allan

61

Journal of Oceanography, Vol. 64, pp. 61 to 80, 2008

Keywords:⋅⋅⋅⋅⋅ Hydrodynamicmodel,

⋅⋅⋅⋅⋅ barotropic tides,⋅⋅⋅⋅⋅ Java Sea,⋅⋅⋅⋅⋅ resonance,⋅⋅⋅⋅⋅ tidal energy,⋅⋅⋅⋅⋅ residual currents,⋅⋅⋅⋅⋅ tidal mixing.

* Corresponding author. E-mail: [email protected]

Copyright©The Oceanographic Society of Japan/TERRAPUB/Springer

Three-Dimensional Modeling of Tidal Circulation andMixing over the Java Sea

ALAN F. KOROPITAN1,2* and MOTOYOSHI IKEDA1

1Graduate School of Environmental Science, Hokkaido University, Kita-ku, Sapporo 060-0810, Japan2Department of Marine Science and Technology, Bogor Agricultural University (IPB), Kampus IPB Darmaga, Bogor 16680, Indonesia

(Received 13 February 2007; in revised form 6 August 2007; accepted 29 August 2007)

A combination of a three-dimensional hydrodynamic model and in-situ measurementsprovides the structures of barotropic tides, tidal circulation and their relationshipwith turbulent mixing in the Java Sea, which allow us to understand the impact of thetides on material distribution. The model retains high horizontal and vertical resolu-tions and is forced by the boundary conditions taken from a global model. The meas-urements are composed of the sea level at coastal stations and currents at mooringsembedded in Seawatch buoys, in addition to hydrographic data. The simulated tidalelevations are in good agreement with the data for the K1 and M2 constituents. TheK1 tide clearly shows the lowest mode resonance in the Java Sea with intensificationaround the nodal point in the central region. The M2 tide is secondary and propa-gates westward from the eastern open boundary, along with a counterclockwiseamphidromic point in the western part. The K1 tide produces a major component oftidal energy, which flows westward and dissipates through the node region near theKarimata Strait. Meanwhile, the M2 tide dissipates in the entire Java Sea. However,the residual currents are mainly induced by the M2 tide, which flows westward fol-lowing the M2 tidal wave propagation. The tidal mixing is mainly caused by K1 tidewhich peaks at the central region and is consistent with the uniform temperature andsalinity along the vertical dimension. This mixing is expected to play an importantrole in the vertical exchange of nutrients and control of biological productivity.

east Sumatra to more than 60 m in its eastern part. Mor-phologically, the Java Sea is roughly rectangular, withmean depth, length and width of 50 m, 950 km and 440km, respectively. In the northern open boundary, the JavaSea is linked with three straits: Karimata, Gaspar andBangka. The eastern and western open boundaries areconnected with the Flores Sea and Sunda Strait, respec-tively.

Several earlier studies have been published on tidesand tidal currents in the Indonesian seas, with a short re-view of the Java Sea region. Wyrtki (1961) presented aqualitative understanding of these phenomena in South-east Asian waters, based on tide gauges and current me-ters. Related to Indonesian throughflow exchange proc-esses, Hatayama et al. (1996) comprehensively reportedtides, tidal currents and the influence of tidal mixing inthe Indonesian seas using a two-dimensional hydrody-namic model and several tide gauge observations. Schiller(2004) then improved our understanding of the mixing

1. IntroductionIn common with many shelf or coastal waters, the

Java Sea is under growing stress from various humandemands. Talaue-McManus (2000) showed that wastesfrom domestic, agricultural and industrial sources, alongwith sediments and solid wastes are the major sources ofpollutants that impinge on coastal systems. A better un-derstanding of physical processes is of great importancefor successful management of the coastal and marine en-vironment.

The Java Sea is located in the middle of three mainislands in the Indonesian archipelago: Kalimantan, Javaand Sumatra (Fig. 1). The Java Sea is a shallow waterwhere depths increase from 20 m off the coast of south-

62 A. F. Koropitan and M. Ikeda

processes in the Indonesian throughflow region using athree-dimensional ocean general circulation model forlong-term simulations. The recent study of tides in theIndonesian seas was briefly reported by Ray et al. (2005)using co-amplitude and co-phase charts based on the dataassimilation work of Egbert and Erofeeva (2002).

A notable feature of the Java Sea tides compared withthe adjacent deep ocean is the dominance of the diurnalover semi-diurnal constituents. This is in contrast withthe Pacific and Indian Oceans, where the tides are pre-dominantly semi-diurnal. Wyrtki (1961) reported that the

predominantly diurnal tide in the Java Sea is related tothe behavior of tidal propagation from the adjacent seas.The semi-diurnal tidal wave entering the Java Sea is weakdue to the effect of deflection of a northward tidal wavefrom the Indian Ocean in the Flores Sea. Moreover, asmaller part of the deflected wave advances further intothe Makassar Strait and meets with the wave from thePacific Ocean. On the other hand, the stronger diurnaltidal wave from the Pacific Ocean is able to penetrateinto the Flores Sea to meet with waves from the IndianOcean through the Lesser Sunda Islands and Timor Sea.

Fig. 1. Model domain and observation locations. The 11 tide gauges (denoted by number) are Belitung (1), Kota Waringin (2),Sampit (3), Barito (4), Pari Island (5), Jakarta (6), Cirebon (7), Semarang (8), Surabaya (9), Kali Anget (10) and Meneng (11).The seven mooring buoys for velocity data (denoted by asterisk) are SW50, SW51, SW52, SW53, SW54, SW55, and SW60which deployed at around 2 m depth.

Modeling of Tidal Circulation and Mixing over the Java Sea 63

There, the two waves are refracted and enter the Java Sea.These phenomena were also reported by Ray et al. (2005)using a data assimilation technique. However, Hoitink(2003) and Ali (1992) showed model results about an in-dication of the resonance that may cause the dominanceof K1 tide in the Java Sea.

Tidal currents induce vertical mixing, particularly ina shallow region. Hatayama et al. (1996) used the Simpsonindex (Simpson et al., 1978) to analyze the role of tidalcurrents in the intensification of vertical mixing in theIndonesian seas. Similar to Schiller (2004), who used thethree-dimension model, Hatayama et al. (1996) discussedan indication of tidal mixing in several shallow regionsincluding the Java Sea. However, since they focused onthe entire Indonesian sea, the particular phenomena con-cerning diurnal and semi-diurnal propagation and its tur-bulent quantities in the Java Sea need a more detaileddescription and closer examination of their mechanisms.

The present paper combines recent in-situ measure-ments with a three-dimensional primitive equation nu-merical model to verify model performance by compar-ing its results with observed elevation and currents. Wealso aim to describe and map the major tidal constitu-ents, and to examine the tidal circulation and its relation-ship with turbulent mixing in the Java Sea. In addition,the hydrographic data are used to reveal the structures oftemperature and salinity related to the tidal mixing.

