1 Introduction

The knowledge of the processes and the effect of turbulence, are important in understanding the dynamics of heat transfer in the ocean and in building models that can predict changes in the ocean and how the ocean interacts with the atmosphere. One of the effect of the turbulence in the Indonesian waters is changing the characteristics of the Pacific Ocean water masses as it flow into the Indian Ocean (Hautala et al., 1996, Hatayama et al., 1996, Hatayama, 2004; Field and Gordon, 1996). Spatial distribution of vertical turbulent in the Makassar Strait is apparently not widely studied.

Studying turbulence in the oceans today use direct observation such as microstructure profiler like TurboMap (Turbulence Ocean Microstructure Acquisition Profiler) (Palmer et al., 2015), AMP (Advanced Microstructure Profiler) or VMP (Vertical Microstructure Profiler) (Kunze et al., 2011). Unfortunately, a direct observation method is still hampered by the unavailability of such instruments, both in research institutions and in various universities (Gargett and Garner, 2007, Naulita, 2014). An alternative method for studying the vertical turbulence in the ocean is to use the CTD data. A CTD (Conductivity Temperature Depth) commonly used in studies of oceanography, so CTD data already widely available and easier to obtain.

Thermocline layer categorized as relatively stable compared to those of mix layer and deep layer. Thermocline layer in Makassar Strait tranversed by Arlindo making this layer so important to the current system and heat exchange globally.

The Indonesian throughflow (ITF) from its Pacific Ocean entrances to its exits into the Indian Ocean, follows different pathways within the Indonesian archipelago. Makassar Strait is one of it and as a major pathways where ITF flow at thermocline layer. Watermass transformation can be detected from the change of salinity of NPSW (North Pasific Subtropical Water) from 34,9 PSU at northern part of Makassar strait to 34,54 PSU at southern part. This indicated strong vertical turbulent at the strait (Hatayama 2004; Robertson dan Field, 2005, Koch-Larrouy et al.,2007, Atmadipoera et al., 2009). Topograhy of Makassar Strait has varies shape at many point, with different slope at west and east side. This slope lead to the breaking of internal waves that supply more energy to create vertical turbulent. The spatial distribution quantity of the vertical turbulent in thermocline layer of Makassar Strait, and the force that trigger it are important knowledge in studying watermass transformation of ITF.

2 Materials and Methods

2.1 Data, Time and Study Area

Observation were carried out between 2°N - 4°S and 115.5°E - 120.5°E in Makassar Strait (Figure 1) from June 3 to June 22, 2013 which is a collaboration between Research Centre for Oceanography (LIPI) with the United Nations Educational Scientific and Cultural Organization (UNESCO) and the Sub-Commission for the Western Pacific (WESTPAC ) using Baruna Jaya VIII research vessel. This study was part of Widya Nusantara Expedition (Ewin) 2013. 

Figure 1 Resarch stations (blue dots) with topography background in Makassar Strait (Source: ETOPO 0.25) and map of Indonesia in right below. Transect 1 and 7 in the north-south dan other transects on the east-west direction. The rectangle is tides station at Donggala. The scale on the right is the topography scale of Makassar Strait.

The accuracy and resolution of the conductivity sensor are 0.0003 S m^-1 and ± 0.00004 S m^-1, meanwhile the accuracy and resolution of the temperature sensor are 0.001 ^oC and ± 0.0002 ^oC. CTD data acquisition were done at sampling rate of 24 Hz (in 1 second there were 24 pulse emitted to retrieve data). The pre-process prosedure was done to the CTD data before being analized using SBE data processing software 5.37e which is follow the processing procedure of McTaggart et al. (2010).

Temperature, conductivity and pressure from the sea surface to 2000 m were observed with CTD (SBE 911plus) at 29 stasions with falling speed of 1 ms^-1. CTD data used in this study is from 100 m to 350 m which is a thermocline layer. The research stations are set into six transects. Transects 1 is the transect in north-south direction of Makassar Strait. While other transects are on the East-West direction. Transect 2 at the southernmost near Labani Channel and so on until transects 6 in the northernmost of Makassar Strait. The north-south transect was created with the purpose to see the difference in the vertical turbulence at the entrance passage of Arlindo in northern Makassar Strait with the exit passage in southern of the strait. Meanwhile the east-west transect, i.e transect 2, 3, 4, 5 and 6 were created to see the difference in the vertical turbulence on the west, middle and east side of Makassar strait. This study was also used tidal data published by DinasHidro-Oseanografi TNI-AL and topographyc data ETOPO 0.25.

