Three-Dimensional Simulation of Water Circulation in the Java Sea ...

Natural Hazards 21: 145–171, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.

145

Three-Dimensional Simulation of Water Circulation in the Java Sea: Influence of Wind Waves on Surface and Bottom Stresses NINING SARI NINGSIH1, TAKAO YAMASHITA2 and LOTFI AOUF3 1 Graduate School of Engineering, Kyoto University; 2 Disaster Prevention Research Institute, Kyoto University; 3 Disaster 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 one of the Indonesian seas located in a tropical area, has been carried out using a three-dimensional hydrodynamic 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 at 10 m above the sea surface were used as a representative wind field. In other respects, the effect of waves on the three-dimensional hydrodynamic model has been represented by the surface and bottom stresses. A third-generation wave model called WAM (WAMDI, 1988) was used to calculate the wave parameters and the wave dependence of the drag coefficient. The trajectory of water particles induced by the calculated velocity fields in the Java Sea was then simulated. In dealing with hazardous phenomena, this model will be extended to predict suspended sediment fluxes, particularly those relating to catastrophic changes in sea bottom topography and beach erosion. It is also an important tool for the prediction of storm surge events. Key words: three-dimensional circulation model, mode splitting, wind-wave effects, monsoon climate, 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 coexistence of air motions, surges, waves, currents, tides, and their mutual interactions. It is important to obtain a good understanding of these processes both for scientific and practical reasons such as the prediction of wave fields, currents, and hazardous phenomena (e.g., storm surges, beach erosion and sea bottom changes caused by sediment transport). To predict and mitigate these kinds of coastal and ocean disasters, a detailed knowledge of flow fields is required in the area of interest. With the development of both computer and numerical methods for solutions of timedependent flows, numerical simulation has become an economic and effective way to obtain the flow parameters required compared to the high cost of performing field observations. Hydrodynamics, which governs the motion of sea water and materials, is the most 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 numerical model which can obtain the profile of current, turbulence, and surge heights; while in transport phenomena, a better representation of the processes near the bottom needs to be investigated. For this purpose and to predict the comprehensive flow fields, three-dimensional models are necessary. In this study a three-dimensional coastal ocean circulation model has been developed based on ideas proposed by Kowalik and Murty (1993). The numerical techniques employed in the developed model are the mode splitting and σ coordinate system. One of the major problems of the three-dimensional model is to reduce the large amount of computational work required. The mode splitting technique that splits the three-dimensional model into vertically integrated equations (external mode) and three-dimensional equations (internal mode) was used for this purpose. In further considerations the transformation of the governing equations from z-coordinate to a dimensionless vertical coordinate (σ ) was performed to achieve 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, which is one of the Indonesian seas which plays an important role in linking the waters of the Pacific and the Indian Oceans. Hence, we need to acquire a better understanding of the water circulation and transport processes in this region. From the view point of disaster prevention, it seems that storm surges may not be a serious problem in the Java Sea. Therefore, it is more appropriate to use the detailed knowledge of flow fields in the area to study catastrophic changes in sea bottom topography, primarily from the view point of sediment transport, erosion, deposition, navigation, and flood defense. Several authors, e.g., Janssen, 1989, 1991; Mastenbroek, 1982, have published on the relationship between the drag coefficient (CD ), the wind speed, and the roughness of the sea surface. This roughness depends essentially upon the total stress and the stress induced by the waves at the free surface. Mastenbroek et al. (1993) found a significant improvement in a storm surge model by using the calculations with the wave-dependent drag on the surface stress. On the bottom there exist enhanced levels of turbulence at the bed and the retarding force due to the wind-wave effects (e.g., Davies and Lawrence, 1995; Grant and Madsen, 1979; Signell et al., 1990). Both for scientific and practical reasons, e.g., for studies such as mixing processes and sediment transport problems, it is important to superimpose waves on current at the near-bed boundary layer. For example, if the enhanced bed friction due to wind-wave effects exceeds a threshold value, the onset of sediment movement will occur. Therefore calculations involving wave effects are important to achieve a better result in simulating circulation in the Java Sea. In this paper two effects of waves on the three-dimensional hydrodynamic model were used, namely the wave dependence of the drag coefficient at the free surface and enhancements in nearbed turbulence due to wind-wave activity. The effects are applied on the surface and 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 dependence of the drag coefficient. In a final calculation, the trajectory of water particles induced by one-year simulation of tide- and wind-driven circulation in the Java Sea was carried out using the three-dimensional hydrodynamic model incorporating the influence of waves. 2. Three-Dimensional Hydrodynamic Model To reduce the large amount of computational work in developing the threedimensional (3D) model, the computations are performed in two time steps: a short time step is used to compute two-dimensional (2D) problems (barotropic mode) by the vertically integrated equations (external mode) and a much longer time step is used 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 in Cartesian coordinates are given by The continuity equation: ∂u ∂v ∂w + + = 0. ∂x ∂y ∂z

