical height , the Miles constant is set equal 0. Janssen(1991) assumes that the wind profile is given by:

in which is the wind speed at height z(10m in the SWAN model) above the

mean water level, si the roughness length. The effective roughness length

depends on the roughness length and the sea state through the wave

induced stress and the total surface stress :

The second of these two equations is a Charnock-like relation in which is a

constant equal to 0.01. The wave stress vector is given by:

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◦ The value of can be determined for a given wind speed and a given wave spectrum from the above set of equations. In the SWAN model the iterative procedure of Mastenbroek et al.(1993) is used.

2.3 Dissipation of wave energy by whitecapping

◦ The processes of whitecapping in the SWAN model is represented by the pulse-based model of Hasselmann(1974). Reformulated in terms of wave number(rather than frequency) so as to be applicable in finite water depth(cf. the WAMDI group, 1988), this expression is:

where and denote the mean frequency and the mean wave number(for expressions see below) respectively and the coefficient depends on the overall wave steepness. This steepness dependent coefficient, as given by the WAMDI group(1988), has been adapted by Günther et al.(1992) based on Janssen(1991a, see Janssen, 1991b):

This overall wave steepness is defined as:

The mean frequency , the mean wave number and the total wave energy:

are defined as(cf. the WAMDI group, 1988):

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2.4 Dissipation of wave energy by bottom friction

◦ The bottom friction models that have been selected for SWAN are the empirical model of JONSWAP(Hasselmann et al., 1973), the drag law model of Collins(1972) and the eddy-viscosity model of Madsen et al.(1988). The formulations for these bottom friction models can all be expressed in the following form:

in which is a bottom friction coefficient that generally depends on the

bottom orbital motion represented by :

◦ Hasselmann et al.(1973) found from the results of the JONSWAP experiment

for swell conditions. Bouws and Komen(1983) selected

a bottom friction coefficient of for fully developed wave conditions in shallow water. Both values are available in SWAN.

◦ The expression of Collins(1972) is based on a conventional formulation for periodic waves with the appropriate parameters adapted to suit a random wave field. The dissipation rate is calculated with the conventional bottom

friction formulation in which the bottom friction coefficient is

with (Collins, 1972). (Note that Collins(1972) contains an error in the expression due to an erroneous Jacobean transformation).

◦ Madsen et al.(1988) derived a formulation similar to that of Hasselmann and Collins(1968) but in their model the bottom friction factor is a function of the bottom roughness height and the actual wave conditions. Their bottom friction coefficient is given by:

in which is a non-dimensional friction factor estimated by using the formulation of Jonsson(1966; cf. Madsen et al., 1988):

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in which (Jonsson and Carlsen, 1976) and is a representative near-bottom excursion amplitude:

and is the bottom roughness length scale. For values of smaller than

1.57 the friction factor is 0.30(Jonsson, 1980).

2.5 Depth-induced wave breaking

◦ To model the energy dissipation in random waves due to depth-induced breaking, the bore-based model of Battjes and Janssen(1978) is used in SWAN. The mean rate of energy dissipation per unit horizontal area due to

wave breaking is expressed as:

in which in SWAN, is the fraction of breaking waves determined by:

in which is the maximum wave height that can exist at the given depth

and is a mean frequency defined as:

◦ Extending the expression of Eldeberky and Battjes(1995) to include the spectral directions, the dissipation for a spectral component per unit time is calculated in SWAN with:

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◦ The maximum wave height is determined in SWAN with , in which is the breaker parameter and is the total water depth(including the wave-

induced set-up if computed by SWAN). In the literature, this breaker parameter is often a constant or it is expressed as a function of bottom slope or incident wave steepness(see e.g., Galvin, 1972; Battjes and Janssen, 1978; Battjes and Stive, 1985; Arcilla and Lemos, 1990; Kaminsky and Kraus, 1993; Nelson, 1987, 1994).