2.2 Data Analysis

The method used to determine the existence of vertical overturn from CTD data is to calculate the Thorpe scale by using equation (Dillon, 1982): L_T=[1/n ∑_(i=1)^n▒〖d_i〗^2 ]^(1/2) where n is the number of density invertion in the sample. L_T is the rms vertical displacement required to reorder the observed profile, ρ_a=ρ_a (z_a) into a  gravitationally stable profile ρ__b=ρ__b (z__b)  (Galbraith and Kelley, 1995). Thorpe displacement values​​  is vertical displacement of water-mass that move upward or downward to form a gravitationally stable profile, and given by, d_i=Z_a-Z_b, where  is initial depth of water-mass of real condition and  is the depth of water-mass after reorderd. Bouyancy forces caused heavy fluids to sink through lighter ones (Stewarts, 2008; Galbraith and Kelley, 1995).

Instrument resolution imposes basic constraints on overturn detection. The vertical resolution are computed from the detection of overturns no thinner than L_z=5δ_z  and L_ρ≈2  g/N^2   δρ/ρ_o (Galbraith and Kelley, 1995). The possibility of detecting overturns in an area of interest can be grossly evaluated if the mixing rate is approximately known. Using Ozmidov length scale (Ozmidov, 1965) L_0=(ε/N^2 )^(1⁄2) a and assuming that the overturn thickness equals Ozmidov scale, the minimal detectable dissipation rate can be calculated as ε_z≈25(δ_z )^2 N^2 (Galbraith and Kelley, 1995).  is turbulent kinetic energy dissipation rate and  is bouyancy frequency formulated -g/ρ_o δ_ρ/δ_z, where g is the gravitational acceleration of the earth (~ 9.8 m s-2 at the equator),  is CTD ability to detect differences in density (0,0006 kg m^-3), L_z is the depth interval (0,04 m), and  is the average density (21.2652 kg m^-3).  minimum that can still be detected is  5δ_z=0,2 m, meaning only Thorpe displacement has greater value than 0, 2 m can be taken into account.

Spurious density inversion can arise if noise is added to a smoothly stratified profile. The noise may result from mismatches in time response of temperature and conductivity probes or from the thermal inertia of conductivity cell (Galbraith and Kelley, 1995). To eliminate this noise a water-mass test of GK test was applied to the density inversion data. The scheme examines each reordering region individually. The simplest models were used to smooth T-S covariance  and ρ_s=a_s+b_s S and ρ_T=a_T+b_T S. The deviations between the observation and these lines are measured by computing the rms value of ρ-ρ_s and ρ-ρ_T. The ratio between the rms value of ρ-ρ_s and ρ-ρ_T with Thorpe scale denotes ξs and ξT, respectively, are positive-definite quantities that approach 0 for tight T-S relationships and 1 for rather loose relationships (Galbraith and Kelley, 1995). And then the test was applied to ξ = max (ξs,ξT). The critical value of ξc = 0,5, meaning that the density inversion region that have value ofξs and ξT less than 0,5 are regarded as signatures of overturning motion.

The rate of dissipation of turbulent kinetic energy per unit mass (ε) is calculated using the equation ε=〖L_o〗^2 N^3 with the Ozmidov length scales L__o=cL__T . The constant c = 0.91 for the waters in the Equatorial Pacific (Cheng and Kitade, 2014). Vertical diffusivity coefficient values ​​are calculated with equation K_ρ=Γε/N^2  where the value of mixing efficiency Γ = 0.2 indicates the conversion efficiency of the turbulent kinetic energy into potential energy of the system, so it can vary depending on the dynamics of turbulence (Osborn, 1980; Thorpe, 2005). The spatial distribution of ε and value k_p as the property of the existence of the vertical turbulence, will be plotted for thermocline layer.

3 Results
3.1 Static Stability

Vertical profile of the average of N² overlaid with potential temperature in thermocline layer in Makassar Strait can be seen in Figure 2. The thermocline layer has a range of N² ​0(10-6 - 10-3) s^-2 meaning this layer is relatively stable. The range of ​​N² values obtained in this study is similar to that by Park et al. (2008) at Kerguelen Plateau, Suteja et al. (2011) at Ombai Strait by order of 0(10^-4 - 10^-3) s^-2 and Purwandana et al. at Alor Strait (10^-3) s^-2. The maximum value of  at termocline layer in Makakssar Strait approaching 0,003 s^-2. This result agreed with the research by Galbraith and Kelley (1995) and Purwandana (2014). Overall, N² value is relatively large with the most common order is 10^-5 s^-2, so it can be said that this layer is relatively stable compared to mix layer and deep layer. The magnitude of this stability does not rule out the possibility for the existance of vertical turbulent in this layer. According to Pond and Pickard (1983), the relativity high value of N² in the thermocline layer caused by the presence of pycnocline layers where the density gradient increases sharply with depth. 