(1)

The equations of motion along the x and y axes are: du ∂u 1 ∂pa ∂ς ∂ − fv = − −g + Nz + Nh 1u, dt ρo ∂x ∂x ∂z ∂z

(2)

dv ∂v 1 ∂pa ∂ς ∂ + fu = − −g + Nz + Nh 1v, dt ρo ∂y ∂y ∂z ∂z

(3)

where u, v, and w are eastward, northward, and vertical components of velocity; t is time; f is the Coriolis parameter; g is the gravitational acceleration; ς represents the surface elevation; ρ o is the density of water; pa is the atmospheric surface pressure; and Nz and Nh are the vertical and horizontal eddy viscosities, respectively. A dynamic boundary condition evaluated at sea surface z = ς will indicate the relation between sea level ς and vertical velocity wς as ∂ς ∂ς ∂ς + uς + vς = wς . ∂t ∂x ∂y

(4)

The vertical velocity at the sea surface wς can be obtained by integrating (1) from the bottom z = −H to the sea surface z = ς .

148

NINING SARI NINGSIH ET AL.

In the present study gradients of the atmospheric pressure given by the first terms in the right-hand side of Equations (2) and (3) are neglected. The external mode is described by the vertically-averaged equations: ∂ u¯ ∂ς ¯ + Ax − f v¯ = −g + Cx + Nh 1u, ∂t ∂x

(5)

∂ v¯ ∂ς ¯ + Ay + f u¯ = −g + Cy + Nh 1v. ∂t ∂y

(6)

Here the terms A and C denote the nonlinear terms and shear stresses, respectively. The nonlinear terms:   Z ς Z ς 1 ∂ ∂ 2 Ax = u dz + uv dz , (7) H ∂x −H ∂y −H 1 Ay = H



∂ ∂x

Z

ς −H

∂ uv dz + ∂y

Z



ς 2

v dz .

(8)

−H

Surface and bottom stresses: Cx = τxs /(Hρo) − τxb /(Hρo),

(9)

Cy = τys /(Hρo) − τyb /(Hρo).

(10)

A sea level change is obtained from the continuity equation for the verticallyaveraged flow: ∂ uD ¯ ∂ vD ¯ ∂ς + + = 0, ∂x ∂y ∂t

(11)

here D = 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¯ + u0

and

v = v¯ + v 0 .

(12)

Subtracting (5) from (2) and (6) from (3) we obtain the internal mode equations: ∂u0 ∂u ∂u ∂u +u +v +w − Ax − f v 0 ∂t ∂x ∂y ∂z   ∂u0 ∂ = Nz − Cx + Nh 1u0 , ∂z ∂z

(13)

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

149

Figure 1. Time-stepping of the splitting method.