◦ In the publication of Battjes and Janssen(1978) in which the dissipation model is described, a constant breaker parameter, based on Miche's criterion, of was used. Battjes and Stive(1985) re-analyzed wave data of a number of laboratory and field experiments and found values for the breaker parameter varying between 0.6 and 0.83 for different types of bathymetry(plane, bar-trough and bar) with an average of 0.73. From a compilation of a large number of experiments Kaminsky and Kraus(1993) have found breaker in the range of 0.6 to 1.59 with an average of 0.79.

2.6 Quadruplet wave-wave interactions

◦ The quadruplet wave-wave interactions are computed with the Discrete Interaction Approximation(DIA) as proposed by Hasselmann et al.(1985). Their source code(slightly adapted by Tolman, personal communication, 1993) has been used in the SWAN model. In the Discrete Interaction Approximation two quadruplets of wave numbers are considered, both with frequencies:

where is a constant coefficient set equal to 0.25. To satisfy the resonance conditions for the first quadruplet, the wave number vectors with frequency

and lie at an angle of and to the two identical wave

number vectors with frequencies and . The second quadruplet is the

mirror of this first quadruplet(the wave number vectors with frequency and

lie at mirror angles of and ).

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◦ Within this discrete interaction approximation, the source term is given by:

where refers to the first quadruplet and to the second quadruplet(he

expressins for are identical to those for for the mirror directions) and:

in which , , . Each of the contributions(i=1, 2, 3) is:

◦ The constant . Following Hasselmann and Hasselmann(1981), the quadruplet interaction in finite water depth is taken identical to the quadruplet transfer in deep water multiplied with a scaling factor R:

where R is given by:

in which is the peak wave number of the JONSWAP spectrum for which the original computations were carried out. The values of the coefficients are:

, and . In the shallow water limit, i.e., the

nonlinear transfer tends to infinity. Therefore a lower limit of is applied(cf. WAM Cycle 4; Komen et al., 1994), resulting in a maximum value

of . To increase the model robustness in case of arbitrarily shaped

spectra, the peak wave number is replaced by (cf. Komen et al., 1994).

2.7 Triad wave-wave interactions

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◦ The Lumped Triad Approximation(LTA) of Eldeberky(1996), which is a slightly adapted version of the Discrete Triad Approximation of Eldeberky and Battjes(1995) is used in SWAN in each spectral direction:

in which is a tunable proportionality coefficient. The biphase is approximated with

with Ursell number

Usually, the triad wave-wave interactions are calculated only for .

But for stability reasons, it is calculated for the whole range . This means that both quadruplets and triads are computed at the same time. The interaction coefficient is taken from Madsen and Sørensen(1993):

2.8 Diffraction

◦ In a simplest case, we assume there are no nurrents. This means that . Let denotes the propagation velocities in geographic and spectral spaces for

the situation without diffraction as: , and . These are given by:

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where is the wave number and n is perpendicular to the wave ray. We consider the following eikonal equation:

with denoting the diffraction parameter as given by:

Due to diffraction, the propagation velocities are given by:

, ,

where .

2.9 General formulation for obstacles

◦ SWAN can estimate wave transmission through a (line-)structure such as a breakwater(dam). Such an obstacle will affect the wave field in two ways, first it will reduce the wave height locally all along its length, and second it will cause diffraction around its end(s). The model is not able to account for diffraction. In irregular, short-crested wave fields, however, it seems that the effect of diffraction is small, except in a region less than one or two wavelengths away from the tip of the obstacle(Booij et al., 1993). Therefore the model can reasonably account for waves around an obstacle if the directional spectrum of incoming waves is not too narrow. Since obstacles usually have a transversal area that is too small to be resolved by the bottom grid in SWAN, an obstacle is modelled as a line. If the crest of the breakwater is at a level where(at least part of the) waves can pass over, the transmission coefficient(defined as the ratio of the(significant) wave height at the downwave side of the dam over the(significant) wave height at the upwave side) is a function of wave height and the difference in crest level and water level. The expression is taken from Goda et al.(1967):

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where is the freeboard of the dam and where is the incident(significant) wave height at the upwave side of the obstacle(dam), is the crest level of the dam above the reference level(same as reference level of the bottom), the mean water level relative to the reference level, and the coefficients , depend on the shape of the dam(Seelig, 1979):

