Three-Dimensional Simulation of Water Circulation in the Java Sea: Influence of Wind Waves on...

Natural Hazards21: 145–171, 2000.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

145

Three-Dimensional Simulation of Water Circulationin the Java Sea: Influence of Wind Waves onSurface and Bottom Stresses

NINING SARI NINGSIH1, TAKAO YAMASHITA 2 and LOTFI AOUF3

1Graduate School of Engineering, Kyoto University;2Disaster Prevention Research Institute, KyotoUniversity;3Disaster Prevention Research Institute, Kyoto University

(Received: 17 July 1998; in final form: 11 December 1998)

Abstract. A one-year simulation of tide- and wind-driven circulation in the Java Sea, which is oneof the Indonesian seas located in a tropical area, has been carried out using a three-dimensionalhydrodynamic model incorporating the influence of the wind waves generated at the sea surface.This area is influenced by the monsoon climate (east- and west-monsoon). Six hourly-wind fields at10 m above the sea surface were used as a representative wind field. In other respects, the effect ofwaves on the three-dimensional hydrodynamic model has been represented by the surface and bottomstresses. A third-generation wave model called WAM (WAMDI, 1988) was used to calculate the waveparameters and the wave dependence of the drag coefficient. The trajectory of water particles inducedby the calculated velocity fields in the Java Sea was then simulated. In dealing with hazardousphenomena, this model will be extended to predict suspended sediment fluxes, particularly thoserelating to catastrophic changes in sea bottom topography and beach erosion. It is also an importanttool for the prediction of storm surge events.

Key words: three-dimensional circulation model, mode splitting, wind-wave effects, monsoon cli-mate, tide- and wind-driven circulation, Java Sea, surface stress, bottom stress.

1. Introduction

In coastal and ocean areas, complex dynamical processes exist due to the coexist-ence of air motions, surges, waves, currents, tides, and their mutual interactions. Itis important to obtain a good understanding of these processes both for scientificand practical reasons such as the prediction of wave fields, currents, and hazardousphenomena (e.g., storm surges, beach erosion and sea bottom changes caused bysediment transport). To predict and mitigate these kinds of coastal and ocean dis-asters, a detailed knowledge of flow fields is required in the area of interest. Withthe development of both computer and numerical methods for solutions of time-dependent flows, numerical simulation has become an economic and effective wayto obtain the flow parameters required compared to the high cost of performingfield observations.

Hydrodynamics, which governs the motion of sea water and materials, is themost important process involved in storm surge and sediment transport problems.

146 NINING SARI NINGSIH ET AL.

In storm surge prediction, it is desirable to develop a more sophisticated numericalmodel which can obtain the profile of current, turbulence, and surge heights; whilein transport phenomena, a better representation of the processes near the bottomneeds to be investigated. For this purpose and to predict the comprehensive flowfields, three-dimensional models are necessary.

In this study a three-dimensional coastal ocean circulation model has beendeveloped based on ideas proposed by Kowalik and Murty (1993). The numer-ical techniques employed in the developed model are the mode splitting andσ -coordinate system. One of the major problems of the three-dimensional model is toreduce the large amount of computational work required. The mode splitting tech-nique that splits the three-dimensional model into vertically integrated equations(external mode) and three-dimensional equations (internal mode) was used for thispurpose. In further considerations the transformation of the governing equationsfrom z-coordinate to a dimensionless vertical coordinate (σ ) was performed toachieve a better simulation of both the surface and bottom mixed layers.

The developed model was used to simulate the flow fields in the Java Sea, whichis one of the Indonesian seas which plays an important role in linking the waters ofthe Pacific and the Indian Oceans. Hence, we need to acquire a better understandingof the water circulation and transport processes in this region. From the view pointof disaster prevention, it seems that storm surges may not be a serious problem inthe Java Sea. Therefore, it is more appropriate to use the detailed knowledge of flowfields in the area to study catastrophic changes in sea bottom topography, primarilyfrom the view point of sediment transport, erosion, deposition, navigation, andflood defense.