Figure 2 Vertical profile of average of bouyancy frequency (N2) overlaid with potential temperature in Makassar Strait. Thermocline layer in the range of 100-350 m is in the rectangl

3.2 Eliminate noise by applying a water-mass test of GK test

Data derived from CTD tools usually contains a lot of noise such as that caused by the mismatch response time temperature and conductivity sensors (Galbraith and Kelley, 1996) or due to the vertical movement of rising and falling of the ship during data retrieval (Johnson and Garrett, 2004). Thorpe displacement at station 11 that have not pass water-mass test can be seen in Figure 3 (a), meanwhile in Figure 3 (b) is already passed the test. Vertical density profile of water mass at thermoclin layer in Makassar Strait can be seen in Figure 3 (c).

Thorpe displacement in the box in Figure 3 (a) at a depth of 310-320 m, has a value of Thorpe displacement (Td) is greater than 0, 2 m but did not pass the water-mass test because of the relatively small value of the relationship between potential temperature and salinity (ξ_s= 0,56 and ξ_T = 0,52) meaning the potential temperature and salinity are relatively loose related. Meanwhile, ξ_s and ξ_T value at a depth about 200 m exceeds the critical value (0,45 and 0,48 respectively), meaning the potential temperature and salinity are relatively close related. The same process is performed also for the entire Thorpe displacement area on all the research station.Calculation is then performed only on Thorpe displacement area that pass this test and having ξ_s and ξ_T value less than 0,7.

Similar results were obtained by Galbraith and Kelley (1995) and Gargett and Garner (2007) when detecting vertical overturn using CTD data in Lawrence Estuary and Svalbard waters of Canada as well as in the Ross Sea waters of Australia. According to Galbraith and Kelley (1995) T-S diagram that form a loop indicated in these areas have more than one type of water masses, where it may be caused by lateral intrusion on water masses.

Figure 3 Thorpe Scale that has not (a) and already passed the water-mass of GK test (b). Initial vertical density profile (thin line) of water mass was reordered in to static stability (thick line) condition (c)

3.3 Thorpe Scale Estimate

Thorpe Scale is root mean square (rms) of Thorpe displacement (Td) at the area of overtun. This value equal to turbulent scale, so this usually use to predict the strength of vertical turbulent. It’s also use in the calculation of the rate of dissipation of turbulent kinetic energy ( ε) and eddy diffusivity coeffisien of density (K_p ).

3.3.1 North - South Transect

Thermocline layer is the most stable layer compared with mix and deep layer. It have most large value of N², and a fewer number of Td. Thorpe displacement at north - south transect (transect 1 and 7) at thermocline layer of Makassar Strait can be seen in figure 4. At the thermocline layer, the value of Td ranging from ± 0,5 to ± 7 m. Relatively large scale of Td was found on the south side of the strait at a depth of 340 m. Thorpe displacement in the north side of the strait (station 27) was found with values ± 5 m. Thermocline layer in the middle of the strait have a relatively larger Td (± 5 m) than the mixed layer and spread almost throughout the water column in this layer. The Td values at this research was smaller compared with the research of Purwandana et al. (2014) at Alor Strait ± 7,5 m, and Suteja et al. (2011) in Ombai Strait of -10 to 27 m.

Figure 4 Td in the thermocline layer at north-south transect in the Makassar Strait that already pass water-mass test

3.3.2 East-west transects

East-west transects consisted of five transects i. e. transects 2, 3, 4, 5 and 6. Td in the thermocline layer for East-West transect can be seen in Figure 5.Td with the highest scale (range ± 10 - ± 15 m) is found on the eastern side of the strait transect 2 (at station 5) at a depth of 320 m, transect 3 (at station 16) at a depth of 300-320 m and transect 6 (at station 25 ) at a depth of 260-280 m. While the smallest Td (± 0.5 m) found in both the West and the East and also at the central part of the strait on all transects. West sides of the strait have relatively larger Td (± 2 to ± 5 m) than the East side (± 1 to ± 3 m).