∂v 0 ∂v ∂v ∂v +u +v +w − Ay + f u0 ∂t ∂x ∂y ∂z   ∂v 0 ∂ = Nz − Cy + Nh 1v 0 . ∂z ∂z

(14)

Equations (13) and (14) do not contain explicitly barotropic oscillations since the sea 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 with the short time step (T2D ) as defined by CFL condition, it was followed by the threedimensional computation (Equations (13) and (14)) with a much longer time step T3D , i.e., T3D = MT2D . A typical value of M ranges from 10 to 50. Further, the velocity distribution was solved by Equation (12). A simplified illustration of the time interaction of the 2D and 3D models is depicted in Figure 1. The 3D model operates with a time step T3D = tm+M −tm while the 2D model is advanced with a time-step T2D = tm+1 − tm . In the three-dimensional calculation, the vertical friction terms in the right-hand side of Equations (13) and (14) are discretized implicitly by the line inversion method (Kowalik and Murty, 1993), whereas other terms are discretized explicitly. 2.3.

SIGMA COORDINATE TRANSFORMATION

The σ -transformation is employed in the vertical direction to achieve a more accurate approximation of the surface and bottom boundary conditions. In the z-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 normalized thicknesses that are uniform in the sigma-coordinate. The transformation can be written as σ =

z−ς . D

(15)

150

NINING SARI NINGSIH ET AL.

The new coordinate transforms the column of water from the surface (z = ς ) to the bottom (z = −H ) into a uniform depth ranging from 0 to −1. The equation of motion for the internal mode in the σ -coordinate becomes ∂u0 ∂u0 ∂ u¯ ∂u0 ∂ u¯ ∂σ ∂u0 +u +u +v +v + − Ax − f v 0 ∂t ∂x ∂x ∂y ∂y ∂t ∂σ   ∂u0 −2 ∂ =D Nσ − [τxs /(Hρo) − τxb /(Hρo)] + Nh 1u0 , ∂σ ∂σ ∂v 0 ∂v 0 ∂ v¯ ∂v 0 ∂ v¯ ∂σ ∂v 0 +u +u +v +v + − Ay + f u0 ∂t ∂x ∂x ∂y ∂y ∂t ∂σ   ∂v 0 −2 ∂ =D Nσ − [τys /(Hρo ) − τyb /(Hρo )] + Nh 1v 0 . ∂σ ∂σ The Cartesian vertical velocity is     ∂D ∂ς ∂D ∂ς ∂D ∂ς w =ω+u σ + +v σ + +σ + , ∂x ∂x ∂y ∂y ∂t ∂t

(16)

(17)

here ω is obtained by solving the following equation ∂Du ∂Dv ∂ω ∂ς + + + = 0. ∂x ∂y ∂σ ∂t

2.4.

(18)

BOUNDARY CONDITIONS

2.4.1. Lateral Boundary Conditions Zero flow normal is applied to solid boundaries, while along open boundaries a radiation condition (Glorioso and Davies, 1995) was applied, namely, q = qm +

c (ς − ςm ), H

(19)

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

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

151

2.4.2. Vertical Boundary Conditions The surface and bottom boundary conditions in the σ -coordinate system can be written as ω(x, y, 0, t) = ω(x, y, −1, t) = 0, ρNσ D



∂u ∂v , ∂σ ∂σ

(20)

 = (τxs , τys ) = ρa CD WT (Wx , Wy ),

at σ = 0,

(21)

where WT = (Wx2 + Wy2 )1/2 with Wx and Wy denoting the component of the wind speed at the altitude 10 m above sea level, CD is the drag coefficient, ρa is the air density. At the seabed, in the absence of wind waves, the bottom stress is given by ρNσ D



∂u ∂v , ∂σ ∂σ

 = (τxb , τyb ) = ρCz [Uh2 + Vh2 ]1/2 (Uh , Vh ),

at σ = −1,

(22)

where Uh and Vh are the near-bed velocities; Cz is a coefficient of bottom friction and will increase in value when wave effects are present. This value can be obtained by the following expression (Mellor, 1996), 

 κ2 Cz = max , 0.0025 , [ln(30zr /kb )]2

(23)

where κ = 0.4 is the von Karman constant, zo is the roughness length, taken here as 0.146 cm, and kb = 30zo is the bed roughness. Numerically, by matching the numerical solution to the “law of the wall” the reference height zr is taken as the 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 coefficient formulation (Mellor, 1996). 2.5.