Several authors, e.g., Janssen, 1989, 1991; Mastenbroek, 1982, have publishedon the relationship between the drag coefficient (CD), the wind speed, and theroughness of the sea surface. This roughness depends essentially upon the totalstress and the stress induced by the waves at the free surface. Mastenbroeketal. (1993) found a significant improvement in a storm surge model by using thecalculations with the wave-dependent drag on the surface stress.

On the bottom there exist enhanced levels of turbulence at the bed and the re-tarding force due to the wind-wave effects (e.g., Davies and Lawrence, 1995; Grantand Madsen, 1979; Signellet al., 1990). Both for scientific and practical reasons,e.g., for studies such as mixing processes and sediment transport problems, it isimportant to superimpose waves on current at the near-bed boundary layer. Forexample, if the enhanced bed friction due to wind-wave effects exceeds a thresholdvalue, the onset of sediment movement will occur.

Therefore calculations involving wave effects are important to achieve a bet-ter result in simulating circulation in the Java Sea. In this paper two effects ofwaves on the three-dimensional hydrodynamic model were used, namely the wavedependence of the drag coefficient at the free surface and enhancements in near-bed turbulence due to wind-wave activity. The effects are applied on the surfaceand bottom stresses, respectively. A third-generation wave model called WAM

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA 147

(WAMDI, 1988) was used to calculate the wave parameters and the wave depend-ence of the drag coefficient. In a final calculation, the trajectory of water particlesinduced by one-year simulation of tide- and wind-driven circulation in the Java Seawas carried out using the three-dimensional hydrodynamic model incorporating theinfluence of waves.

2. Three-Dimensional Hydrodynamic Model

To reduce the large amount of computational work in developing the three-dimensional (3D) model, the computations are performed in two time steps: a shorttime step is used to compute two-dimensional (2D) problems (barotropic mode) bythe vertically integrated equations (external mode) and a much longer time step isused to solve for the 3D problems (internal mode).

2.1. RUDIMENTS OF THE MODE-SPLITTING TECHNIQUE

The system of equations with the Boussinesq and hydrostatic approximation inCartesian coordinates are given byThe continuity equation:

∂u

∂x+ ∂v∂y+ ∂w∂z= 0. (1)

The equations of motion along thex andy axes are:

du

dt− f v = − 1

ρo

∂pa

∂x− g ∂ς

∂x+ ∂

∂zNz∂u

∂z+Nh1u, (2)

dv

dt+ f u = − 1

ρo

∂pa

∂y− g ∂ς

∂y+ ∂

∂zNz∂v

∂z+Nh1v, (3)

whereu, v, andw are eastward, northward, and vertical components of velocity;t is time; f is the Coriolis parameter;g is the gravitational acceleration;ς rep-resents the surface elevation;ρo is the density of water;pa is the atmosphericsurface pressure; andNz andNh are the vertical and horizontal eddy viscosities,respectively.

A dynamic boundary condition evaluated at sea surfacez = ς will indicate therelation between sea levelς and vertical velocitywς as

∂ς

∂t+ ∂ς∂xuς + ∂ς

∂yvς = wς. (4)

The vertical velocity at the sea surfacewς can be obtained by integrating (1) fromthe bottomz = −H to the sea surfacez = ς .


In the present study gradients of the atmospheric pressure given by the firstterms in the right-hand side of Equations (2) and (3) are neglected. The externalmode is described by the vertically-averaged equations:

∂u

∂t+ Ax − f v = −g ∂ς

∂x+ Cx +Nh1u, (5)

∂v

∂t+ Ay + f u = −g ∂ς

∂y+ Cy +Nh1v. (6)

Here the termsA andC denote the nonlinear terms and shear stresses, respectively.The nonlinear terms:

Ax = 1

H

[∂

∂x

∫ ς

−Hu2 dz + ∂

∂y

∫ ς

−Huv dz

], (7)

Ay = 1

H

[∂

∂x

∫ ς

−Huv dz+ ∂

∂y

∫ ς

−Hv2 dz

]. (8)

Surface and bottom stresses:

Cx = τ sx /(Hρo)− τ bx /(Hρo), (9)

Cy = τ sy /(Hρo)− τ by /(Hρo). (10)

A sea level change is obtained from the continuity equation for the vertically-averaged flow:

∂uD

∂x+ ∂vD

∂y+ ∂ς∂t= 0, (11)

hereD = H + ς is the total depth.The internal mode equations are derived by defining the velocity components

as a sum of the average and variations around this average:

u = u+ u′ and v = v + v′. (12)

Subtracting (5) from (2) and (6) from (3) we obtain the internal mode equations:

∂u′

∂t+ u∂u

∂x+ v ∂u

∂y+ w∂u

∂z− Ax − f v′

= ∂

∂z

(Nz∂u′

∂z

)− Cx +Nh1u′, (13)


Figure 1. Time-stepping of the splitting method.

∂v′

∂t+ u∂v

∂x+ v ∂v

∂y+ w∂v

∂z− Ay + f u′

= ∂

∂z

(Nz∂v′

∂z

)− Cy +Nh1v′. (14)

Equations (13) and (14) do not contain explicitly barotropic oscillations since thesea level variations were deleted in the subtraction process.

2.2. IMPLEMENTATION OF THE SPLITTING METHOD

The computational scheme of the motion equations was carried out in two stages.Starting with the depth-integrated equations (5), (6) and (11) that were solved withthe short time step (T2D) as defined by CFL condition, it was followed by the three-dimensional computation (Equations (13) and (14)) with a much longer time stepT3D, i.e., T3D = MT2D. A typical value ofM ranges from 10 to 50. Further, thevelocity distribution was solved by Equation (12). A simplified illustration of thetime interaction of the 2D and 3D models is depicted in Figure 1.

The 3D model operates with a time stepT3D = tm+M− tm while the 2D model isadvanced with a time-stepT2D = tm+1 − tm. In the three-dimensional calculation,the vertical friction terms in the right-hand side of Equations (13) and (14) arediscretized implicitly by the line inversion method (Kowalik and Murty, 1993),whereas other terms are discretized explicitly.

2.3. SIGMA COORDINATE TRANSFORMATION

Theσ -transformation is employed in the vertical direction to achieve a more accur-ate approximation of the surface and bottom boundary conditions. In thez-coordinate system, the layer thicknesses are uniform in the horizontal. Otherwise,in the sigma-coordinate they vary widely from grid point to grid point. It is the nor-malized thicknesses that are uniform in the sigma-coordinate. The transformationcan be written as

σ = z− ςD

. (15)


The new coordinate transforms the column of water from the surface (z = ς ) tothe bottom (z = −H ) into a uniform depth ranging from 0 to−1. The equation ofmotion for the internal mode in theσ -coordinate becomes

∂u′

∂t+ u∂u

′

∂x+ u∂u

∂x+ v ∂u

′

∂y+ v ∂u

∂y+ ∂σ∂t

∂u′

∂σ− Ax − f v′

= D−2 ∂

∂σ

(Nσ∂u′

∂σ

)− [τ sx /(Hρo)− τ bx /(Hρo)] +Nh1u′,

∂v′

∂t+ u∂v

′

∂x+ u∂v

∂x+ v ∂v

′

∂y+ v ∂v

∂y+ ∂σ∂t

∂v′

∂σ− Ay + f u′

= D−2 ∂

∂σ

(Nσ∂v′

∂σ

)− [τ sy /(Hρo)− τ by /(Hρo)] + Nh1v′. (16)

The Cartesian vertical velocity is

w = ω + u(σ∂D

∂x+ ∂ς∂x

)+ v

(σ∂D

∂y+ ∂ς∂y

)+ σ ∂D

∂t+ ∂ς∂t, (17)

hereω is obtained by solving the following equation

∂Du

∂x+ ∂Dv

∂y+ ∂ω∂σ+ ∂ς∂t= 0. (18)

2.4. BOUNDARY CONDITIONS

2.4.1. Lateral Boundary Conditions

Zero flow normal is applied to solid boundaries, while along open boundaries aradiation condition (Glorioso and Davies, 1995) was applied, namely,

q = qm + c

H(ς − ςm), (19)

whereq is the normal component of depth-mean current,c = (gH)1/2, qm andςm are the meteorological terms which can be derived from far-field atmosphericforcing through the model’s open boundary. In this paper,qm andςm were set tozero since we are concerned with only the local wind effects. In cases where tide-driven currents are considered, tidal elevation is applied along open boundaries.