Figure 5 Td at thermocline layer at transects 2 (a), 3 (b), 4 (c), 5 (d) and 6 (e) at Makassar Strait that already pass water-mass test

3.4 Spatial distribution of Vertical Turbulence Parameters
3.4.1 North - South Transect

Spatial distribution of vertical turbulent in thermocline layer can be seen in Figure 6. The range of ε on this transect is 0(10^-9 - 10^-7) Wkg^-1, while the K_p value  range from 0(10^-5 - 10^-2) m²s^-1 wich categorized as relatively strong vertical turbulent. More intensive vertical turbulence occurs in the southern part than in the northern part of Makassar Strait. This can be seen in Figure 6 (c) by the discovery of relatively large K_p value of (more than 10^-4) m²s^-1 located at station 1 and 2 near Labani Channel. Meanwhile, in the northern part, relatively large K_p value of  was only founded at several area. Vertical turbulent in the middle part of Makassar Strait also have some relatively strong ε and K_p values. The narrowing of Labani Channel begins at a depth of ± 500 m. Meanwhile, internals waves in the Labani Channel formed at a depth of ± 450 m (Purwandana et al., 2013).

 K_p value is almost identical to the research of Purwandana et al. (2013) in Alor Strait 0(10^-4 -10^-3) m²s^-1 and Suteja et al. (2011) 10^-3m²s^-1 in the Ombai strait. This result is similar to that obtained by Stansfield et al (2011) with K_p  = 10^-4 m²s^-1 at Juan de Fuca Strait, Columbia. The range of ​​  K_p values in this study is higher compared with the research by Matsuno et al (2005) 0(10^-6 - 10^-4) m²s^-1 at East China Sea at a depth about 200 m.

Figure 6  Spatial distribution of the vertical turbulence in Makassar Strait at thermocline layer. Research stations (red dots) are circled blue is the value of vertical diffusivity 10-5 m2s-1(a), 10-4 m2s-1(b) and> 10-4 m2s-1(c)

3.4.2 East-West transect

Vertical turbulence in transect 2 are more intensified in the Eastern side of the strait. This can be seen in Figure 6 (c) by relatively large value of K_{p larg}at station 4 and 5. While the strength of vertical turbulent at transect 3 and 6 is almost the same on both sides with  K_p values are equally strong on West and East sides of the strait. Vertical turbulence at transect 4 are stronger at west sides than the East sides of the strait. This can be seen from the discovery of a relatively strong  value (more than 10^-4) m²s^-1 at stations 15, 16 and 17. Relatively strong K_p vertical turbulence found in all parts of the transect 5. Figure 6 (b) and (c) shows the presence of relatively large K_p values at all stations on transect 5. Vertical turbulence occurred throughout the transect 5. This is due to Arlindo flowing at maximum speed in this transect. Horhoruw (2016) has found Arlindo with maksimum speed reach 1 ms^-1 at the entrance point at northern part of Makassar strait.

4 Discussion

Figure 7 show the correlation between log10(A_int) and log10(K_p) at all transect. Meanwhile Figure 8 shows the contours of the potential density in the thermocline layer overlaid with vertical turbulence and tidal conditions at the corresponding time. Potential density contour at several depths have a pattern that could be considered similar to the tidal patterns. There are several isopycnal line that connects the stations in the transects. This isopycnal line have relatively large amplitude and form a wave pattern with periods as same as surface tide. Tide pattern at station 1 to 3 have periods about 32 hours. Meanwhile isopycnal contours seem to have flat pattern with low-water pattern at a depth 250-300 m. Several vertical turbulence with relatively medium log10( K_p) value do exist at this contours. Relatively low correlation value (r=0,4) strongly suspected that vertical turbulent not much affected by internal wave.

Isopycnal pattern at station 4 to 8 on transect 2 have different pattern but the same period, about 20 hours, with surface tide. Isopycnal contour form ascending while surface tide descending pattern. Vertical turbulence at transects 2 exist at West and East sides of the straits. Relatively large log10( K_p) value found at a depth about 320 m with  value about 10^-7 Wkg^-1 and categorize as strong vertical turbulent. Some vertical turbulence with relatively medium log10( K_p) value have found in the middle part of the strait, but it can be said not caused by internal tide. It can be seen from correlation value (r = 0,5) between the internal tide and log10(K_p) value which is not too high.

