Prediction Model of the Forces on FPSO in Internal Solitary Waves with Different Propagation Directions

High-resolution, non-hydrostatic simulation of internal tides and solitary waves in the southern East China Sea

<p>The slope area northeast of Taiwan was known as a hotspot for internal tides and internal solitary waves (ISWs), while their specific sources and generation mechanism of ISWs remain unclear. We investigate the generation and evolution processes of internal tides and ISWs with realistic configuration based on the high resolution non-hydrostatic numerical simulations. The ISWs northeastern Taiwan show a complex pattern according to the satellite image and our numerical results. ISWs propagate to various direction, and both shoreward and seaward propagating ISWs are generated on the continental slope. The ISWs observed on the continental slope-shelf region northeastern Taiwan can be generated by two ways. One is the local tide-topography interaction, and the other is the disintegration of remote internal tides generated over the I-Lan Ridge. The generated internal tides propagate northward to the Okinawa Trough, and can reach the continental slope-shelf region. During the propagation of the internal tides, the internal tides start to steepen and internal solitary waves are formed about 80 km north of I-Lan Ridge. The amplitude of the generated internal solitary waves is about 30 m. Furthermore, the Kuroshio is important to modulate the propagation and evolution of internal tides and ISWs, especially to the complexity of the ISW spatial pattern. We revealed most of the generated internal wave energy is dissipated locally over the double-canyon region, and strong mixing occur over the canyons.</p>

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.

Forces on a semi-submersible in internal solitary waves with different propagation directions

A temperature and current velocity mooring, located on the upper continental slope of the northern South China Sea, recorded a number of second baroclinic mode (mode 2) internal solitary waves (ISWs). These types of waves are seldom observed in nature. The mode 2 ISWs typically showed upward (downward) displacement of isotherms in the upper (lower) water column and three layers of eastward, westward, and eastward current from the uppermost to bottommost portions of a wave. In summer, westward‐propagating mode 2 ISWs were observed only occasionally. These waves generally appeared after mode 1 ISWs, a feature that may relate to the diurnal tide with a period of approximately 24 hours. The displacement of isotherms induced by mode 2 ISWs was 20 ± 14 m at 75 m and −22 ± 15 m at 240 m, and the characteristic time scale was approximately 8.0 ± 4.3 min. In winter, mode 2 ISWs were more active but mode 1 ISWs were rarely observed. Isotherm displacement by mode 2 ISWs in winter was 30 ± 18 m at 75 m and −26 ± 16 m at 240 m, and the average characteristic time scale was 6.9 ± 4.6 min. The mode 2 ISWs thus had larger amplitudes and smaller time scales in winter than they did in summer. The observed vertical temperature profile also showed notable seasonal change. The thermocline was shallow in summer and deep in winter. In winter, vertical temperature profiles indicated that the main thermocline was located near middepth over the upper continental slope near the 350 m isobath. Mode 1 ISWs were more active in summer than in winter, reflecting the larger Ursell numbers for mode 1 ISWs in summer. Among mode 2 ISWs in summer, 90% appeared after mode 1 ISWs. These results suggest that mode 2 ISWs could be related to mode 1 ISWs. In contrast, mode 2 ISWs were more active in winter than in summer, with larger mode 2 Ursell numbers also found in winter. Among winter mode 2 ISWs, 72% appeared without mode 1 ISWs. Mode 2 ISWs in winter could be related to the main thermocline being located near middepth. These seasonal variations of mode 2 ISWs were correlated with the seasonal change of local stratification. Further study on the different generating mechanisms of mode 2 ISWs in summer and winter is needed.

Internal solitary waves (ISWs) in the northwestern South China Sea are studied from three spaceborne synthetic aperture radar images. ISWs are observed in the same area 18.5–20.5°N, 112–114°E. The common characteristics of the ISWs are: 1) their propagation directions are 270 ∼ 300 degrees with respect to north; 2) the wavelength is about 1.2–1.6 km; 3) the distance between two neighboring ISW packets is about 10 km, but it is not a constant; 4) in two images, the easternmost ISWs evolve into multiple rank‐ordered soliton on the shelf (ISW fission); and 5) near Shenhu Shoal, a local uplift at 19.5°N, 112.9°E, one ISW packet splits into two ISW packets. Based on their propagation direction and barotropic tidal forcing analysis, we suggest that these ISWs originate from tide‐topography interactions in the Luzon Strait. It takes the internal tide about 100 hours to propagate 880 km from the Luzon Strait to the observation site.