2.4.2. Vertical Boundary Conditions

The surface and bottom boundary conditions in theσ -coordinate system can bewritten as

ω(x, y,0, t) = ω(x, y,−1, t) = 0, (20)

ρNσ

D

(∂u

∂σ,∂v

∂σ

)= (τ sx , τ sy ) = ρaCDWT (Wx,Wy), atσ = 0, (21)

whereWT = (W 2x +W 2

y )1/2 with Wx andWy denoting the component of the wind

speed at the altitude 10 m above sea level,CD is the drag coefficient,ρa is the airdensity.

At the seabed, in the absence of wind waves, the bottom stress is given by

ρNσ

D

(∂u

∂σ,∂v

∂σ

)= (τ bx , τ by ) = ρCz[U2

h + V 2h ]1/2(Uh, Vh), atσ = −1, (22)

whereUh andVh are the near-bed velocities;Cz is a coefficient of bottom frictionand will increase in value when wave effects are present. This value can be obtainedby the following expression (Mellor, 1996),

Cz = max

[κ2

[ln(30zr/kb)]2 ,0.0025

], (23)

whereκ = 0.4 is the von Karman constant,zo is the roughness length, takenhere as 0.146 cm, andkb = 30zo is the bed roughness. Numerically, by matchingthe numerical solution to the “law of the wall” the reference heightzr is taken asthe first grid point nearest the bottom. Where the bottom is not so well resolved,30zr/kb is large, hence Equation (23) reverts to an ordinary bottom-drag coefficientformulation (Mellor, 1996).

2.5. SECOND ORDER MODEL OF TURBULENCE CLOSURE

The surface and bottom mixed layer play a very important role in the dynamics ofthe water column for coastal oceans. Therefore, it is necessary to parameterize thevertical mixing as accurately as possible. The vertical mixing coefficientNσ is ob-tained by the second order closure model of turbulence adopted from POM’s model(the Princeton Ocean Model) based on the work of Mellor and Yamada (1982). Theturbulence model is characterized by two quantities, the turbulence kinetic energyq2/2 and the turbulence macroscalel. To find details of this turbulence model,please refer to “Users guide for a three-dimensional, primitive equation, numericalocean model” by Mellor (1996).


3. Wave Effects on the Surface Stress

Since both theoretical and experimental evidence of the wave-dependent drag coef-ficient (CD) have been given extensively in the literature (Janssen, 1989, 1991,1992; Mastenbroek, 1992; Mastenbroeket al., 1993), only a very brief descriptionwill be presented here. The surface stress as one of the ocean-circulation generatingforces depends on the wind speed and roughness of the sea surface. This apparentroughness depends on the presence of waves that have momentum gained fromthe atmospheric boundary layer. Then, those growing waves change the verticaldistribution of turbulence and wind profile.

The drag coefficient is defined byCD = u2∗/W(10)2, whereu∗ = √τ/ρa is thefriction velocity, andW (10) is the wind speed at 10 m above the sea surface. Byneglecting the influence of the air viscosity, the total stress at the free surfaceτ isdefined as the sum of the turbulent stress and the stress induced by the waves:τ =τt + τw. Janssen (1992) described a theory to model the effect of waves on the dragcoefficientCD by using the following equations. The effective roughnessze whenwaves are present:

ze = zo√1− τw/τ , (24)

wherezo is the roughness length given by the Charnock relation:zo = αu2∗/g, withα = 0.0185. The wind profile is given by

u(z) = u∗κ

ln

(z+ ze − zo

ze

), (25)

τ (or u∗), zo, and ze can be calculated by solving iteratively an implicit set ofequations given by (24), (25) and the Charnock relation. HenceCD can be obtained.This procedure was implemented in the WAM model.