Figure 7 linear correlation between log10(Aint) and log10(Kp) at transct 1 (a), 2 (b), 3 (c), 4 (d), 5 (e) dan 6 (f) at thermocline layer

Stations 9 to 13 on transect 3 has about 24-hour in periods. Isopycnal line only forming a half of wave patterns, meanwhile the tidal surface form completely 2 wave lenght. It seems that the isopycnal pattern on transect 3 does not represent the internal tide patterns because it has different period. Thermocline layer on transect 3 has vertical turbulence at station 14 at a depth about 250 m with  K_p value 10^-2 m²s^-1 and categorize as strong vertical turbulent.

Wave pattern with a period of ± 12 hours seen connecting stations 15, 16, 17 and 18 in transect 4. From station 15, 16 and approaching station 17, the isopycnal contour form a pattern similar with surface-tides low water, while stations 17 and 18 form a pattern of high water. Seem vertical turbulence in these transects are not much influenced by the internal tide. This can be seen from relatively low correlation Values (r = 0,3) between the internal tide and log10( K_p).

Figure 8 shows stations 24, 23 and 22 in transect 5 has period of 12-13 hours. Isopycnal line form an ascending pattern of stations 23 to 24, while the tidal-surface form a low-water. Between stations 23 and 24, there are no station and also no data retrieval, so it can not accurately known actual isopycnal pattern. Meanwhile, from station 22 to 23 have the same pattern of isopycnal with tidal-surface. Relatively large scale of vertical turbulence (K_p value 10^-3 m²s^-1) were also found at stations 23 and 24 at a depth about 200-250 m.

At Station 25 to 29 at transect 6 with closest position to Pacific Ocean, has a ± 24-hour period. Low-water pattern of isopycnal connecting stations 27 to 29 and can be said to be similar to the pattern of its surface tidal. Meanwhile, from stations 25 to 27, isopycnal only in a straight line, while the tide patterning high-water. Several vertical turbulent are found at station 26 to 29 with relatively medium to high K_p0(10^-4 -10^-2) m²s^-1 value.

Tidal type in the Makassar Strait is Mixed Tide Prevailing semidiurnal (Dihidros-Navy, 2013), with dominant period of 12,42 hours of M₂ type (Hatayama, 2004; Ray et al., 2005; Robertson and Field, 2005; Stewart, 2008). According to Hatayama et al (1996) M₂ tide propagate to the north of the southern part of Makassar Strait. According to Robertson and Field (2005) M₂ tide entering Indonesian waters both from Pacific Ocean and Indian Ocean, passing through Timor Sea and Lombok Strait and entered the southern part of Makassar Strait. A west to east propagation of M₂ tide is also exist in the southern part of Makassar Strait (Robertson and field, 2005).

Figure 8 Vertical contour of potential density is overlaid with vertical turbulent in thermocline layer at transect 1 and 2 (a), 3 and 4 (b) and 5 and 6 (c)

5 Conclusion

Vertival turbulent at thermocline layer in Makassar Strait were categorized as relatively mediun to high turbulent. More intensive vertical turbulent occurs in the northern and middle part of Makassar Strait at a depth of 100-200 m. Meanwhile in the southern part of the strait is not that intensive.  Areas near the Labani Channel (station 1) does not shows the vertical turbulence. This is because from surface to thermocline layers of Labani Channel that locate at southern part of Makassar Strait is wider compare with middle and northern part of the strait. Vertical turbulent at transect 2 was more intensified in the West side of the strait at a depth of 100-180 m, while at transect 4 and 6 on the East side of the strait at a depth of 100-200 m. Relatively large value of ε was found in the central part of Makassar Strait ranging from north to south at Arlindo path, at station 28, 17, 11 and 3. Meanwhile, relatively smaller value of ε were found in West and East sides of the strait. It seem vertical turbulent at thermocline layer of the strait is related to shape of topographic of the strait. Some isopycnal line connecting stations at several transect have relatively large amplitude. The lines seem have pattern and periods as same as surface tide, with some relatively high vertical turbulent exist on this line.