The arrangement of this paper is as follows: we be-gin Section 2 with an introduction of the hydrodynamicmodel and discuss how it is driven at the open bounda-ries by barotropic tides in the global model. Section 3then describes the observations of coastal sea level andcurrents, analyzing the barotropic tides by standard meth-ods. The modeled tidal elevation of co-amplitude and co-phase, and their comparison with the in-situ data for di-urnal and semi-diurnal constituents are described in Sec-tion 4, in which we also report a dedicated numerical ex-periment on different tidal forcing at the open boundaryand nonlinear interactions among the constituents.Modeled tidal current ellipses and their comparison withfield observations are described in Section 5. In order tofurther describe the behavior of tidal propagation, we usethe model to calculate tidal energy of the main tidal con-

stituents, as well as their residual currents. Section 6 fo-cuses on the contribution of the dominant constituent toturbulent mixing. A summary and discussion are presentedin Section 7.

2. Hydrodynamic ModelThis study of the tidal effect in the Java Sea is pre-

ceded by several numerical model studies regarding tidesof the Indonesian seas. Hatayama et al. (1996) applied aglobal tidal equation to a two-dimensional hydrodynamicmodel with 5′ by 5′ grid resolution. Their two-dimen-sional, high resolution approach described tides and tidalcirculation on the entire Indonesian seas, with only amoderate result compared to field observations, even us-ing high resolution. The standard deviations for the M2constituent between data and model are 13.71 cm and22.12° for amplitude and phase, respectively. On the otherhand, the K1 constituent has standard deviations of 10.16cm and 18.30° for amplitude and phase, respectively.Since the bathymetric data are important in a regionaltidal model (Kantha and Clayson, 2000), their model hada mean depth of the Java Sea less than 30 m and neededimprovement in bathymetry.

Another model was presented by Schiller (2004),who used an ocean general circulation model with 0.5°by 0.33° grid resolution. This coarse grid model underes-timates tides measured at coastal tide gauge stations. Onthe other hand, Setiawan (2000) reported an operationalthree-dimensional model as part of the Seawatch programof Indonesia. The model used 10′ by 10′ grid resolutionand covered the whole Sunda Shelf combined with theMakassar Strait and Flores Sea. However, there is a dis-crepancy between the model results and current data col-lected from the Seawatch buoys, which may be due to thecoarse resolution of the model, which ignores detailedbathymetry and the near-coastline to inter-channel loca-tions of the buoys.

The most important input to a barotropic tidal modelfor a small shallow region is the bottom topography(Kantha and Clayson, 2000). Our model therefore uses arelatively high resolution of 2′ by 2′ grid size. Thebathymetry adopted by the model is taken from the WorldOcean Topography Data (ETOPO2). However, this dataset

Case study Tidal constituent Purpose

F8 O1, K1, M2, S2, P1, Q1, N2 and K2 Sensitivity of the K1 and M2 tides (amplitude and phase) to the open boundaryrelated to nonlinear effect

F4 O1, K1, M2 and S2

F2 K1 and M2

K1 tide K1 Calculation of tidal energy flow, residual current and mixing quantitiesM2 tide M2

Table 1. Cases study of numerical experiment.


Table 2(a). Comparison of observed and modeled tidal elevation at reference sites forced by the eight tidal constituents (case F8).

Station Amplitude-H (cm) Phase-Ø (°G)

Observed Modeled ∆H Observed Modeled ∆Ø

O1

Belitung1) 42 39.44 2.56 341.40 345.94 –4.54Kota Waringin1) 16 21.75 –5.75 131.40 246.27 –114.87

Sampit B.1) 31 29.33 1.67 166.40 213.33 –46.93Barito R.1) 33 26.83 6.17 169.46 206.32 –36.86Pari2) 12.21 21.02 –8.81 8.89 (+360) 326.51 42.38Jakarta3) 13.75 23.08 –9.33 25.32 (+360) 326.14 59.18Cirebon1) 5 27.51 –22.51 57.40 (+360) 277.12 140.28Semarang1) 8 26.83 –18.83 134.40 260.94 –126.54Surabaya3) 14.85 25.99 –11.14 167.13 187.89 –20.76Kali Anget1) 24 23.67 0.33 161.40 167.71 –6.31Meneng2) 19.35 18.4 0.95 158.45 165.9 –7.45

K1

Belitung1) 72 65.63 6.37 33.71 42.86 –9.15Kota Waringin1) 36 29.55 6.45 220.71 240.65 –19.94Sampit B.1) 60 66.13 –6.13 230.71 231.1 –0.39Barito R.1) 64 65.33 –1.33 219.67 236.30 –16.63Pari2) 21.29 29.40 –8.11 18.82 62.44 –43.62Jakarta3) 25.17 31.37 –6.2 34.73 59.21 –24.48Cirebon1) 14 16.23 –2.23 302.71 309.32 –6.61Semarang1) 22 23.25 –1.25 247.71 267.35 –19.64Surabaya3) 33.69 49.01 –15.32 204.35 213.24 –8.89Kali Anget1) 42 42.1 –0.1 193.71 198.09 –4.38Meneng2) 30.95 30.94 0.01 176.59 189.78 –13.19

M2

Belitung1) 8 6.49 1.51 224.11 225.9 –1.79Kota Waringin1) 22 21.34 0.66 335.11 324.11 11Sampit B.1) 49 42.5 6.5 306.11 293.53 12.58Barito R.1) 34 28.24 5.76 279.13 291.93 –12.8Pari2) 1.76 4.76 –3 91.89 92.22 –0.33Jakarta3) 5.41 7.26 –1.85 140.85 125.32 15.53Cirebon1) 16 16.69 –0.69 101.11 102.01 –0.9Semarang1) 10 10.11 –0.11 55.11 73.04 –17.93Surabaya3) 35.04 43.90 –8.86 115.06 112.94 2.12Kali Anget1) 39 45.55 –6.55 111.11 106.82 4.29Meneng2) 45.88 45.1 0.78 77.54 70.98 6.56

S2

Belitung1) 7 8.71 –1.71 175 173.05 1.95Kota Waringin1) 6 8.71 –2.71 266 313.68 –47.68Sampit B.1) 11 15.26 –4.26 203 271.39 –68.39Barito R.1) 5 13.25 –8.25 201 282.13 –81.13Pari2) 3.04 4.6 –1.56 54.74 89.44 –34.7Jakarta3) 5.04 4.45 0.59 78.80 102.12 –23.32Cirebon1) 10 4.39 5.61 327 56.98 (+360) –89.98Semarang1) 8 3.91 4.09 307 24.33 (+360) –77.33Surabaya3) 20.67 28.87 –8.2 123.69 120.34 3.35Kali Anget1) 19 26.43 –7.43 118 111.83 6.17Meneng2) 22.52 27.43 –4.91 111.18 96.82 14.36


Table 2(b). Comparison of observed and modeled tidal elevation at reference sites forced by the two tidal constituents (case F2).