4. Wave Effects on the Bottom Stress

In this section we present the main steps in the formulation of the wave–currentinteraction model. For simplicity, we use only collinear waves and current in thecalculation. A detailed description of this model can be found in Grant and Madsen(1979), Davieset al. (1988), and Signellet al. (1990).

The bed-stress and the coefficient of bottom frictionCz related to the near-bedvelocityUh andVh using a quadratic friction law in the absence of wind waves, aregiven in (22) and (23), respectively. In the presence of waves, the bottom frictioncoefficientCz will increase in value due to the wave effect enhancing the bed stressand given by

Cz = max

[1

2fc,0.0025

], (26)


wherefc is the current friction factor defiend by

fc = 2

[κ

ln(30zr/kbc)

]2

, (27)

wherekbc is the apparent bottom roughness felt by the current when the waves arepresent.

The total bed shear stressτT based on an instantaneous current shear stressτcand the maximum wave bottom stressτw for collinear flow is given by

τT = τc + τw, (28)

with

τw = 1

2fwρU

2w, (29)

whereUw is the maximum near-bed orbital velocity and is given by

Uw = awω

sinh(kh). (30)

The wave-numberk is determined from the linear dispersion relation:

ω2 = (gk) tanh(kh). (31)

The wave friction factorfw is obtained using the empirical expression from Grantand Madsen (1982):

fw = 0.13(kb/Ab)0.40 → kb/Ab < 0.08

0.23(kb/Ab)0.62 → 0.08< kb/Ab < 1.000.23→ kb/A > 1.00,

(32)

whereAb = Uw/ω is the near-bed excursion amplitude.To reduce the number of computations, an assumption that the current does not

influence the wave field (Signellet al., 1990) is also used in the present model.However, the wave field influences the current bed stressτc. Therefore, the third-generation wave model WAM is solved externally and then the results are sup-plied to the 3D-hydrodynamic model. Based on this assumption, the wave-frictionvelocity is computed by

U∗w =(τw

ρ

)1/2

. (33)

Steps of the wave-effect computation described above are as follows:


At time t = 0, an initial current factorfc = 2Cz is computed without waveeffects from Equation (23). Then the current friction velocityU∗c is computed from

U∗c =(τc

ρ

)1/2

, (34)

whereτc is the vector sum of the bed-stress componentsτcx andτcy from (22).Having determinedU∗c, the combined friction velocityU∗cw for waves and

currents is given by

U∗cw = (U2∗c + U2

∗w)1/2. (35)

The apparent bottom roughnesskbc is defined by

kbc = kb[24U∗cwUw

Ab

kb

]β, (36)

where

β = 1− U∗cU∗cw

. (37)

At the next time step, this value ofkbc is then used to determinefc due tothe presence of wind wave effects, by using (27). Then, the bed stress in the 3D-hydrodynamic model from Equation (22) can be readily computed.

5. Application of the Model to the Java Sea

Figure 2 shows the computational domain and bathymetry of the Java Sea locatedat tropical area (105◦–115◦E and 8◦20′–2◦40′S) as well as extra-tropical regioninfluenced by monsoon climate. The grid sizes, the 2D- and 3D- time step used inthe simulation are 18.5× 18.5 km, 60 s, and 1800 s, respectively. We used 6-hourlywind field vectors at 10 m above the sea surface as representative wind field data.The wind field vectors representing typical times of west- and east-monsoon canbe seen in Figure 3.