Abstract. The Amazon shelf is a key region for intense internal tides (ITs) and nonlinear internal solitary wave (ISWs) generation associated with them. The region shows well-marked seasonal variability (from March to July, MAMJJ, and from August to December, ASOND) of the circulation and stratification, which can both induce changes in the ISW physical characteristics. The description of the seasonal and neap–spring tidal variability in the ISWs off the Amazon shelf is performed for the first time using a meaningful data set composed of 140 MODIS-Terra imagery from 2005 to 2021, where about 500 ISW signatures were identified in the sun glint region. Previous studies have documented the existence of mode-1 ISWs, but the region appears as a newly described hotspot for mode-2 ISWs. ISW packets separated by typical mode-1 (95–170 km; 2.1–3.8 m s−1) and mode-2 (46–85 km; 1.0–1.9 m s−1) IT wavelengths have been identified and mapped coming from different IT generation sites. For each ISW, a group of waves (3 to 10) is generally follows the largest crest. The intra-packet distance between each wave in the group is about 10 to 20 km. Regions of higher occurrence of ISWs are spaced by a IT mode-1 wavelength. We make the assumption that it might correspond to the IT reflection beams at the surface, which may generate newer ISWs. The mean mode-1 and mode-2 inter-packet distances do not show significant differences according to their IT generation sites. The ISW activity is higher (more than 60 % of signatures) during spring tides than neap tides. In the region under the influence of the North Equatorial Counter Current (NECC), ISWs are separated by a mean mode-1 IT wavelength which is 14.3 % higher during ASOND than during MAMJJ due to a deeper thermocline and the reinforcement of the NECC. These ISWs are also characterized by a wider inter-packet distance distribution (higher standard deviation) that may be related to the stronger eddy kinetic energy (EKE) during ASOND compared to MAMJJ. The mean inter-packet distance of mode-2 ISWs remains almost unchanged during the two seasons, but the inter-packet distance distribution is wider in ASOND than in MAMJJ as for mode 1. Note that these results need to be treated with caution, as only few occurrences of mode-2 waves were found during MAMJJ. In the region of the NECC, the direction of propagation for all modes is very similar in MAMJJ (about 30∘ clockwise from the north), whereas, for ASOND, the ISWs propagate in a wider pathway (from 0 to 60∘ clockwise from the north), due to a much larger eddy activity. During ASOND, as the background flux goes further east, the inter-packet distances become larger (4 % for mode 1 and 7.8 % for mode 2). These results show that the reinforcement of the NECC in ASOND appears to play a role in diverting the waves towards the east, increasing their phase velocities and their eastern traveling direction component when compared to MAMJJ. Calculations of the IT velocities using the Taylor–Goldstein equation supported our results regarding the presence of ISWs associated with mode-2 ITs and additionally the IT seasonal variability.

Satellite data-driven and knowledge-informed machine learning model for estimating global internal solitary wave speed

When Osborne and Burch [1] reported their observations of large-amplitude, long internal waves in the Andaman Sea that conform with theoretical results from the physics of nonlinear waves, a new research field on ocean waves was immediately set out. They described their findings in the frame of shallow-water solitary waves governed by the K-dV equation, which occur because of a balance between nonlinear cohesive and linear dispersive forces in a fluid. It was concluded that the internal waves in the Andaman Sea were solitons and that they evolved either from an initial waveform (over approximately constant water depth) or by a fission process (over variable water depth). Since then, there has been a great deal of progress in our understanding of Internal Solitary Waves (ISWs), or solitons in the ocean, particularly making use of satellite Synthetic Aperture Radar (SAR) systems. While two layer models such as those used by Osborne and Burch[1] allow for propagation of fundamental mode (i.e. mode-1) ISWs, continuous stratification permits the existence of higher mode internal waves. It happens that the Andaman Sea stratification is characterized by two (or more) maxima in the vertical profile of the buoyancy frequency N(z), i.e. a double pycnocline, hence prone to the existence of mode-2 (or higher) internal waves. In this paper we report solitary-like internal waves with mode-2 vertical structure co-existing with the large well know mode-1 solitons. The mode-2 waves are identified in satellite SAR images (e.g. TerraSAR-X, Envisat, etc.) because of their distinct surface signature. While the SAR image intensity of mode-1 waves is characterized by bright, enhanced backscatter preceding dark reduced backscatter along the nonlinear internal wave propagation direction (in agreement with Alpers, 1985[2]), for mode-2 solitary wave structures, the polarity of the SAR signature is reversed and thus a dark reduced backscatter crest precedes a bright, enhanced backscatter feature in the propagation direction of the wave. The polarity of these mode-2 signatures changes because the location of the surface convergent and divergent zones is reversed in relation to mode-1 ISWs. Mode-2 ISWs are identified in many locations of the Andaman Sea, but here we focus on ISWs along the Ten Degree Channel which occur along-side large mode-1 ISWs. We discuss possible generation locations and mechanisms for both mode-1 and mode-2 ISWs along this stretch of the Andaman Sea, recurring to modeling of the ray pathways of internal tidal energy propagation, and the P. G. Baines[3] barotropic body force, which drives the generation of internal tides near the shallow water areas between the Andaman and Nicobar Islands. We consider three possible explanations for mode-2 solitary wave generation in the Andaman Sea: (1) impingement of an internal tidal beam on the pycnocline, itself emanating from critical bathymetry; (2) nonlinear disintegration of internal tide modes; (3) the lee wave forming mechanism to the west of a ridge during westward tidal flow out of the Andaman Sea (as originally proposed by Osborne and Burch for mode-1 ISWs). SAR evidence is of critical importance for examining those generation mechanisms.