1)Tidal constituents from Tide Table, DISHIDROS TNI-AL, Indonesia.2)Tidal constituents based on hourly data from UHSLC Hawaii (contributed by Center for Oceanological Research and

Development, Indonesia).3)Tidal constituents based on hourly data from UHSLC Hawai (contributed by BAKOSURTANAL, Indonesia).

is inaccurate in the central and coastal regions of the JavaSea, and hence we corrected it by incorporating thebathymetry chart of the Java Sea (map no. 66, edition1991) from DISHIDROS TNI-AL (Hydro-OceanographicDivision of Indonesian Navy). We set up a grid manuallyin the naval charts, where the gridded data of ETOPO2were adjusted with the charts. In this case, we just fo-cused on the extreme value, which we found in the cen-tral part and near-coastal region.

The hydrodynamic model used here is the PrincetonOcean Model (POM), a three-dimensional, nonlinear,primitive equation model with Boussinesq and hydrostaticapproximations (Blumberg and Mellor, 1987). POM hasbeen applied to many oceanic regions, and the most re-cent tidal application to a regional model was reported indetail by He and Weisberg (2002). Our model uses a Car-tesian coordinate system in the horizontal and a sigmacoordinate system in the vertical. The model domain cov-ers from 2°42′ to 8°14′ S and from 105°42′ to 114°42′ E

(Fig. 1). Along the vertical, the domain is divided into 21unequal sigma levels (σ = 0 at the sea surface and –1 atthe sea bottom), with higher resolution near the bottomto resolve the bottom boundary layer. The four sigma lay-ers nearest the bottom are σ = –0.929, –0.964, –0.982,and –0.991. Note that the bottom stress and friction ve-locity in the present sigma coordinate model are calcu-lated using the currents and the drag coefficients at thelowest current level, which is depth-dependent. Bottomstress is obtained by a quadratic drag law in which thedrag coefficient is calculated on the basis of a specified(0.01 m) bottom roughness length. The model has a totalof 270 × 166 × 21 grid points, and the time step for theexternal mode is 10 s.

In this study, water density is assumed to be homo-geneous. The vertical eddy viscosity is computed usingthe Mellor and Yamada (1982) level-2.5 turbulent clo-sure scheme. The horizontal eddy viscosity is calculatedusing the shear-dependent Smagorinsky formulation

Station Amplitude-H (cm) Phase-Ø (°G)

Observed Modeled ∆H Observed Modeled ∆Ø

K1

Belitung1) 72 59.48 12.52 33.71 31.49 2.22Kota Waringin1) 36 28.39 7.61 220.71 227.55 –6.84Sampit B.1) 60 62.03 –2.03 230.71 218.26 12.45Barito R.1) 64 63.65 0.35 219.67 222.26 –2.59Pari2) 21.29 26.40 –5.11 18.82 41.43 –22.61Jakarta3) 25.17 28.69 –3.52 34.73 38.76 –4.03Cirebon1) 14 16.64 –2.64 302.71 292.75 9.96Semarang1) 22 23.21 –1.21 247.71 254.60 –6.89Surabaya3) 33.69 44.98 –11.29 204.35 201.41 2.94Kali Anget1) 42 38.18 3.82 193.71 186.27 7.44Meneng2) 30.95 28.09 2.86 176.59 177.87 –1.28

M2

Belitung1) 8 6.63 1.37 224.11 222.90 1.21Kota Waringin1) 22 22.05 –0.05 335.11 320.60 14.51Sampit B.1) 49 45.42 3.58 306.11 290.25 15.86Barito R.1) 34 31.07 2.93 279.13 281.68 –2.55Pari2) 1.76 4.88 –3.12 91.89 91.68 0.21Jakarta3) 5.41 7.36 –1.95 140.85 123.67 17.18Cirebon1) 16 19.07 –3.07 101.11 96.53 4.58Semarang1) 10 12.42 –2.42 55.11 69.76 –14.65Surabaya3) 35.04 43.44 –8.4 115.06 109.72 5.34Kali Anget1) 39 45.44 –6.44 111.11 104.65 6.46Meneng2) 45.88 45.67 0.21 77.54 69.58 7.96


(Smagorinsky, 1963) with a coefficient of 0.2. The tidalforcing of the model is imposed at the open boundariesfacing the eastern part, the northern part at Karimata andGaspar Straits, and the western part at Sunda Strait. Tidalelevations are specified by linear interpolation of the out-put from the global tidal model ORI.96 with assimilatedTOPEX/Posseidon altimeter data (Matsumoto et al.,1996). This barotropic model has 0.5° × 0.5° resolutionand provides eight tidal constituents (M2, S2, N2, K2, K1,O1, P1, Q1). As a special boundary in the narrow BangkaStrait, there are no data in the global model, nor fieldobservations. Hence, we use a radiation boundary condi-tion.

The case study is designed with several cases, assummarized in Table 1. The particular objectives are totest several numbers of tidal constituents for open bound-ary forcing in order to understand the response of eachcase under the nonlinear effects. Tidal elevation and cur-rent were computed by integrating the model forward intime. From an initial state of rest the basin is then sub-jected to forcing of cases along the open boundaries. Wechoose a 10-day spin-up period, which is judged to besufficient for the model to become independent of theinitial condition. The subsequent 60-day output is thenanalyzed using harmonic analysis to retrieve the indi-vidual constituent amplitude and phase distributions overthe model domain. Especially for the individual case ofK1 and M2 tides in Table 1, we analyzed the root-mean-square (RMS) value over fifty tidal cycles, after the spin-up period.

3. Observational DataThe observations were taken from eleven tide gauges

and seven current meter mooring buoys (Fig. 1). Theeleven tide gauges are referred to as Belitung (St. 1), KotaWaringin (St. 2), Sampit (St. 3), Barito (St. 4), Pari Is-land (St. 5), Jakarta (St. 6), Cirebon (St. 7), Semarang(St. 8), Surabaya (St. 9), Kali Anget (St. 10) and Meneng

(St. 11). However, only four stations provide hourly tidalelevation data records, namely: Pari Island, Jakarta,Surabaya, and Meneng. The hourly data were taken fromthe Joint Archive for Sea Level of the University of Ha-waii, contributed by BAKOSURTANAL (National Coor-dinating Agency for Surveys and Mapping, Indonesia) andP2O-LIPI (Research Center for Oceanography, Indone-sia). The other seven tide gauges predicted the amplitudeand phase of the four main tidal constituents O1, K1, M2and S2. This information is available from the Tide Tableof Indonesian Archipelago 2003 provided by DISHIDROSTNI-AL. The velocity data were taken from current me-ters attached to around 2 m-depth buoys, which are trans-mitted in real time to the ground station via satellite. Theseven buoys were deployed by the Agency for the As-sessment and Application of Technology (BPPT), Indo-nesia, in collaboration with Oceanor, Norway, andBandung Institute of Technology, Indonesia, through theIndonesian Seawatch Program, 1996–2000.