5.1. RESULTS AND DISCUSSIONS

Due to the lack of data for the Java Sea, for verification we only compared thesimulation results of elevation induced by tide-driven circulation with those of tidalprediction at some locations, namely Rembang, Jakarta, Surabaya, Pasuruan, andBanjar Masin (marked R, J, S, P, and B, respectively in Figure 2). Tidal elevationused in open boundary as a generating force was obtained by carrying out tidal pre-diction based on information of the four principal harmonic constituents (M2, S2,K1, and O1) published by the International Hydrographic Bureau of Monaco. The


Figure 2. Computational domain and bathymetry of the Java Sea (in meters).

verification results of elevation at those places can be seen in Figure 4. Generally,elevations obtained from the simulation show a good agreement with those of tidalprediction in some locations, namely at Rembang (R) and Jakarta (J) (respectivelyin Figure 4(a), (b)), although at Pasuruan (P) and Banjar Masin (B) (in Figure 4(d),(e), respectively) there is a slight phase shift between the simulated and predictedelevations. However, the verification at Surabaya (S) in Figure 4(c) is not good,probably due to the estimation of the effect of the bottom friction which doesnot reproduce adequately the nonlinear interaction of the extremely strong tidalcurrents with the bottom topography.

5.1.1. Tide-Driven Circulation

Figure 5 shows current circulation at flood and ebb condition during a spring tide.Tidal prediction at Rembang (R) was chosen as the reference time of the flood andebb condition. The figure clearly shows the existence of currents that flow back andforth representing flood and ebb conditions. At spring flood condition the currentsaround Rembang flow eastward; they flow westward at spring ebb condition.

5.1.2. Tide- and Wind-Driven Circulation

A one-year simulation of tide- and wind-driven circulation in 1996 was carried outsimultaneously to get a better understanding of the complicated phenomena in theJava Sea. Figure 6 shows the circulation pattern during west- and east-monsoonsfor spring flood conditions.

During spring flood conditions, there is flow coming from South-China Seainto the Java Sea through Gaspar and Karimata strait indicated as N1 and N2 inFigure 2, respectively. The wind forces clearly influence the previous circulation


Figure 3. Typical wind fields of the Java Sea; (a) West-monsoon; (b) East-monsoon.


Figure 4. Verification of free surface elevation between tidal prediction (...........) andsimulation results (———) at (a) Rembang; (b) Jakarta; (c) Surabaya; (d) Pasuruan; and (e)Banjar Masin.

158N

ININ

GS

AR

ININ

GS

IHE

TA

L.

Figure 5. Tide-driven circulation during spring tide at (a) Flood conditions; and (b) Ebb conditions.

TH

RE

E-D

IME

NS

ION

AL

SIM

ULA

TIO

NO

FW

AT

ER

CIR

CU

LAT

ION

INT

HE

JAVAS

EA

159

Figure 6. Tide- and wind-driven circulation for spring flood condition at (a) West-monsoon; and (b) East-monsoon.


that was only driven by tide. During west-monsoon, the effects of wind increase themagnitude of currents and the circulation flows mainly eastward. Otherwise, duringthe east-monsoon, the easterly wind-driven currents flow in the opposite directionto the tide-driven circulation during the spring flood conditions. Consequently,we can observe that there is a decrease of the magnitude of the currents at theregion around the Karimata Strait (N2); while in other areas where the easterlywind-driven currents are more dominant than the tide-driven currents, the resultantcurrents flow westward.

5.2. WAVE FIELDS IN THE JAVA SEA

To calculate the wave fields in the Java Sea, a third-generation wave model WAMhas been used. A detailed description of this model can be found in the literature(WAMDI Group, 1988; Güntheret al., 1992). The model was run externally andthen its output, such as the wave fields and the wave-dependent drag coefficient,were supplied to the 3D-hydrodynamic model for incorporating the influence ofwaves on the surface and bottom stresses.

The wave fields and the 2D-spectra at Surabaya (S) and Rembang (R) are shownin Figure 7(a), (b), respectively. The magnitude of significant wave height (Hs) dur-ing the west-monsoon is greater than during the east-moonsoon. We also noticedthat the wave direction follows the main direction of the wind fields (as illustratedin Figure 3). For typical west-monsoon, the maximum value of significant waveheight (Hs) reaches about 2.8 m in the southern region of the eastern part of theJava Sea, while for the east-monsoon it reaches about 1 m in the region close to theKarimata Strait (N2). From the 2D-spectra figures it is found that the wave peakfrequency (fp) at Surabaya (S) and Rembang (R) is about 0.26–0.27 Hz at thewest-monsoon and about 0.33–0.34 Hz at the east-monsoon. This range of valuesof fp is equal to periods of 2.9–3.8 s, which are within those of Emeryet al. (1972)of about 2–4 s.

