Observation of Internal Tides, Nonlinear Internal Waves and Mixing Chapter 5Estimates in the Lombok Strait, Indonesia (Paper to be submitted)

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Internal tides in the Indonesian seas

When the barotropic tide (horizontal velocities are uniform with depth) interacts with sloping bottom topography in a stratified fluid, internal or baroclinic tides (horizontal velocities vary with depth) are generated. This generation depends on the stratification, the steepness of the topographic slope, and the barotropic tidal strength and period (Baines, 1982; Robertson and Ffield, 2005). Once generated, internal tides undergo various evolutions during their propagation (reflexion, interactions with the mean current and internal wave field, etc.) that may lead to instabilities and internal wave breaking with ultimately energy dissipation and turbulent mixing. The impact of internal tide induced mixing on the ocean stratification is significant at a global scale and especially for the deep ocean as pointed out by numerous studies (e.g. Munk and Wunsch, 1998).
The Indonesian seas is one of the regions where the strongest internal tides are observed. This results from the specific geometry of the Indonesian Seas with numerous straits and shelf break topographies around the thousands islands of the archipelago that favour internal tide generation. Hence internal tides have been suggested the main driver for the ITF water masses transformation in the internal Indonesian seas (e.g., Hatayama, 2004; Hatayama et al., 1996; Robertson and Ffield, 2005; Schiller, 2004). Modelling studies aimed at characterizing baroclinic tides in the Indonesian Seas. The first studies based upon coarse grid models (~0.5o or ~50 km) by Schiller (2004) and Simmons et al. (2004) demonstrated the requirement for a high spatial resolution in respect with the typical internal tidal wavelength ranging from ~20-50 km. Holloway (2001) suggested that the grid cells of 4-5 km or finer are required to resolve the internal wavelengths, especially in the shallow waters.
Using a 5 km spatial resolution model, the Regional Ocean Model System (ROMS), Robertson and Ffield (2005) tried to estimate the baroclinic tidal field, focusing on a single constituent, the M2 tide. They showed that strong baroclinic M2 tides are generated along the shelf break and within straits. These results were validated by TOPEX/Poseidon satellite crossover observation of elevation and mooring observations using INSTANT program dataset. The Indonesian Seas internal tides have a complex spatial pattern that result from the interference between internal tides propagating from different basins. The limitation of the ROMS model is its lack of representation of the mean circulation and it incapacity to simulate the nonlinear processes, such as ISWs generated by non-hydrostatic terms (Robertson and Ffield, 2005).
Higher resolution simulations of internal tides, of about 1/100 degree (~1 km grid), were performed by Nagai and Hibiya (2015) using the MITGCM. The model was forced by prescribing M2 barotropic tidal currents. This very high-resolution grid allowed to characterize internal tides generation in narrow passages, such as the Lifamatola, Manipa, Ombai, and Lombok Straits, and the Sulu and Sibutu Island chains with a wavelength of about 130 km, and propagation speeds of 3 m s-1. Figure 1.9 shows model-predicted vertical isopycnal displacement at a depth of 1000 m. Such high-resolution study indicated that there were large isopycnal displacements in some locations even though located far away from the generation sites because of interferences between internal tides generated from various sources. Such finding is in agreement with the Arlindo Mixing Project results where vigorous internal tides have been observed in the Indonesian Seas with isotherm heaving up to 90 m in the Seram Sea during 14 hour yo-yo stations (Ffield and Gordon, 1996).

Spotting internal solitary waves in the Indonesian seas

ISWs are very specific mono-crest waves, similar to solitons though they are often observed as trains of solitary waves. There are most often generated when the internal tide steepens as a result of nonlinear interactions. ISWs are associated with large vertical isopycnal displacements, are of fairly small scale and can propagate over long distances. These characteristics, not resolved by hydrostatic models, explain why their study has been neglected by previous model-based vertical mixing studies. ISWs activity is expected to contribute to the dissipated energy and mixing away from its generation sites (hereinafter termed as ‘far field’) in the Indonesian seas (e.g. Nagai and Hibiya, 2015). Indeed, Indonesian seas is a favorable zone for the generation of ISWs as they combine large amplitude internal tides and strong currents. The appearance of ISWs can be tracked from their sea surface signature and is well captured by Moderate Resolution Imaging Spectro-radiometer (MODIS) satellite images in the Indonesian seas where ISWs are of large amplitude (see Figure 1.10). Using MODIS images, Jackson (2007) performed an impressive statistical study on the ISWs appearance in this region. Here we present some locations where ISWs are frequently observed from satellite which allow localizing their source and identifying their propagation pathways.
Sulu Sea and Sulawesi Sea are separated by shallow passages, namely Sibutu passages in the Sulu Islands chain. The Sulawesi Sea is connected to the Pacific Ocean by Mindanao Strait, a narrow passage, located in the northernmost of Sangihe Islands chain (see Figure 1.10.b). Barotropic tidal currents forcing over the passages potentially triggers the generation of internal tides that propagate in the Sulawesi Sea as frequently on the satellite images (see Figure 1.10.a, b).
The barotropic tidal current flowing over the sill of the Lifamatola Strait triggers the generation of internal tides that propagate in the Maluku Sea. The appearance of ISWs packet in the Maluku Sea is frequently observed on satellite images along the propagation pathway of internal between Lifamatola passage and the north tip of the Sulawesi islands (see Figure 1.10.c).
The main source for the observed ISWs appearance in the Banda Sea is the Ombai Strait. The Ombai Strait is the largest channel in the Lesser Sunda Islands chain that directly allows the Pacific water masses flow from Makassar Strait and Flores Sea into the Banda Sea. This strait is also the deepest channel where the barotropic M2 tide incoming from the Indian Ocean passes through. This barotropic tidal current flowing over the strait is responsible for the generation of the ISWs frequently observed on satellite images (see Figure 1.10.d).