The sea level data were analyzed using the leastsquares method in MATLAB, referred to as the t_tideprogram (Pawlowicz et al., 2002). This program is simi-lar to the FORTRAN code described by Godin (1972),Foreman (1977), and Foreman (1978). However, unlikethose authors, the t_tide program directly uses complexalgebra rather than dealing with sine and cosine separately.The analysis includes as many as 146 possible tidal con-stituents, 45 of them being astronomical in origin whilethe remaining 101 are shallow water constituents.

The four tide gauges of Pari Island, Jakarta, Surabayaand Meneng generally differed in terms of record lengthand initial time. The records were collected at differentperiods from 1984 and 1990. We generally used the en-tire record length available at each site, which varied fromone to two years. Since Surabaya station is located in anarrow passage of Madura Strait, we only consider theobserved tidal elevation with the low-frequency variationsremoved (period of 27 hours). The tidal harmonic analy-

Table 3. The amplitude ratio between the principal diurnal and semi-diurnal tides, and tidal type.

Tide gauge stations Ratio of (O1 + K1)/(M2 + S2) Tidal type

Belitung 7.60 DiurnalKota Waringin 1.86 Mixed tide, mainly diurnalSampit 1.52 Mixed tide, mainly diurnalBarito 2.49 Mixed tide, mainly diurnalPari 6.98 DiurnalJakarta 3.72 DiurnalCirebon 0.73 Mixed tide, mainly semi-diurnalSemarang 1.67 Mixed tide, mainly diurnalSurabaya 1.30 Mixed tide, mainly semi-diurnalKali Anget 1.14 Mixed tide, mainly semi-diurnalMeneng 0.74 Mixed tide, mainly semi-diurnal


sis indicated that tides with eight principal constituents(O1, K1, M2, S2, P1, Q1, N2 and K2) explain about 71.4%,83.0%, 82.2% and 90.1% of the total variance of the ob-served tide gauges at Pari Island, Jakarta, Surabaya andMeneng, respectively. If we consider the original datarecord of Surabaya Station, the eight principal constitu-ents explain 39% of the variance. This could be improvedto 45% by including as many tidal constituents as possi-ble, such as the shallow water tidal constituents.

We focus on the four main tidal constituents (O1, K1,M2 and S2) only. The amplitudes and phases (relative tothe Greenwich meridian) for the eleven tide gauge sta-tions are summarized in Table 2(a). We note that the di-urnal tides in the western and eastern parts are larger thanthose in the central part, whereas the semi-diurnal tidesare larger in the eastern part of the Java Sea. The M2 tidein particular peaks around the southern coast ofKalimantan. The ratio between amplitudes of the princi-pal diurnal and semi-diurnal tide constituents, (O1 + K1)/(M2 + S2), and tidal type for the eleven tide gauge sta-tions are shown in Table 3. The Java Sea tidal regime isgenerally characterized as mixed tide having a main di-urnal signal. Semi-diurnal tides mostly cover the south-eastern part of the Java Sea.

Similar to sea level, the analysis of velocity data wasalso conducted using the least squares method of the t_tideprogram (Pawlowicz et al., 2002). The seven buoys weregenerally not co-deployed, and the transmitting systemfrom the buoys to the ground station was sometimes shutdown due to weather disturbances. Furthermore, the tidalcurrent data were not collected during the same periodand their records varied from two weeks to one year (Ta-ble 4).

The result of the harmonic analysis showed that theoverall observed tidal currents in the Java Sea vary be-tween 13–61 cm/s. In this case, the analysis has includedas many tidal constituents as possible. In addition, thesetidal currents are faster near the coastline than the off-shore regions. Among the principal constituents, K1 cur-rent is the strongest, with the highest amplitude in thecentral part (SW50) of the Java Sea. On the other hand,

M2 current is weaker. Its amplitude tends to increase inthe eastern and western parts of the Java Sea.

4. Modeled Tidal Elevation

4.1 Co-amplitude and co-phaseFigure 2 presents the co-amplitude and co-phase

charts of the modeled diurnal (O1 and K1) and semi-diur-nal (M2 and S2) constituents, respectively. We used caseF8 for this application. In general, our simulation showsthat diurnal and semi-diurnal tides propagate westwardparallel to the closed boundary i.e., the northern coast ofJava and southern coast of Kalimantan. These tides arethen deflected to the northerly direction in the westernpart of the Java Sea. Wyrtki (1961) reported that the diur-nal tide from the Java Sea meets the wave from the SouthChina Sea in the Gaspar and Karimata Straits. Meanwhile,the semi-diurnal tide penetrates further to the north andmerges in the west of Kalimantan Island with those fromthe South China Sea. Especially for the M2 tide, Hatayamaet al. (1996) found similar behavior to that reported byWyrtki (1961).

Hence, we present the specific propagation of thefour tidal constituents and their specific responses, re-lated to the dimension of Java Sea basin and bottom fric-tion. The co-amplitude and co-phase of K1 tide show thatthe tidal wave propagates slower and decreases its am-plitude in the central part of the Java Sea. This is typicalof a standing wave. The phase difference between theeastern and western parts is about 12 hours. Therefore,when the flood condition occurs in the eastern part, theebb condition occurs in the western part and vice versa.This phenomenon indicates a node in the central part andantinodes in the eastern and western parts of the Java Sea,supporting co-oscillation tides or a resonance effect. Theamplitudes and phases of co-oscillation tides depend onthe closeness of a resonance frequency to one of the tidalfrequencies. Since the Java Sea is nearly a rectangularbasin with a length of 950 km and a depth of 50 m, thebasin’s period of resonance is estimated to be 23.8 hours.The period of the Java Sea basin is very close to the K1

Table 4. Description of the SEAWATCH hourly observed data.

Station Period Record length(hours)

Gap numbers(hours)

Tanjung Karawang (SW50) June 1997–May 1998 8760 366Pluit (SW51) November 1996–February 1997 1607 225Jepara (SW52) February–April 1998 1528 99Bawean (SW53) November 1998 275 0Masalembo (SW54) October–November 1998 322 0P. Kelapa (SW55) November 1998–January 1999 1030 5Indramayu (SW60) April–July 2000 1872 265


constituent’s period of 23.9 hours, and is thus responsi-ble for the resonance in the Java Sea. The node andantinodes of the K1 tide are also shown in the data-as-similation results (Ray et al., 2005), where the positionof the zero degree phase is similar to the present one. Ourmodel result of co-oscillation tides is also similar withthose models of Hoitink (2003) and Ali (1992).