5.3. WAVE EFFECTS

5.3.1. Effect of Waves on the Bottom Stress by Using Constant Value of Hs and fp

Before using the wave fields and the wave-dependent drag coefficient obtained bythe WAM model, we have considered as a test case that the peak frequency,fp= 0.17 Hz, and the significant wave height,Hs = 2 m, of the wind waves remainconstant in space and time.

Enhancement in bed stress due to the wind waves depends upon the wind waveorbital velocityUw given by Equation (30) which decreases rapidly with respect tothe water depth and the wave frequency. Following Davies and Lawrence (1995),we give some examples ofUw computation, namely forfp = 0.17 Hz andHs = 2m,Uw = 0.62 m s−1 at depth 10 m and 0.1 m s−1 at depth 50 m, while forfp = 0.10Hz andHs = 2 m,Uw = 0.85 m s−1 at depth 10 m and 0.16 m s−1 at depth 50 m.


Figure 7(a). The significant wave height (in meters) and the wave direction in the Java Seafor the typical west- and east-monsoon.

Therefore the flow field retarded by the increased bed-turbulence due to the waveeffects will occur more in a shallow water regions than in a deep ones.

Figures 8 and 9 show that the flow fields decrease due to the wave effects on thebottom stress. Also, it can be seen that the retarded flow occurs at the location R(depth = 28 m) more than at the location D (depth = 73 m).


Figure 7(b). 2D energy spectrum at Surabaya (S) and Rembang (R).


Figure 8. Variation of the free surface elevation and the total velocity at the free surface andnear the bottom in the period of 27 February 1996 to 2 March 1996 at Rembang (R) by usingthe drag coefficientCD = 0.003 (constant): (...........) with waves; (———) no waves.

5.3.2. Effect of Waves on the Surface Stress by Using the Wave Dependence ofthe Drag Coefficient (CD)

In this section, we have compared the computation results by using the wave de-pendence of the drag coefficient (CD) as output from the WAM model with theconstant value ofCD = 0.003 on the surface stress. Figure 10 shows the variationof the drag coefficientCD with the wind speed for the period of 27 February 1996to 2 March 1996 at Rembang (R) location. These values obtained by the WAMmodel vary between 0.0015–0.0018.

Let us compare the computation using the constant value of the drag coefficient(CD = 0.003) and the variable values of the drag coefficient (CD < 0.003) obtainedby the WAM model. We show that the current velocity components at the freesurface decrease with the smaller value ofCD, while the free surface elevationincreases, as illustrated in Figure 11.

We are now interested in the effect of the waves on the surface and bottom stressfor the case using the spatial and temporal variation of the significant wave heightHs, the peak frequencyfp, and the drag coefficientCD which are obtained by theWAM model. Figure 12 shows that the current velocity components decrease withwater depth and also for the smaller value of the drag coefficient.


Figure 9. Variation of the velocity components with the water depth at 2300 UTC on 29February 1996 at Rembang R (depth = 28 m) and at D (depth = 73 m) locations: (...........) withwaves; (———) no waves.


Figure 10. Variation of the drag coefficientCD with respect to the wind speed and for theperiod from 27 February 1996 to 2 March 1996 at Rembang (R): (...........)CD from WAM;(———) CD = 0.003 (constant); (- - - - - - ) wind speed.

Figure 11. Variation of the free surface elevation and the current velocity components for theperiod from 27 February 1996 to 2 March 1996 at Rembang (R): (...........) with waves (CD <

0.003); (———) no waves (CD = 0.003).


Figure 12. Variation of the current velocity components with respect to the water depthat 2300 UTC on 29 February 1996 at Rembang (R): (...........) with waves (CD < 0.003);(———) no waves (CD = 0.003).


Figure 13. Initial location of the water particles on the surface and bottom layer.