SECOND ORDER MODEL OF TURBULENCE CLOSURE

The surface and bottom mixed layer play a very important role in the dynamics of the water column for coastal oceans. Therefore, it is necessary to parameterize the vertical mixing as accurately as possible. The vertical mixing coefficient Nσ is obtained 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). The turbulence model is characterized by two quantities, the turbulence kinetic energy q 2 /2 and the turbulence macroscale l. To find details of this turbulence model, please refer to “Users guide for a three-dimensional, primitive equation, numerical ocean model” by Mellor (1996).

152

NINING SARI NINGSIH ET AL.

3. Wave Effects on the Surface Stress Since both theoretical and experimental evidence of the wave-dependent drag coefficient (CD ) have been given extensively in the literature (Janssen, 1989, 1991, 1992; Mastenbroek, 1992; Mastenbroek et al., 1993), only a very brief description will be presented here. The surface stress as one of the ocean-circulation generating forces depends on the wind speed and roughness of the sea surface. This apparent roughness depends on the presence of waves that have momentum gained from the atmospheric boundary layer. Then, those growing waves change the vertical distribution of turbulence and wind profile. √ The drag coefficient is defined by CD = u2∗ /W (10)2 , where u∗ = τ/ρa is the friction velocity, and W (10) is the wind speed at 10 m above the sea surface. By neglecting the influence of the air viscosity, the total stress at the free surface τ is defined 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 drag coefficient CD by using the following equations. The effective roughness ze when waves are present: ze = √

zo , 1 − τw /τ

(24)

where zo is the roughness length given by the Charnock relation: zo = αu2∗ /g, with α = 0.0185. The wind profile is given by   u∗ z + ze − zo u(z) = , (25) ln κ ze τ (or u∗ ), zo , and ze can be calculated by solving iteratively an implicit set of equations given by (24), (25) and the Charnock relation. Hence CD 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–current interaction model. For simplicity, we use only collinear waves and current in the calculation. A detailed description of this model can be found in Grant and Madsen (1979), Davies et al. (1988), and Signell et al. (1990). The bed-stress and the coefficient of bottom friction Cz related to the near-bed velocity Uh and Vh using a quadratic friction law in the absence of wind waves, are given in (22) and (23), respectively. In the presence of waves, the bottom friction coefficient Cz will increase in value due to the wave effect enhancing the bed stress and given by   1 Cz = max fc , 0.0025 , (26) 2

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

153

where fc is the current friction factor defiend by 

κ fc = 2 ln(30zr /kbc )

2 ,

(27)

where kbc is the apparent bottom roughness felt by the current when the waves are present. The total bed shear stress τ T based on an instantaneous current shear stress τc and the maximum wave bottom stress τw for collinear flow is given by τT = τc + τw ,

(28)

with τw =

1 fw ρUw2 , 2

(29)

where Uw is the maximum near-bed orbital velocity and is given by Uw =

aw ω . sinh(kh)

(30)

The wave-number k is determined from the linear dispersion relation: ω2 = (gk) tanh(kh).

(31)

The wave friction factor fw is obtained using the empirical expression from Grant and Madsen (1982):   0.13(kb /Ab )0.40 → kb /Ab < 0.08 fw = 0.23(kb /Ab )0.62 → 0.08 < kb /Ab < 1.00 (32)  0.23 → kb /A > 1.00, where Ab = 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 (Signell et al., 1990) is also used in the present model. However, the wave field influences the current bed stress τc . Therefore, the thirdgeneration wave model WAM is solved externally and then the results are supplied to the 3D-hydrodynamic model. Based on this assumption, the wave-friction velocity is computed by  U∗w =

τw ρ

1/2 .

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

(33)

154

NINING SARI NINGSIH ET AL.

At time t = 0, an initial current factor fc = 2Cz is computed without wave effects from Equation (23). Then the current friction velocity U∗c is computed from  U∗c =

τc ρ

1/2 ,

(34)

where τc is the vector sum of the bed-stress components τcx and τcy from (22). Having determined U∗c , the combined friction velocity U∗cw for waves and currents is given by 2 2 1/2 U∗cw = (U∗c + U∗w ) .