【Coefficients , depend on the shape of the dam】<Table 2.1>

case

vertical thin wall 1.8 0.1

caisson 2.2 0.4

dam with slope 1:3/2 2.6 0.15

◦ The above expression is based on experiments in a wave flume, so strictly speaking it is only valid for normal incidence waves. Since there are no data available on oblique waves it is assumed that the transmission coefficient does not depend on direction. Another phenomenon that is to be expected is a change in wave frequency since often the process above the dam is highly nonlinear. Again there is little information available, so in SWAN it is assumed that the frequencies remain unchanged over an obstacle(only the energy scale of the spectrum is affected and not the spectral shape).

3. Experimental condition

【Experimental condition】<Table 3.1>

Item Contents

Object▪Calculation for shallow water wave transformation▪Harbor calm examination

Topographic data

▪World Coarse 1′depth data(National Ocean and Atmo sphere Administration, USA)▪Field observed depth data

Application model

▪SWAN model(Used Wave Action equation)

Wave condition Test wave i ii iii

Return 100 year

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Period

Direction N60°E

Grid Infomation

Coarse

Height 5.99m - -

Period 12.0s - -

Area 40.0km × 50.0km

Grid Space 100m(Uniform)

Grid Number

400 × 500(200,000)

(CaseA)

Fine

Height▪Coarse Result

4.2m 3.5m

Period 12.0s 12.0s 9.4s

Area 4.0km × 5.0km


Grid Number

400 × 500(200,000)

(CaseB)

Fine

Height▪Coarse Result

4.2m 3.5m

Period 12.0s 12.0s 9.4s

Area 10.0km × 12.5km


Grid Number

400 × 500(200,000)

Test Plan▪CaseA-0 ▪CaseA-i ▪CaseA-ii ▪CaseA-iii

▪CaseB-0 ▪CaseB-i ▪CaseB-ii ▪CaseB-iii

Depth Conversion

▪Oman Design Tide Level(+3.2m CD)

4. Experimental Result4.1 Plan A

【Range of Wave Height on Quay(CaseA)】<Table 4.1> (unit : m)

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Target Area

Plan Test Wave Q1 Q2 Q3 Q4 Q5

CaseA-0

I0.93～1.05

ii1.03～1.07

iii0.89～0.91

CaseA-1

i0.90～1.31

0.56～1.35

0.56～1.13

1.32～1.61

0.86～1.39

ii0.90～1.30

0.64～1.61

0.64～1.35

1.39～1.71

0.95～1.66

iii0.75～1.07

0.51～1.34

0.51～1.12

1.20～1.45

0.83～1.41

CaseA-2

i1.11～1.49

0.71～1.47

0.71～1.21

1.32～1.61

0.87～1.40

ii1.10～1.48

0.76～1.70

0.76～1.41

1.39～1.71

0.96～1.66

iii0.91～1.21

0.60～1.42

0.60～1.17

1.20～1.45

0.83～1.41

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CaseA-3

i0.92～1.37

0.56～1.35

0.56～1.13

1.32～1.61

0.87～1.39

ii0.90～1.36

0.64～1.61

0.63～1.35

1.39～1.71

0.96～1.66

iii0.75～1.12

0.51～1.34

0.51～1.12

1.20～1.45

0.83～1.41

※ Coffer Dam Design Wave Height refer to CaseA-0 Q2 area wave heights.

4.2 Plan B

【Range of Wave Height on Quay(CaseB)】<Table 4.2> (unit : m)