Potential mixing hotspots and related water mass transformation in the Indonesian seas

Observational studies of potential mixing hotspots have been conducted based on hydrographic measurements showing the strong erosion of Pacific water masses along their pathway toward the Indian Ocean. In the absence of microstructure measurements, indirect estimates were used to characterize turbulence. Ffield and Gordon (1992) provided an overview of turbulent mixing with global estimates for each interior sea of a diffusivity coefficient inferred from a simple advection-diffusion model applied to the observed T/S profiles. Later on, Ffield and Robertson (2008) performed an analysis of a 21 years database, from 1981 to 2006, of expandable bathythermographs (XBT). They used finescale temperature variance as a proxy of vertical turbulent mixing and provided an overview of the contrasted signal along different pathways. The main, unsurprising conclusion was that mixing hotspots were preferentially along the shelf break and within straits, thus making a clear link with internal tide generation area (Figure 1.11). Ffield and Robertson (2008) also pointed out that mixing should be considerably reduced about 35 km away from potential mixing hotspots, which also may give insights on the spatial extension of tidally induced turbulent mixing. This suggests that internal tides rather dissipate locally, near their generation area, as a result of the direct breaking near the rough supercritical topographic features (Klymak et al., 2012). Moreover the fraction of the internal tide energy that is not dissipated near the generation site remain mostly trapped in the semi-enclosed basins, implying that a large amount of the total power transferred to internal tides is available for vertical mixing (Alford et al., 1999; Koch-Larrouy et al., 2007; Nagai et al., 2017; Nagai and Hibiya, 2015; Robertson, 2010). The part of the internal tides escaping the near field dissipation can break through various processes, such as scattering of internal wave energy from bottom topography and interaction of incident and reflected waves, as well as friction-generated boundary shear.

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Generation mechanism of internal solitary waves

Internal solitary waves (ISW) are short horizontal scale (~km) high frequency (~minute-1) large amplitude (pycnocline deviation reaching tens of meters) waves that can propagate over several hundreds of kms. In the ocean, they are mostly generated from a large amplitude internal wave, which is most of the time generated by tides. The region of convergence and divergence generated by the surface horizontal currents associated with these waves modify the sea surface roughness, these changes can be detected from space in by satellite imagery (SAR, MODIS). Figure 2.7.a shows geographical distribution of observed nonlinear internal waves by MODIS satellite from August 2002 to May 2004, with a mechanisms the way satellite imagery detects the appearance of the ISW is shown in Figure 2.8.
The most impressive observations of oceanic ISW were reported close to sill affected by strong tidal forcing such as the Camarinal sill in the strait of Gibraltar (Alonso et al., 2002), the Knight Inlet sill in British Columbia (Farmer and Smith, 1980), the Sibutu passage in the Sulu sea (Apel et al., 1985) and Stellwagen bank in Massachusetts Bay (Halpern, 1971). Maxworthy (1979) was the first to provide dynamical explanations to the formation of large ISW train near sills using hydraulic model experiments. The basic process can be explained by the fact that a tidal flow over a sill can get periodically supercritical, that is the ratio of the barotropic tidal flow velocity to the internal wave phase speed (the Froude number, Fr) overcomes the value of 1. Let’s consider the increasing and decreasing phase of the ebb tide (Figure 2.7). When the tidal flow increases, the critical value of the Fr is reached, a stationary depression then grows on the downstream side of the sill (Figure 2.7.b(i)). When the tidal flow decreases, the Fr drops below one and the large depression formed can then propagates upstream (Figure 2.7.b(ii)), and eventually evolves into a solitary wave packet (Figure 2.7.b(iii)) following the KdV mechanism described by Eq.(2.24).