(35)

The apparent bottom roughness kbc is defined by  kbc = kb

U∗cw Ab 24 Uw kb

β ,

(36)

where β =1−

U∗c . U∗cw

(37)

At the next time step, this value of kbc is then used to determine fc due to the presence of wind wave effects, by using (27). Then, the bed stress in the 3Dhydrodynamic 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 located at tropical area (105◦ –115◦ E and 8◦ 200 –2◦ 400 S) as well as extra-tropical region influenced by monsoon climate. The grid sizes, the 2D- and 3D- time step used in the simulation are 18.5 × 18.5 km, 60 s, and 1800 s, respectively. We used 6-hourly wind 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 can be seen in Figure 3. 5.1.

RESULTS AND DISCUSSIONS

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

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

155

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 tidal prediction in some locations, namely at Rembang (R) and Jakarta (J) (respectively in 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 predicted elevations. 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 does not reproduce adequately the nonlinear interaction of the extremely strong tidal currents 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 and ebb condition. The figure clearly shows the existence of currents that flow back and forth representing flood and ebb conditions. At spring flood condition the currents around 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 out simultaneously to get a better understanding of the complicated phenomena in the Java Sea. Figure 6 shows the circulation pattern during west- and east-monsoons for spring flood conditions. During spring flood conditions, there is flow coming from South-China Sea into the Java Sea through Gaspar and Karimata strait indicated as N1 and N2 in Figure 2, respectively. The wind forces clearly influence the previous circulation

156

NINING SARI NINGSIH ET AL.

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

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

157

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

158 NINING SARI NINGSIH ET AL.

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

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

159

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

160

NINING SARI NINGSIH ET AL.

that was only driven by tide. During west-monsoon, the effects of wind increase the magnitude of currents and the circulation flows mainly eastward. Otherwise, during the east-monsoon, the easterly wind-driven currents flow in the opposite direction to 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 the region around the Karimata Strait (N2 ); while in other areas where the easterly wind-driven currents are more dominant than the tide-driven currents, the resultant currents flow westward. 5.2.

WAVE FIELDS IN THE JAVA SEA

To calculate the wave fields in the Java Sea, a third-generation wave model WAM has been used. A detailed description of this model can be found in the literature (WAMDI Group, 1988; Günther et al., 1992). The model was run externally and then its output, such as the wave fields and the wave-dependent drag coefficient, were supplied to the 3D-hydrodynamic model for incorporating the influence of waves on the surface and bottom stresses. The wave fields and the 2D-spectra at Surabaya (S) and Rembang (R) are shown in Figure 7(a), (b), respectively. The magnitude of significant wave height (Hs ) during the west-monsoon is greater than during the east-moonsoon. We also noticed that the wave direction follows the main direction of the wind fields (as illustrated in Figure 3). For typical west-monsoon, the maximum value of significant wave height (Hs ) reaches about 2.8 m in the southern region of the eastern part of the Java Sea, while for the east-monsoon it reaches about 1 m in the region close to the Karimata Strait (N2 ). From the 2D-spectra figures it is found that the wave peak frequency (fp ) at Surabaya (S) and Rembang (R) is about 0.26–0.27 Hz at the west-monsoon and about 0.33–0.34 Hz at the east-monsoon. This range of values of fp is equal to periods of 2.9–3.8 s, which are within those of Emery et 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 by the 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 remain constant in space and time. Enhancement in bed stress due to the wind waves depends upon the wind wave orbital velocity Uw given by Equation (30) which decreases rapidly with respect to the water depth and the wave frequency. Following Davies and Lawrence (1995), we give some examples of Uw computation, namely for fp = 0.17 Hz and Hs = 2 m, Uw = 0.62 m s−1 at depth 10 m and 0.1 m s−1 at depth 50 m, while for fp = 0.10 Hz and Hs = 2 m, Uw = 0.85 m s−1 at depth 10 m and 0.16 m s−1 at depth 50 m.