Similar to the K1 tide, the O1 tide shows a standingwave in the western part caused by a solid boundary andprogressively deflected to the north through KarimataStrait. A node region is clearly revealed in Karimata Strait,caused by its narrow passage. However, the simulated O1tide propagation does not resolve the same phenomenonof resonance with the K1 tide, even though they are simi-lar diurnal tides. The longer period of 25.8 hours may beresponsible for the O1 tide reaching further north.

The modeled semi-diurnal (M2 and S2) tides showmore progressive waves in the eastern part of the JavaSea, standing waves in the western part caused by the

solid boundary and amplification in the southeast coastof Kalimantan Island. Hence, the amplitudes increase upto 40 cm and 15 cm for M2 and S2 tides, respectively. TheM2 features are similar to those presented by Ray et al.(2005). The effect of wave refraction in shallow water(due to decreases in the propagation speed and the wave-length) has an important role in the wave amplification.The M2 tide presents a counterclockwise amphidromicpoint near the Sunda Strait region, quite similar to thatreported by Ray et al. (2005). In this case, the westwardM2 tide meets with a penetrating wave from the IndianOcean via Sunda Strait.

Unlike M2, the S2 tide shows more complicated wavepropagation behavior due to the incoming wave throughKarimata and Sunda Straits. There are two amphidromicpoints of the S2 tide. The first one is located near KarimataStrait and is caused by the incoming S2 tide throughKarimata Strait, where it meets with the progressive wavefrom the eastern part of the Java Sea to produce a clock-

K1

O1

Fig. 2. Modeled co-amplitude and co-phase (relative to the Greenwich meridian) distribution for K1, O1, M2 and S2 tidal constitu-ents, case F8. Solid (dashed) lines denote amplitude (phase) with contour intervals 15° and 30° for diurnal and semi-diurnaltides, respectively.

M2

S2


wise amphidromic point. The other one is an anticlock-wise amphidromic, located near the east coast of Java Is-land and Madura Island. The anticlockwise amphidromicpoint is caused by the refraction effect due to interac-tions between wave propagation from the southeasternpart and Madura Island. In general, the semi-diurnal tidesare smaller than the diurnal tides.

4.2 Case study with different tidal forcingThe present model is forced by tidal elevation at the

open boundary, so the boundary condition is the key tothe model results (Davies and Hall, 1998; Davies et al.,2004). The main tidal constituents (K1 and M2) are morereliable than the others (O1, K1, M2, S2, P1, Q1, N2, K2). Ifthe nonlinear effect of one constituent on others is treatedas negligible, we would be able to separate the effect ofeach constituent. However, the Java Sea is small and shal-low with complex bottom topography, so nonlinear ef-fects may be important. Westerink et al. (1989) found thatsecondary nonlinear interactions between the astronomi-cal and the shallow water tides can significantly affectovertides, compound tides and even astronomical tides.In this section we take a closer look at the sensitivity ofK1 and M2 to the open boundary condition by investigat-ing the three cases (F2, F4 and F8) shown in Table 1.

Table 2(a) provides comparisons of amplitudes andphases between model results and observed elevations ofO1, K1, M2 and S2 at the eleven coastal tide gauge sta-tions, for case F8. Amplitude differences of all four con-stituents are generally less than 10 cm, the exceptionsbeing Cirebon (O1 tide), Semarang (O1 tide) and Surabaya(O1 and K1 tides). Most phase differences in M2 are lessthan 1 hour (or 28.98°). However, the other three con-stituents have several stations with more than 1 hour de-viations in phase, which are especially large in O1 andS2. RMS values of phase differences of constituents O1,K1, M2 and S2 are 72.79° (5 hours 13.33 min), 18.98° (1hour 15.71 min), 9.89° (20.48 min) and 51.89° (1 hour43.78 min), respectively. Comparative analyses showedthat M2 tide has better results while K1 tide seems to bemoderate.

The comparisons of amplitudes and phases for caseF4 (table not shown) are almost similar to case F8, espe-cially for O1, M2 and S2. However, K1 tide is improvedwith an RMS value of phase difference of 11.63° (46.41min). There are two K1 tide stations which have a phasedifference of more than one hour (Pari Island and Jakarta),and an amplitude difference of more than 10 cm (Belitung-11.89 cm, Surabaya-11.72 cm).

The results of our experiment for case F2 are sum-marized in Table 2(b). The M2 tide is almost similar tothe previous results for the other two cases. The analysisshows the best results for the K1 tide, which has a phasedifference of 9.31° (or 37.14 min). However, there are

still some discrepancies for the K1 tide; e.g., at Pari Is-land the phase difference is more than 1 hour, while atBelitung and Surabaya there is an amplitude differenceof more than 10 cm. The discrepancies in these stationsare difficult to avoid since they are located in very nar-row passages. Both amplitude and phase differences haveequal positive and negative values, indicating that themodeled tides are not biased.

Unlike coastal tide gauge data, tidal propagation overthe Java Sea shows a discrepancy in phase caused by thedifferent tidal forcing. We now focus on comparison be-tween cases F8 and F2 for K1 and M2 tides. The K1 tideshows that the central and western parts of the Java Seahave a phase difference of about 1 hour, while the otherregions are below 1 hour. On the other hand, the M2 tideshows a phase difference of about 1 hour in regions nearSunda Strait at the western part and northern coast alongeast Java and Madura Islands. Therefore, the sensitiveregions related to the different tidal forcing are affectedby the behavior of specific tidal constituents. In this case,the K1 tide has a resonance effect or node region in thecentral part and incident wave in the solid boundary ofthe western part of the Java Sea. The M2 tide has anamphidromic point near Sunda Strait and anotheramphidromic point is indicated near the northern coastalong east Java and Madura Islands.

In summary, the three cases of tidal forcing can beused to explain the behavior of tidal elevation in the JavaSea. However, we cannot justify any one of them due tothe limited observations available. The important pointis to determine what magnitude of tidal current will yieldtidal mixing and residual current. In the next section wefocus on whether there is any significant difference incurrent magnitudes among these three cases.

5. Modeled Flow Pattern

5.1 Tidal currentsSince the results of the three cases F8, F4 and F2 are

fundamentally consistent with each other, we focus ourexamination on tidal currents associated with K1 and M2in case F2 and compare K1 between cases F2 and F8. Fig-ure 3 compares the surface tidal current ellipses for theK1 and M2 tides, at the mooring buoy locations shown inFig. 1. In this figure, a line within each ellipse representsthe direction of a current vector at maximum flood tide,and the arrow attached to the tip of this line indicates thedirection of the current vector rotation. Qualitatively, thecomparisons are most reasonable for both K1 and M2 tidalcurrents. There are two stations (SW51 and SW60) forthe calculated K1 tidal currents, and one station (SW54)for the calculated M2 tidal current, which have oppositesemi-major axis to the observed data.