Turbulent length scales Ozmidov length scale (LO)

Ozmidov scale represents the scale at which buoyancy forces equal inertial forces. It is usually considered as the upper bound of the turbulence convective inertial range, that is the range between the largest overturns and the dissipation scale. Indeed above this scale overtuns are inhibited by the stabilizing effect of stratification (Moum, 1996a). This scale is expressed as (Gargett, 1988), 𝐿𝑂≡(𝜀𝑁3⁄)1/2 (2.28).
with ε and N is dissipation rate and buoyancy frequency, respectively. Interestingly, if one can derive a typical scale representative of the largest overturns from measurements then this scale can be compared to 𝐿𝑂 and the relationship Eq. (2.28) inverted to get an estimation of ε. This is the goal of two length scales that can be computed from observations: the Thorpe scale and the Ellison scale.


The large dataset ensemble we consider allows to track the water mass transformation along the ITF with unprecedented spatial coverage. Figure 3.2 shows T/S diagrams in each basin from the archived data sets used in this study while Figure 3.3 provides a horizontal map of the salinity for given density ranges. Both figures illustrate the transformation of North and South Pacific waters along the eastern (Sulawesi Sea/SLA-Makassar Strait/MAK-Flores Sea/FLO-Lesser Sunda Seas/LES) and western routes (Halmahera Sea/HAL-Maluku Sea/MAL-Banda Sea/BAN-Lesser Sunda Seas/LES).
The descriptive analysis below refers to the vertical characteristics of the water masses as shown in Figure 3.2. The north Pacific sub-region (NPA) and South Pacific sub-region (SPA) are regions characterized by the presence of NPSW and SPSW in the thermocline layer, and SPIW and NPIW in the intermediate layer. In the NPA and SPA (σθ 22-26; Smax>35 psu), core layers of NPSW/ SPSW in the thermocline layer and NPIW/SPIW (σθ 26-27; Smin 34.1-34.5 psu), in the intermediate layer are clearly identified.

Table of contents :

Chapter 1
1.1 Rationale
1.2 Physical characteristics of the Indonesian seas
1.2.1 Indonesian through flow
1.2.2 Barotropic tides in the Indonesian seas
1.2.3 Internal tides in the Indonesian seas
1.2.4 Spotting internal solitary waves in the Indonesian seas
1.2.5 Potential mixing hotspots and related water mass transformation in the Indonesian seas
1.3 Aims and objectives
Turbulence and Mixing
2.1 The energy flux path to turbulence in the ocean
2.2 Energy equation of turbulence
2.3 Internal waves
2.3.1 Spectrum
2.3.2 Generation mechanism of internal solitary waves
2.4 Turbulence measurements
2.4.1 Turbulent length scales
2.4.2 Determination of vertical diffusivity, Kρ
2.4.3 Mixing efficiency
2.4.4 Double diffusion influence on mixing
Spatial Structure of Turbulent Mixing in the Indonesian Seas (Submitted Chapter 3Paper to Progress in Oceanography)
3.1 Introduction
3.2 Methodology
3.2.1 Dataset
3.2.2 Mixing estimates
3.2.3 Numerical model outputs
3.3 Results and discussion
3.3.1 Hydrography
3.3.2 Relevance of the turbulence estimates: comparison with microstructure measurements
3.3.3 Turbulence and mixing of the Pacific water masses layer
3.3.4 Model comparisons: spatial variations of turbulence and insights on mechanisms85
3.4 Concluding remarks
3.5 Acknowledgments
3.6 Appendix
3.6.1 Snapshot CTD stations by year
3.6.2 Spatial grid averaging for the sparsely distributed CTD casts
3.6.3 Overturn selection criterion
3.6.4 Analysis of step structures in the repeated stations
3.6.6 Repeated CTD cast sampling times
Mixing Estimates Enhanced by Shoaling Internal Solitary Wave in the Chapter 4Manado Bay, Sulawesi, Indonesia (Paper to be submitted)
4.1 Introduction
4.2 Methodology
4.2.1 In situ observations
4.2.2 Numerical modeling
4.2.3 Mixing estimates
4.3 Internal Tides Generation
4.3.1 Generation processes
4.3.2 Energetic aspects
4.4 Shoaling Internal Solitary Waves
4.4.1 High frequency and small-scale patterns over the Manado shelf break and slope in the Shoaling simulation
4.4.2 Energetics of the shoaling ISW trains
4.4.3 Enhanced Mixing due to Shoaling ISW
4.5 Summary
4.6 Acknowledgments
4.7 Appendix: criteria for Thorpe scale computation
Observation of Internal Tides, Nonlinear Internal Waves and Mixing Chapter 5Estimates in the Lombok Strait, Indonesia (Paper to be submitted)
5.1 Introduction
5.2 Methodology
5.2.1 In situ observations
5.2.2 Mixing estimates
5.3 Results and discussion
5.3.1 Hydrography
5.3.2 ISWs characteristics
5.3.3 Dissipation estimates
5.4 Concluding remarks
5.5 Acknowledgments
5.6 Appendix
Conclusions and Perspectives
6.1 Summary of the main results
6.2 Perspectives
6.2.1 Mixing estimates from historical datasets in the Indonesian seas
6.2.2 Internal tide generation and enhanced mixing due to ISW breaking events


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