References 

Cheng L, Kitade Y. Quantitative evaluation of turbulent mixing in the Central Equatorial Pacific. 2014. J Oceanogr. 70:63-79

https://doi.org/10.1007/s10872-013-0213-5

Delpeche NC, Soomere T, Lilover MJ. 2010. Diapycnal mixing and internal waves in the Saint John River Estuary, New Brunswick, Canada with adiscussion relative to the Baltic Sea. Estonian J Eng. 16 (2): 157–175

https://doi.org/10.3176/eng.2010.2.05

Dillon TM. 1982. Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J GeophysRes.87: 9601-9613

https://doi.org/10.1029/JC087iC12p09601

Ffield A, Gordon AL. 1996. Tidal mixing signature in the Indonesian seas.JGeophys Res. 26: 1924-1935

https://doi.org/10.1175/1520-0485(1996)026%3C1924:tmsiti%3E2.0.co;2

Galbraith PS, Kelley DE. 1995. Identifying Overturns in CTD Profiles. J Atmos Ocean Tech. 13:688-702

https://doi.org/10.1175/1520-0426(1996)013%3C0688:IOICP%3E2.0.CO;2

Gargett A, Garner T. Determining Thorpe Scales from Ship-Lowered CTD Density Profiles. 2007. JAmetsoc. 25:1657-1670

Grant ALM dan Belcher SE. 2011. Wind-Driven Mixing below the Oceanic Mixed Layer. J Phys Oceanogr. 41: 1546-1575

Hatayama T, Awaji T, Akimoto K. 1996. Tidal Current in the Indonesian Seas and their effect on tansport and mixing. J Geophys Res.101: 12353-12373

https://doi.org/10.1029/96JC00036

Hatayama T. 2004. Transformation of the Indonesian through flow water by vertical mixing and its relation to tidally generated internal waves. J Geophys Res.60:569-585

https://doi.org/10.1023/b:joce.0000038350.32155.cb

Hautala S, Reid JL, Bray NA. 1996. The distribution and mixing of Pacific water masses in Indonesian Seas. J Geophys Res. 101:375-390

https://doi.org/10.1029/96JC00037

Horhoruw SM. 2016. StrukturdanvariabilitasArlindo di Selat Makassar [tesis]. Bogor (ID): InstitutPertanian Bogor

Johnson HL, Garret C. 2004. Effect of noise on Thorpe scale and run lengths. J PhysOceanogr 34:2359-2372

https://doi.org/10.1175/JPO2641.1

Kitade Y, Matsuyama M, Yoshida J. 2003. Distribution of Overturn Induced by Internal Tides and Thorpe Scale in Uchiuro Bay. J PhysOceanogr. 59:845-850

https://doi.org/10.1023/B:JOCE.0000009575.29339.35

Kunze E, MacKay C, McPhee-Shawn E, Morrice K, Girton JB, Terker SR.  2011. Turbulent Mixing and Exchange with Interior Waters on Sloping Boundaries. J PhysOceanogr. 42: 910-927

 https://doi.org/10.1175/JPO-D-11-075.1

Nash JD, Kunze E, Toole JM, Schmitt RW. 2004. Internal Tide refflection and Turbulent Mixing on the Continental Slope. JAmetsoc. 34:1117-1134

Naulita Y. 2014. Aplikasi Wavelet denoisingpadasinyal CTD (Conductivity Temperature Depth) untukmeningkatkankualitasdeteksi overturn Region. J IlmudanTeknologiKelautanTropis 6:241-252

Palmer MR, Inall ME, Sharples J. 2013. The physical oceanography of Jones Bank: a mixing hotspot in Celtic Sea. Progress in Oceanography, Elsevier. 117: 9-24

 https://doi.org/10.1016/j.pocean.2013.06.009

Park YH, Fuda JL, Durand I, Garabato ACN. 2008. Internl Tides and Vertical Mixing over the Kerguelen Plateau. Deep-Sea Res. 55:582:593

Pickard GL, Emery WJ. 1990. Descriptive Physical Oceanography. An Introduction. Oxford: Pergamon Press

Purwandana A. 2014. Turbulent mixing in Kanallabani, Makassar Strait. J Osean Limn Ind 40(2):153-167

Stewart RH. 2008. Introduction to Physical Oceanography. Texas A & M University. Texas. America

Suteja Y, Purba M, Atmadipoera AS. Turbulent Mixing in Ombai Strait. J ITKT 7(1) : 71-82

Thomson RE dan Fine IV. 2003. Estimating Mixed Layer Depth from Oceanic Profile Data.JAmetsoc.40:319-329

Thorpe SA. 2005. The Turbulent Ocean. Cambridge University Press. New York. America

https://doi.org/10.1017/CBO9780511819933

Winkel SP, Gregg MC, Sanford TB. 2002. Pattern of gradienvertikalkecepatan and turbulence accross Florida current. JAmetsoc. 32:3269-3285

Yang QA, Zhao W, Tian MJ. 2014. Spatial Structure of Turbulent Mixing in the Northwestern Pacific Ocean. J Geophys Res. 44: 2235-2247

https://doi.org/10.1175/jpo-d-13-0148.1