The differences between model results and the ob-


served semi-major axes of K1 and M2 are in general lessthan 10 cm/s. There are a few exceptions however; e.g. atSW60 the difference is 20.59 cm/s for K1, and at SW55 itis 13.53 cm/s for M2. The differences in semi-minor axesof K1 and M2 are less than 3 cm/s. Inequality in orienta-tion is generally less than 15° except at SW51, where itis 138.28°, and at SW60, where it is 161.80° for K1, andat SW54, where it is 73.74° for M2. On the other hand,the phases of tidal ellipses do not agree well with theobservations. The calculated RMS values are 64.17° and112.52° for K1 and M2, respectively. It is not, however,surprising that the model should have such discrepanciesfrom observations since the moorings are located verynear the coastline or between small islands that were notproperly resolved by the model domain.

The calculated K1 tidal ellipses at the sea surface(σ = 0) and the fifth level (σ = –0.929) above the bottomare shown in Fig. 4. At the surface (Fig. 4(a)) a nearlyrectilinear flow is found along the coast of southeastSumatra. Over the central part of the Java Sea the flowpatterns are more circular and nearly rectilinear towardsthe Karimata Strait due to K1 tidal wave deflection. The

orientations of major axes of tidal ellipses almost con-verge to the southern coast of Kalimantan. The spatialpattern of tidal ellipses near the bottom (Fig. 4(b)) is simi-lar to that of the surface, but the magnitude of the bottomcurrent is significantly reduced by bottom friction.

In general, the results of the model show that thecurrent magnitude of K1 near the surface varies between10 and 60 cm/s. The calculated K1 tidal ellipses showstrong tidal currents in the central part (node region) andnarrow passages, where the maximum current magnitudeat the surface reaches 40–60 cm/s. The intensification ofK1 tidal current in the node region can be explained interms of a small elevation in the middle of the antinoderegions, thus triggering large currents. The intensifica-tion of K1 tidal current in the central part is thereforecaused by the co-oscillation tides. Han (2000) found suchintensification in the Newfoundland shelf due to a reso-nance between continental shelf wave and the K1 tide.Pereira et al. (2002) also found similar intensification inthe southern Weddell Sea due to proximity of the criticallatitude for the M2 tide.

As shown and described earlier using Fig. 3, if the

Fig. 3. Comparison between field observations (full line) and model results (dashed line) for K1 and M2 tidal currents, case F2.


line is located on a semi-major axis, the maximum veloc-ity occurs at the same phase as the maximum flood tide,reflecting the characteristic of the progressive wave propa-gation in the direction of the line. On the other hand, ifthe line is located at the tip of a semi-minor axis, the ve-locity change occurs in advance of elevation by a phaseof 90°, reflecting the feature of the standing wave in thedirection of the semi-major axis. In Fig. 4, K1 tidal el-lipses are dominated by the standing wave in the westernand central parts and the progressive wave in the easternpart of the Java Sea. The counterclockwise rotation isdominant over the central part, while the clockwise rota-tion occurs in the eastern and western regions.

Figure 4(c) shows the calculated M2 tidal currentellipses at the sea surface. We found that the M2 currentis in most cases weak compared to the K1 current. In gen-eral, the magnitude of the M2 current varies between 3and 10 cm/s, with the exception of the strong current atthe narrow passage of Madura Island, which is approxi-mately 70 cm/s. Our model result is similar to those ofHatayama et al. (1996) and Ray et al. (2005). At the east-ern part, the M2 tidal ellipse orientation is consistent with

the maximum tidal current, reflecting the progressivewave characteristics. On the other hand, the standing waveis dominant in the western part.

Focusing now on the different cases of tidal forcingat the open boundary, Fig. 5 shows the calculated K1 tidalellipses at the sea surface for case F8. In comparison withcase F2 (Fig. 4(a)), the model results have no significantdifference. Therefore case F2 presents a robust solutionfor understanding the intensification of the K1 tidal cur-rent in the central region of the Java Sea caused by theresonance effect.

5.2 Tidal energy flow and residual currentIn this simulation we analyze tidal energy flow and

its fate in relation to tidal dissipation. The residual cur-rents induced by tides are also calculated since they cantransport materials over large distances. This analysisconsiders both the dominant K1 and the less dominantM2. The calculated tidal energy flow and residual cur-rents are forced separately by each of these main tidalconstituents (Table 1). We follow Davies and Kwong(2000), and Sheng and Wang (2004) in calculating the

Fig. 3. (continued).


tidally averaged (time mean) energy flux vectors (here-after referred to as tidal energy). The formula is

E ET

u v gu v

dzdtx y h

T, , ,( ) = ( ) + +

( )

−∫∫ρ η

η02 2

0 21

where (Ex, Ey) are eastward and northward componentsof the energy flux vector, (u, v) are components of thehorizontal velocity vector, η is a surface elevation, ρ0 andg denote the water density and the acceleration due togravity, respectively, h is a water depth, and T is the tideperiod.

Figure 6 shows the tidal energy of the K1 and M2tides. The tidal energy patterns of K1 and M2 are almostsimilar along the westward direction. However, the tidalenergy inflow of M2 is very small compare to K1. The K1tidal energy enters the Java Sea from the eastern part witha magnitude of about 0.4 kW/m. When K1 tidal energypasses the central part (node region), the energy dissi-pates very quickly. This corresponds to the low tidal el-evation of K1 in the node region. On the other hand, theK1 tidal energy along the northern coast of Java Island isable to penetrate the western region. Similar to K1 tidalwave propagation, the K1 tidal energy shows an influx inGaspar Strait and outflux in Bangka Strait with a largemagnitudes of more than 0.5 kW/m. Small parts of thetidal energy influx from Gaspar Strait join the tidal en-ergy in the northern coast of Java Island and flow towardsSunda Strait. The M2 tidal energy is also consistent withits tidal wave propagation. However, the M2 tidal energydissipates in the whole Java Sea basin.

Next we calculate the depth-averaged residual flow

0.50 m/s

0.50 m/s

0.50 m/s

Fig. 4. Modeled K1 tidal ellipse (a) at the surface, σ = 0; (b) ata near-bottom level, σ = –0.929 and modeled M2 tidal el-lipse; (c) at the surface, σ = 0 for case F2. The bold (light)ellipses denote counterclockwise (clockwise) circulation.

0.50 m/s

Fig. 5. Modeled K1 tidal ellipse at the surface (σ = 0) for caseF8. The bold (light) ellipses denote counterclockwise (clock-wise) circulation.


(hereafter referred to as residual flow) from the modelresults using each of K1 and M2 tidal forcings (Table 1),as shown in Fig. 7. The K1 residual flow shows a verycomplicated flow pattern in the western part with a mag-nitude of about 4 cm/s. Strong currents are found in thenarrow passages and several capes with a maximum mag-nitude of 10 cm/s. The crowded residual flow pattern isprobably caused by the incident waves of K1 tide at thesolid boundary of Sumatra. At the central part, the K1residual flow follows the co-amplitude pattern of K1 tidewhere the water column moves from the high amplitudein Karimata Strait to the small amplitude in the node re-gion. Finally, the K1 residual flow deflects towards theeastern part with a magnitude of about 0.2 cm/s.