5.4. TRAJECTORY OF WATER PARTICLES IN THE JAVA SEA

One-year simulation of tide- and wind-driven circulation is performed to determinethe trajectory of the water particles at the surface and bottom layers by using theEuler–Langrangian method. In this simulation, we have taken into account theinfluence of waves on the surface and bottom stresses described in Section 5.3.2.The initial location of the water particles is shown in Figure 13.

The results show qualitatively the main location where the water particles willaccumulate and which boundaries will be passed by the water particles that moveout from the Java Sea. The trajectories of the water particles on the surface layerare illustrated in Figure 14. In the west-monsoon (from 6–14 January), most wa-ter particles move out from the Java Sea through the boundary on the east side(marked E in Figure 2). The accumulation was found in the coastal water aroundthe northern part of Java Island, while in the east-monsoon (in May) this waterparticle accumulation moves to the southern part of Kalimantan Island and someof the water particles move out from the Java Sea into the South China Sea throughthe Gaspar Strait (marked N1 in Figure 2).

Figure 15 shows trajectories of the water particles on the bottom layer. Unlikeon the surface layer where most water particles move out rapidly from the JavaSea, on the bottom layer they move out slowly due to the magnitude of currents onthe bottom layer being smaller than that on the surface. During the west-monsoon(January) and the transitional season from west to east monsoon (April), the accu-mulation exists in the coastal water around the southern part of Kalimantan Islandand the central part of the Java Sea, and most water particles move out from theJava Sea through the eastern part (marked E in Figure 2). Whereas, during the east-monsoon (August) and the transitional season from east to west monsoon (October)the water particles accumulate around Surabaya Beach (marked S in Figure 2) andmost water particles move out from the Java Sea through the northern part (markedN1 and N2 in Figure 2).

168N

ININ

GS

AR

ININ

GS

IHE

TA

L.

Figure 14. Trajectory of the water particles on the surface layer.

TH

RE

E-D

IME

NS

ION

AL

SIM

ULA

TIO

NO

FW

AT

ER

CIR

CU

LAT

ION

INT

HE

JAVAS

EA

169

Figure 15. Trajectory of the water particles on the bottom layer.


6. Concluding Remarks

A three-dimensional hydrodynamic model has been developed to simulate tide-and wind-driven circulation, incorporating the influence of waves on the surfaceand bottom stresses. The developed model was applied to simulate the flow fieldsin the Java Sea whose environment has been rapidly changing due to the develop-ment of its coastal and ocean area. This causes many hazardous situations such ascatastrophic beach erosion, destroyed coastal and offshore structures, and disruptednavigation because of the excess deposition of sediment materials.

The application of the model to the Java Sea showed that the existence of themonsoon wind fields plays an important role in the general circulation of watersin this area. Changes in the surface and bottom stresses by incorporating the effectof waves have significantly influenced the three-dimensional model of tide andwind-driven circulation. This wave-current interaction effect is important in shal-low regions such as the Java Sea due to the enhanced bed stress in shallow areaswhich induces a significant decrease of the flow.

The calculated velocity fields were then applied to simulate the trajectory ofwater particles in the region. In this present study, we have only considered non-continuous sources of particles, whereas in reality it would be essential to considercontinuous and main sources of particles such as rivers that move various sedimentsinto the Java Sea (e.g., silts and muds which are the major sediments that coverthe floor of the region, Emeryet al., 1972). The model can also be extended topredict suspended sediment fluxes by solving the advection-diffusion equation forsediments, in dealing with hazardous phenomena, particularly catastrophic changesin sea bottom topography and beach erosion of the Java Sea. These kinds of studiesare currently in progress as an extension of this research program. In addition,the developed 3D-hydrodynamic model is also important for simulation of currentfields and surge height distribution, especially in hazardous areas of storm surgessuch as the United States and Bangladesh. We can cite as an example, the applica-tion of a three-dimensional hydrodynamic model to the northern South China Seawhich was carried out to hindcast a storm surge event generated by typhoon Ellen(Zhang and Li, 1996).

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