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

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Physical characteristics of the Indonesian seas

Indonesian seas have a very complex seabed topography, surrounded by several major islands (e.g. Sumatera, Borneo/Kalimantan, Java, Celebes/Sulawesi, and Papua/New Guinea) and many minor islands separated by narrow straits (Figure 1.5). The Indonesian Seas can be subdivided into two main domains: the shallow domain (<75 m) in the western region and the deep domain (>1000 m) in the eastern region consisting of deep basins connected by shallower sills. The shallow region includes the Java Sea and the Natuna Sea at the southern end of South China Sea. The basin of these shallow waters is known also as Sunda Shelf, which is part of the Asian plate, geologically. There is a narrow channel connecting Natuna Sea and Java Sea, namely Karimata Strait that separates Sumatera and Borneo Island. In the eastern Indonesian Seas, there are Makassar Strait, Sulawesi Sea, Flores Sea, Banda Sea, Seram Sea, Maluku Sea, Halmahera Sea, Savu Sea and Arafura Sea. The transition between these two regions is located along an axis connecting the western sides of Makassar and Lombok Straits. The eastern boundary of the deep-sea regions is the shallow Sahul Shelf, Arafura Sea, connecting Australia and Papua New Guinea.

Indonesian through flow

As the pioneer focusing on physical oceanography of the Indonesian seas, Wyrtki (1961) evidenced the spreading of Pacific waters into the Indian Ocean. Wyrtki (1961) identified the pressure gradient between the western Pacific and eastern Indian Oceans as the primary driver of the ITF, mainly caused by the monsoon (Wyrtki, 1987). More recently the modulation of the ITF by decadal phenomena such as El Niño event leading to a sea level decrease in the western Pacific hence diminishing the transport via the Lombok Strait, has been identified (Chong et al., 2000).
The predominant source of the ITF is the North Pacific water, flowing through the western branch, passing by Sulawesi Sea and Makassar Strait, and then exit through the straits of Lombok, Ombai and Timor Passage (Gordon and Fine, 1996). Figure 1.3 also shows the general circulation patterns of the ITF with transport estimates from observations. The throughflow contains North Pacific Subtropical Water, NPSW; and North Pacific Intermediate Water, NPIW; it was estimated that around two thirds of the flow recirculates in the Sulawesi Sea and eventually flows back to Pacific while the remaining one third of the water masses enters the Makassar Strait (Masumoto and Yamagata, 1996).

Barotropic tides in the Indonesian seas

The Indonesian Seas are well-known for being one of the most energetic region for tides. Barotropic tides are inferred from tidal models with data assimilation from the Topex/Poseidon altimeter (Ray and Egbert, 2005; Robertson and Ffield, 2005). The semidiurnal M2 constituent appears to be the largest in the internal Indonesian seas (Egbert and Erofeeva, 2002). As shown in Figure 1.7.a, M2 tides are dominantly propagating from the Indian Ocean into Indonesian seas, first into Banda Sea and then into Flores and Java Sea. Its energy flux exceeds 500 kW m-1 while passing narrow Timor passage and Savu Strait (Figure 1.8).
The weaker M2 tides propagating from the Pacific Ocean enters the Indonesian Seas via Mindanao Strait, Maluku Strait and north Halmahera Strait. Its amplitude increases while entering the Sulawesi Sea and slightly decreases as it propagates through the Makassar Strait. Meanwhile, its amplitude is rapidly decreasing when entering the Maluku Sea and Halmahera Sea (Figure 1.7.a & Figure 1.7.c).

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).

Restricting passages in the Lesser Sunda Islands

We consider here the main straits of the arch of lesser Sunda Island: Sape Strait, Alor Strait, Sumba Strait, Sawu Strait, and Ombai Strait. These are regions of enhanced water mass mixing resulting from the acceleration of the current passing through narrow channels favoring shear instabilities, and very strong internal tides. Another striking feature is the appearance of internal solitary waves which are frequently observed from satellite images, mainly in the Ombai Strait (Jackson, 2007). This phenomenon was also confirmed by the INDOMIX cruise where isopycnal heaving of about 100m and enhanced kinetic energy dissipation between [10-7, 10-5] m2s-3, and increased eddy vertical diffusivity between [10-3, 10-1] m2s-1 were observed (Bouruet-Aubertot et al., 2018; Koch-Larrouy et al., 2015).
In the Sumba Strait, , large dissipation values were observed of the order of 10-7- 10-6 m2s-3 using the indirect mixing estimates (Koch-Larrouy et al., 2015). In the Alor Strait, a snapshot mixing estimates revealed enhanced kinetic energy dissipation and diffusivity over the sill (Purwandana, 2014). Unfortunately, there are no mixing estimates yet in the Sawu Strait.

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The energy flux path to turbulence in the ocean

In fluid dynamics, turbulence describes a chaotic state of fluid, characterized by a wide range of temporal and spatial scales. The first mechanical description of turbulence was given by Reynolds (1883) who studied in laboratory experiments the disruption of a laminar flow as the fluid increases. Reynolds brought the idea that the state of the fluid (laminar, transitory, turbulent) was determined by the Reynolds number, a ratio between inertial and viscous forces. In the well-controlled laboratory experiment the definition of the Reynold number emerges naturally from the existence of a well-defined velocity scale U, spatial scale L and the value of the fluid kinematic viscosity as Re=UL/. In 1895 Reynolds introduced the concept of a decomposition of the fluid velocity and scalar properties (density, temperature) between a mean and fluctuating (turbulent quantities) which enlightens the way small scale turbulent fluctuations could affect the mean large-scale state. . Similarly, in the ocean, small-scale turbulence mixes the fluid properties, affecting the global ocean balance of heat salt and momentum. It is also a major driver of biogeochemical fluxes and is for instance a key process in the input of nutrient in the euphotic layer. A major issue is that it represents a sub grid scale process for state of the art ocean models which rely on a parameterization of this process, while its characterization from in-situ measurement remain challenging and sparse.
Ocean turbulence and mixing happens as a final step of the energy cascade where the energy is injected at large scale mainly by tidal flow over topography, wind, and buoyancy forcing at the sea surface. The turbulence is generally maximum at the ocean-atmosphere and ocean-bottom interface, producing thin mixed layer at these boundaries. Within the stratified ocean interior, the energy input by tides and atmosphere is transported mainly in the form of internal waves, which propagate horizontally and vertically. These waves are sustained by the presence of the buoyancy and Coriolis restoring force and by the spatial variations of the forcing. It was estimated that over at total of 20.6 TW are transferred to internal waves, ~1TW are generated by tides, 0.3-1 TW is generated by the atmospheric forcing and a last contribution of 0.2-0.6 TW is expected from Lee waves generation by geostrophic currents over the bottom topography (MacKinnon et al., 2017). The fraction of this energy flux available for deep mixing and the upwelling of deep water masses sustaining the global overturning circulation remains a debated question (de Lavergne et al., 2016; MacKinnon et al., 2017; Wunsch and Ferrari, 2004). Although the energy is mainly injected into large scale internal waves (~100 km spatial scale, ~1 day time scale) a wide spectrum of internal waves build up though interaction with the mesoscale structures and wave-wave interactions. The classical picture is that within the stratified ocean interior, the energy transits from large to smalls scale waves. Wave breaking leading to turbulence eventually occur when the vertical shear associated to the small scale becomes large enough to overcome the stabilization effect of stratification. Figure 2.1 shows a sketch of distribution of turbulent mixing processes in the ocean.

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).

Table of contents :

Abstract
Acknowledgments
List of Figures
List of Tables
List of Abbreviations
List of Symbols
Introduction
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
Bibliography

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