Compared to K1 residual flow, the M2 residual flowis generally stronger, except in the western Java Sea. TheM2 residual flow shows a clear northwestward flow pat-tern with a magnitude of about 0.7 cm/s. Incoming andoutgoing residual flow located at the southeastern sec-

tion and the narrow passages of Karimata/Gaspar Straits,respectively, have large magnitudes of more than 10cm/s. In general the M2 residual flow follows along itstidal wave propagation.

Following Kantha and Clayson (2000), we considera uniform channel of shallow water depth H, with a tidalcurrent amplitude U and tidal elevation amplitude η. Thisconfiguration is such that the ratio (η/H) is not negligi-ble. The transport is proportional to U(H + η) during theflood phase and to U(H – η) during the ebb phase. Whenaveraged over a full tidal cycle there is therefore a nettransport proportional to 2Uη and a residual flow of mag-nitude 2Uη/H in the direction of propagation. In contrast,we found that the K1 residual flow is mainly opposite toits tidal wave propagation which comes from the easternpart. Therefore, the role of co-oscillations tide is impor-tant for the residual flow pattern of the K1 tide in the JavaSea. Here, the residual flow is not in the direction of pro-

0.5 kW/mK1

0.5 kW/mM2

5 cm/sK1

5 cm/sM2

Fig. 6. Time mean energy flux vectors of K1 and M2 tides cal-culated from the model results over fifty tidal cycles.

Fig. 7. Depth integrated residual flow calculated from the modelresults forced by K1 and M2 tidal elevation over fifty tidalcycles.


gressive wave propagation but follows the reflected wave.The K1 residual flow is minor compared with the M2 re-sidual flow, and hence the role of K1 residual flow inmaterial transport is not crucial. The present simulatedM2 residual flow pattern is consistent with that of Schiller(2004), who calculated the Java Sea residual current basedon a long term calculation (eight model years) forced bythe eight main tidal constituents. The residual flow pat-tern in the Java Sea seems to form a part of what he calledthe “residual western boundary current” all along thecoastline of the Asian landmass.

6. Tidal MixingIn this section we closely examine the calculated tur-

bulence mixing using bottom stress with a quadratic draglaw. The calculated turbulence mixing is forced separatelyby each of the two main tidal constituents, K1 and M2(Table 1). The spatial variations of K1 and M2 bottom fric-tion velocities reflect the spatial variations in the tidalcurrent magnitude (Fig. 8, M2 is not shown). The bottomfriction velocities for K1 and M2 tides near the easternopen boundary and western solid boundary are mostlywithin 1–2 cm/s. Regions with larger K1 bottom frictionvelocity are associated with the stronger K1 tidal currentsin the central part of the Java Sea and narrow passages.In particular, the range of K1 bottom friction velocity inthe central part varies within the range of 3–6 cm/s, whilethat of M2 is about one-tenth of K1.

Given the bottom friction velocity, we can estimatethe thickness of the bottom boundary layer or Ekman layerthickness. We follow He and Weisberg (2002) to estimatethe Ekman layer thickness (δ) for steady-state flow re-gimes; that is

δσ

=+( ) ( )cu

f* , 2

where u∗ is the bottom friction velocity, σ is tidal fre-quency of each of K1 and M2, f is the local Coriolis pa-rameter and c = 0.1–0.4 (Loder and Greenberg, 1986).The friction velocity u∗ is obtained as (τb/ρ0)1/2. There-fore, the distribution pattern of the bottom boundary layerthickness is similar to the bottom friction velocity (fig-ure not shown). Using a low range value of c = 0.1, thethickness of K1 over the central part of the Java Sea isestimated to be about 45–60 m, and all the narrow pas-sages to be about 120 m. In general, the thickness of K1for the whole Java Sea bottom layer is about 20–30 m.However, the thickness for M2 is about one-tenth of K1in the central part and one-third of K1 near the easternopen boundary and western solid boundary. The smallervalue of M2 is related to its tidal frequency in the de-nominator of Eq. (2). Consequently, tidal mixing aloneseems sufficient to mix the water column, especially inthe central region of the Java Sea.

The height of the log-layer thickness can be estimatedusing 0.1δ (Soulsby, 1983; He and Weisberg, 2002). Based

(b)

(a)

Fig. 8. RMS value of bottom friction velocity (cm/s) for K1tide calculated from the model results over fifty tidal cy-cles.

Fig. 9. RMS value of vertical eddy viscosity (m2/s) for K1 tidecalculated from the model results over fifty tidal cycles at(a) ten meter depth and (b) cross section along 4°S.


on values of the bottom boundary layer thickness, themean K1 log-layer thickness over the Java Sea is esti-mated to be 2–3 m, while the central part and the narrowpassages have greater log-layer thicknesses, in the rangeof 4.5–6.0 m.

Since we are concerned with the role of tidal mixingin vertical exchange of nutrients for future research, weanalyze the vertical eddy viscosity using the level-2.5turbulent closure scheme in Mellor and Yamada (1982).Similarly to the bottom friction velocity, we calculatedthe RMS value of vertical eddy viscosity using the samemethod (Table 1). In this simulation we only consider theK1 tide due to the large bottom boundary layer thicknesscompared to the M2 tide. Figure 9(a) shows the horizon-tal distribution of the vertical eddy viscosity at 10 m depth.Related to the effect of K1 tidal resonance, the verticaleddy viscosity also shows intensification in the centralpart of the Java Sea and varies within 0.01–0.02 m2/s.

A simple z-dependent mixing length, lz, is proposedas

l zz

hz = −

( )κ 1 3

1 2/

,

where κ = 0.4 is von Kármán’s constant, h is the totalwater depth and z is the height above the bottom (Simpsonet al., 1996). Figure 9(b) shows the vertical profile of thevertical eddy viscosity along 4°S over the Java Sea. Thevertical profile is nearly parabolic, which is consistentwith the simple z-dependent mixing length. The verticalprofile is also consistent with the horizontal distributionwhich shows an intensification of tidal mixing in the cen-tral part of the Java Sea. The maximum vertical eddy vis-cosity in the central part is 0.025 m2/s. We have no directobservations to verify the calculated vertical eddyviscosities, particularly the large values in the central part.As an analogy, we refer to the observed vertical eddy vis-cosity in a tidal channel reported by Lu et al. (2000). Thewidth and depth of the channel are around 1 km and 30m, respectively. The observed tidal current at mid-depth

Track 1

Fig. 10. Hydrographic data profile during southeast monsoon (October 1993), track 1.


varied within 25–100 cm/s. They found that the observedvertical eddy viscosity at mid-depth varied within 0.001–1 m2/s, with a mean value of about 0.01 m2/s. Thus, ourmodel results are reasonable in comparison to the otherfield observations.