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

161

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

Therefore the flow field retarded by the increased bed-turbulence due to the wave effects 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 the bottom 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).

162

NINING SARI NINGSIH ET AL.

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

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

163

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

5.3.2. Effect of Waves on the Surface Stress by Using the Wave Dependence of the Drag Coefficient (CD ) In this section, we have compared the computation results by using the wave dependence of the drag coefficient (CD ) as output from the WAM model with the constant value of CD = 0.003 on the surface stress. Figure 10 shows the variation of the drag coefficient CD with the wind speed for the period of 27 February 1996 to 2 March 1996 at Rembang (R) location. These values obtained by the WAM model 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) obtained by the WAM model. We show that the current velocity components at the free surface decrease with the smaller value of CD , while the free surface elevation increases, as illustrated in Figure 11. We are now interested in the effect of the waves on the surface and bottom stress for the case using the spatial and temporal variation of the significant wave height Hs , the peak frequency fp , and the drag coefficient CD which are obtained by the WAM model. Figure 12 shows that the current velocity components decrease with water depth and also for the smaller value of the drag coefficient.

164

NINING SARI NINGSIH ET AL.

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

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

165

Figure 10. Variation of the drag coefficient CD with respect to the wind speed and for the period 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 the period from 27 February 1996 to 2 March 1996 at Rembang (R): (...........) with waves (CD < 0.003); (———) no waves (CD = 0.003).

166

NINING SARI NINGSIH ET AL.

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

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

167

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 determine the trajectory of the water particles at the surface and bottom layers by using the Euler–Langrangian method. In this simulation, we have taken into account the influence 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 will accumulate and which boundaries will be passed by the water particles that move out from the Java Sea. The trajectories of the water particles on the surface layer are illustrated in Figure 14. In the west-monsoon (from 6–14 January), most water 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 around the northern part of Java Island, while in the east-monsoon (in May) this water particle accumulation moves to the southern part of Kalimantan Island and some of the water particles move out from the Java Sea into the South China Sea through the Gaspar Strait (marked N1 in Figure 2). Figure 15 shows trajectories of the water particles on the bottom layer. Unlike on the surface layer where most water particles move out rapidly from the Java Sea, on the bottom layer they move out slowly due to the magnitude of currents on the 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 accumulation exists in the coastal water around the southern part of Kalimantan Island and the central part of the Java Sea, and most water particles move out from the Java Sea through the eastern part (marked E in Figure 2). Whereas, during the eastmonsoon (August) and the transitional season from east to west monsoon (October) the water particles accumulate around Surabaya Beach (marked S in Figure 2) and most water particles move out from the Java Sea through the northern part (marked N1 and N2 in Figure 2).

168 NINING SARI NINGSIH ET AL.

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

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

169

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

170

NINING SARI NINGSIH ET AL.

6. Concluding Remarks A three-dimensional hydrodynamic model has been developed to simulate tideand wind-driven circulation, incorporating the influence of waves on the surface and bottom stresses. The developed model was applied to simulate the flow fields in the Java Sea whose environment has been rapidly changing due to the development of its coastal and ocean area. This causes many hazardous situations such as catastrophic beach erosion, destroyed coastal and offshore structures, and disrupted navigation because of the excess deposition of sediment materials. The application of the model to the Java Sea showed that the existence of the monsoon wind fields plays an important role in the general circulation of waters in this area. Changes in the surface and bottom stresses by incorporating the effect of waves have significantly influenced the three-dimensional model of tide and wind-driven circulation. This wave-current interaction effect is important in shallow regions such as the Java Sea due to the enhanced bed stress in shallow areas which induces a significant decrease of the flow. The calculated velocity fields were then applied to simulate the trajectory of water particles in the region. In this present study, we have only considered noncontinuous sources of particles, whereas in reality it would be essential to consider continuous and main sources of particles such as rivers that move various sediments into the Java Sea (e.g., silts and muds which are the major sediments that cover the floor of the region, Emery et al., 1972). The model can also be extended to predict suspended sediment fluxes by solving the advection-diffusion equation for sediments, in dealing with hazardous phenomena, particularly catastrophic changes in sea bottom topography and beach erosion of the Java Sea. These kinds of studies are currently in progress as an extension of this research program. In addition, the developed 3D-hydrodynamic model is also important for simulation of current fields and surge height distribution, especially in hazardous areas of storm surges such as the United States and Bangladesh. We can cite as an example, the application of a three-dimensional hydrodynamic model to the northern South China Sea which was carried out to hindcast a storm surge event generated by typhoon Ellen (Zhang and Li, 1996).