Target Area

Plan Test Wave Q1 Q2 Q3 Q4 Q5

CaseB-0

i 0.52

ii 0.68

iii 0.52

CaseB-1

i0.21～0.66

0.17～0.77

0.16～0.43

0.63～0.95

0.05～0.98

ii0.28～0.85

0.23～1.00

0.21～0.57

0.83～1.23

0.07～1.26

iii0.21～0.66

0.18～0.75

0.16～0.47

0.68～1.02

0.07～1.06

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CaseB-2

i0.28～0.78

0.20～0.83

0.19～0.46

0.64～0.96

0.05～0.98

ii0.36～1.02

0.27～1.08

0.25～0.61

0.84～1.23

0.07～1.26

iii0.27～0.78

0.21～0.80

0.20～0.49

0.68～1.03

0.07～1.06

CaseB-3

i0.22～0.78

0.19～0.83

0.19～0.46

0.64～0.95

0.05～0.98

ii0.28～1.02

0.25～1.07

0.25～0.60

0.83～1.23

0.07～1.26

iii0.21～0.78

0.20～0.80

0.19～0.49

0.68～1.03

0.07～1.06

※ Coffer Dam Design Wave Height refer to CaseA-0 Q2 area wave heights.

【Coarse Topography(CaseA)】

<Figure 4.1>

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【Fine Topography(CaseA)】

<Figure 4.2>

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【Coarse Topography(CaseB)】

<Figure 4.3>

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【Fine Topography(CaseB)】

<Figure 4.4>

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【Wave vectors and Wave Height Contour(Coarse, CaseA-0, Test Wave i)】

<Figure 4.5>

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【Wave Height Distribution(Coarse, CaseA-0, Test Wave i)】

<Figure 4.6>

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【Wave vectors and Wave Height Contour(Fine, CaseA-0, Test Wave i)】

<Figure 4.7>

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【Wave Height Distribution(Fine, CaseA-0, Test Wave i)】

<Figure 4.8>

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<Figure 4.9>

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<Figure 4.10>

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<Figure 4.11>

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<Figure 4.12>

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<Figure 4.13>

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<Figure 4.14>

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<Figure 4.15>

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<Figure 4.16>

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<Figure 4.17>

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<Figure 4.18>

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<Figure 4.19>

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<Figure 4.20>

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【Wave vectors and Wave Height Contour(Fine, CaseA-0, Test Wave ii)】

<Figure 4.21>

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【Wave Height Distribution(Fine, CaseA-0, Test Wave ii)】

<Figure 4.22>

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<Figure 4.23>

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<Figure 4.24>

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<Figure 4.25>

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<Figure 4.26>

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<Figure 4.27>

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<Figure 4.28>

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【Wave vectors and Wave Height Contour(Fine, CaseA-0, Test Wave iii)】

<Figure 4.29>

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【Wave Height Distribution(Fine, CaseA-0, Test Wave iii)】

<Figure 4.30>

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<Figure 4.31>

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<Figure 4.32>

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<Figure 4.33>

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<Figure 4.34>

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<Figure 4.35>

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<Figure 4.36>

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【Wave vectors and Wave Height Contour(Coarse, CaseB-0, Test Wave i)】

<Figure 4.37>

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【Wave Height Distribution(Coarse, CaseB-0, Test Wave i)】

<Figure 4.38>

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【Wave vectors and Wave Height Contour(Fine, CaseB-0, Test Wave i)】

<Figure 4.39>

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【Wave Height Distribution(Fine, CaseB-0, Test Wave i)】

<Figure 4.40>

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<Figure 4.41>

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<Figure 4.42>

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<Figure 4.43>

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<Figure 4.44>

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<Figure 4.45>

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<Figure 4.46>

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<Figure 4.47>

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<Figure 4.48>

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<Figure 4.49>

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<Figure 4.50>

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<Figure 4.51>

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<Figure 4.52>

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【Wave vectors and Wave Height Contour(Fine, CaseB-0, Test Wave ii)】

<Figure 4.53>

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【Wave Height Distribution(Fine, CaseB-0, Test Wave ii)】

<Figure 4.54>

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<Figure 4.55>

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<Figure 4.56>

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<Figure 4.57>

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<Figure 4.58>

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<Figure 4.59>

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<Figure 4.60>

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【Wave vectors and Wave Height Contour(Fine, CaseB-0, Test Wave iii)】

<Figure 4.61>

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【Wave Height Distribution(Fine, CaseB-0, Test Wave iii)】

<Figure 4.62>

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<Figure 4.63>

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<Figure 4.64>

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<Figure 4.65>

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<Figure 4.66>

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<Figure 4.67>

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<Figure 4.68>

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