7. Summary and DiscussionWe have applied the barotropic model combined with

the field observations to examine the structures ofbarotropic tides, tidal circulation and their relationshipto turbulent mixing in the Java Sea. In general, the simu-lated tidal elevations for the K1 and M2 constituents arein good agreement with in-situ observations, while theO1 and S2 constituents show notable discrepancies. Thefeatures of K1 and M2 tides are also similar to previousreports by Wyrtki (1961), Hatayama et al. (1996), Ray etal. (2005), Hoitink (2003) and Ali (1992). The calculatedtidal currents are mostly reasonable compared with in-situ observations, within observational limitations.

Based on comparison between model and observa-

tions, we found that the discrepancies in tidal elevationare related to the inaccuracies of tidal forcing input alongthe open boundaries and their nonlinear interactions withother constituents. This was also conclusion of other re-searchers, concerned with other basins, e.g. Westerink etal. (1989); Davies and Hall (1998); and Davies et al.(2004). For case F8, some discrepancies in phase of theK1 tide were noted at several stations. In this study we donot focus on the specific effects of changes in tidal forc-ing due to a lack of tidal elevation data along the openboundaries and offshore regions. In addition, compari-son among the three cases over the Java Sea showed thatthe amplitude differences are mostly below 7 cm. Modelresults regarding tidal current do not diverge greatlyamong these three cases. We can therefore use any of thesecases to describe the tidal circulation and turbulent mix-ing in the Java Sea.

Our model can explain the dominance of the diurnaltide constituent K1 over the Java Sea, while the adjacentdeep Pacific and Indian Oceans are dominated by semi-

Track 2

Fig. 11. Hydrographic data profile during southeast monsoon (October 1993), track 2.


diurnal components. The previous researches of Wyrtki(1961) and Ray et al. (2005) explained that, unlike thediurnal wave, the semi-diurnal wave is weak when itpropagates to the Java Sea. The present study, on the otherhand, clearly shows a resonance effect that increases theamplitude of K1 in the Java Sea, as suggested by Hoitink(2003) and Ali (1992). This resonance is related to tidalcurrent, tidal energy and residual current. For example,the intensification of tidal current in the node region isinfluenced by the existence of the tidal resonance, suchthat it can enhance the K1 tidal current in the Java Sea. Inaddition, the resonance effect produces unusual patternsof the tidal energy flux and residual currents. Tidal en-ergy dissipation is not found in shallower parts but mainlyin the node region, so that the bottom friction does notsignificantly affect the tidal energy flux of the Java Sea.Meanwhile, the residual current usually follows the tidalwave propagation but the role of tidal resonance couldchange the residual current pattern to follow the reflectedwave in the opposite direction.

Track 1

Fig. 12. Hydrographic data profile during northwest monsoon (February/March 1994), track 1.

While the M2 tide is a secondary tide, its residualflow makes a major contribution, especially in the east-ern and central regions of the Java Sea. The magnitudeassociated with M2 tide is higher than the K1 tide, and theM2 tide is connected with the long term residual flow inthe Indonesian seas, as suggested by Schiller (2004).Hence, the major progressive waves of the M2 tide fromthe adjacent sea (Flores Sea) through the open boundaryare responsible for its residual flow. However, we sug-gest that the dissipation of the M2 tide is mainly causedby the relatively shallow topography of the Java Sea com-pared to the adjacent seas.

The calculated turbulent mixing quantities in the JavaSea revealed the important role of mixing in the region.The estimated tidal bottom boundary layer (Ekman layerthickness) significantly exceeds the water depth due tothe strong tidal current, especially in the central part. Anexception is found in the deeper eastern part. The inter-action between a strong tidal current and high tidal bot-tom boundary layer is also found in other regions by us-


ing similar methods, e.g. the region between the Kintyrepeninsula and the coast of Ireland (Davies et al., 2004).In these regions, the calculated bottom boundary layercan exceed 300 m, where water depths are only around100 m. The Ekman layer thickness is the key to the strati-fication and the transition region (tidal front) betweenstratified and well-mixed conditions. Consider theoreti-cally, if the main tidal turbulent boundary layer (in thiscase is K1 tide) exceeds the water depth, the water col-umn should remain well mixed.

In order to verify the intensification of tidal mixingin the central part, we used the hydrographic data fromthe AARD/ORSTOM Java Sea Small Pelagic FisheriesAssessment Project 1992–1995 (Durand and Petit, 1997;Pasaribu et al., 2004). As a part of Southeast Asian wa-ters, the Indonesian seas are mostly under the monsoonsystem with dry and rainy seasons during southeast andnorthwest monsoons, respectively. We therefore focusedon the data taken between October 8 to 21, 1993 (end ofsoutheast monsoon) and February 21, 1994 to March 6,

1994 (strong northwest monsoon). During the southeastmonsoon, track 1 (Fig. 10) and track 2 (Fig. 11) showthat the front appeared at around 110°E and 111°E, andthe well-mixed water column extended eastward from thefront. The existence of the front supports the model re-sults on tidal mixing intensification in the central part ofthe Java Sea. When the strong northwest monsoon blows,the front at track 1 (Fig. 12) became wider and showed afreshwater penetration from the Sunda shelf at the sur-face layer due to river discharge in the rainy season(Wyrtki, 1961). Meanwhile, the front at track 2 (Fig. 13)became weak and was pushed upward until around 113°Ewhere the freshwater still appeared in the western part.Thus, the intensification of tidal mixing caused by reso-nance may play an important role, even under the strongmonsoon in the central Java Sea. Related to the environ-mental problems, the intensification of tidal mixing inthe central part could play an important role in verticalexchange of nutrients and control of biological produc-tivity.

Fig. 13. Hydrographic data profile during northwest monsoon (February/March 1994), track 2.

Track 2


We realize that our model has some limitations thatmay qualify our strong conclusion on tidal mixing. Theimportant terms may be stratification and baroclinic flow(internal tides) from Flores Sea, which induce verticalmixing, as pointed out by Robertson and Ffiled (2005).Related to the tidal currents, these model results still needmore accurate quantitative estimates. Therefore, a higherhorizontal resolution is required, especially to resolvesome small islands. Improved performance can also beobtained through more accurate bathymetry.

AcknowledgementsWe wish to thank Dr. Hary Budiarto and Ms. Ressy

Oktivia of the Seawatch Program, BPPT Indonesia forproviding the hourly current data and Mr. Duto Nugrohoof Research Institute for Marine Fisheries, Ministry ofMarine Affairs and Fisheries, Indonesia for providing thehydrographic data. We also thank Dr. Agus Setiawan ofBPPT for sharing the code of harmonic analysis embed-ded in the POM, as well as English proofreading byTakayoshi Ikeda. Comments from two anonymous review-ers were also very helpful in improving the manuscript.The first author is awarded a scholarship by Ministry ofEducation, Culture, Sports, Science and Technology(MEXT), Japan.

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