References Davies, A. G., Soulsby, R. L., and King, H. L.: 1988, A numerical model of the combined wave and current bottom boundary layer, J. Geophys. Res. 93, 491–508. Davies, A. M. and Lawrence, J.: 1995, Modeling the effect of wave-current interaction on the threedimensional wind-driven circulation of the Eastern Irish Sea, J. Phys. Oceanog. 25, 29–45. Emery, K. O., Uchupi, E., Sunderland, J., Uktolseja, H. L., and Young, E. M.: 1972, Geological structure and some water characteristics of the Java Sea and adjacent continental shelf, CCOP Tech. Bull. 6, 197–221. Glorioso, P. D. and Davies, A. M.: 1995, The influence of eddy viscosity formulation, bottom topography, and wind wave effects upon the circulation of a shallow bay, J. Phys. Oceanog. 25, 1243–1264.

THREE-DIMENSIONAL SIMULATION OF WATER CIRCULATION IN THE JAVA SEA

171

Grant, W. D. and Madsen, O. S.: 1979, Combined wave and current interaction with a rough bottom, J. Geophys. Res. 84, 1797–1808. Grant, W. D. and Madsen, O. S.: 1982, Movable bed roughness in unsteady oscillatory flow, J. Geophys. Res. 87, 469–481. Günther, H., Hasselmann, S. and Janssen, P. A. E. M.: 1992, The WAM model, Cycle 4, Report No. 4, Hamburg. Janssen, P. A. E. M.: 1989, Wave-induced stress and the drag of airflow over sea waves, J. Phys. Oceanog. 19, 745–754. Janssen, P. A. E. M.: 1991, Quasi-linear theory of wind wave generation applied to wave forecasting, J. Phys. Oceanog. 21, 1631–1642. Janssen, P. A. E. M.: 1992, Experimental evidence of the effect of surface waves on the air flow, J. Phys. Oceanog. 22, 1600–1604. Kowalik, Z. and Murty, T. S.: 1993, Numerical Modeling of Ocean Dynamics, World Scientific, Singapore. Mastenbroek, C.: 1992, The effect of waves on surges in the North Sea. Coastal Engineering, Proc. of the Twenty-third International Conference, Venice, Italy, October. Mastenbroek, C., Burgers, G., and Janssen, P. A. E. M.: 1993, The dynamical coupling of a wave model and a storm surge model through the atmospheric boundary layer, J. Phys. Oceanog. 23, 1856–1866. Mellor, G. L.: 1996, Users Guide for a Three-Dimensional, Primitive Equation, Numerical Ocean Model, Princeton University, Princeton. Mellor, G. L., and Yamada, T.: 1982, Development of a turbulence closure model for geophysical fluid problems, Rev. Geophys. Space Phys. 20, 851–875. Signell, R. P, Beardsley, R. C., Graber, H. C., and Capotondi, A.: 1990, Effect of wave-current interaction on wind-driven circulation in narrow, shallow embayments, J. Geophys. Res. 95, 9671–9678. WAMDI Group: 1988, The WAM model – A third-generation ocean wave prediction model, J. Phys. Oceanog. 18, 1775–1810. Zhang, M. Y. and Li, Y. S.: 1996, A semi-implicit three-dimensional hydrodynamic model incorporating the influence of flow-dependent eddy viscosity, bottom topography and wave-current interaction, Appl. Ocean Res. 18, 173–185.