High‐frequency mooring data were collected near the northern shelf edge of the Bay of Biscay to investigate the generation and propagation of internal tides and internal solitary waves (ISWs). During spring tide, strong nonlinear internal tides and large amplitude ISWs are observed every semidiurnal tidal period. While onshore propagation was expected since the mooring is located shoreward of the maximum internal tidal generation location, both onshore and seaward traveling internal tides are identified. Within a tidal period at spring tide, three ISW packets are observed. Like internal tides, different ISW packets have opposite (seaward and shoreward) propagating direction. Based on realistic hydrostatic HYCOM simulations, it is suggested that advection by the barotropic tide affects wave generation and propagation significantly and is essential for the seaward traveling internal tides to appear shoreward of their generation location. A two‐layer idealized nonhydrostatic model derived by Gerkema (1996) further confirms the effect of advection on the generation and propagation of internal tides. Moreover, the two‐layer model reproduces one seaward propagating ISW packet and one shoreward propagating ISW packet, indicating that the offshore and onshore traveling ISWs are excited by nonlinear steepening of the seaward and shoreward traveling internal tides, respectively.

Microstructure and fine‐scale measurements collected in the central Bay of Biscay during the MOUTON experiment are analyzed to investigate the dynamics of internal waves and associated mixing. Large‐amplitude internal tides (ITs) that excite internal solitary waves (ISWs) in the thermocline are observed. ITs are dominated by modes 3 and 4, while ISWs projected on mode 1 that is trapped in the thermocline. Therein, ITs generate a persistent narrow shear band, which is strongly correlated with the enhanced dissipation rate in the thermocline. This strong dissipation rate is further reinforced in the presence of ISWs. Dissipation rates during the period without ISWs largely agree with the MacKinnon‐Gregg scaling proposed for internal wavefields dominated by a low‐frequency mode, while they show poor agreement with the Gregg‐Henyey parameterization valid for internal wavefields close to the Garrett‐Munk model. The agreement with the MacKinnon‐Gregg scaling is consistent with the fact that turbulent mixing here is driven by the low‐frequency internal tidal shear.

A two‐dimensional, regularized long‐wave equation model is developed to study the dynamic mechanisms of the propagation and evolution of the internal solitary waves (ISWs) in the northern South China Sea (SCS). It is shown that the bottom topography would cause the polarity reversal of ISWs, the change of the local wave crestline shape, and some diminution in wave amplitude; even if the ISWs are induced at the small sill channel along the Luzon Strait, they could propagate westward with their crestlines covering a large area in the latitudinal direction in the northern SCS. When there are two trains of ISWs propagating from the same source site with a time lag but different amplitudes of initial solitons, the latter train of ISWs with a larger amplitude may catch then swallow the former one with a smaller amplitude, and the wave amplitude of the merged ISW train decreases while the wave number increases. When there are two trains of ISWs propagating from the different source sites at the same time with the same amplitude of initial solitons, the crestlines of the two ISW trains may meet and a new leading soliton is induced at the connection point. Once the ISW trains collide with the island, before the island, a weak ISW train is reflected; behind the island, the former crestlines of the ISW train are torn by the island into two new trains, which may reconnect after passing around the island. The propagation direction, the wave amplitude, and the reconnection point of the new merged ISW train behind the island depend on the relative orientation of the original soliton source site to the island.

Both internal solitary waves (ISWs) and mesoscale eddies are ubiquitous in the northern South China Sea (SCS). In this study, the authors examine the impacts of mesoscale eddies on the ISWs transiting the northern SCS deep basin that evolve from the steepening internal tide generated in the Luzon Strait, using in situ data collected from a specifically designed mooring array. From November 2013 to January 2014, an energetic mesoscale eddy pair consisting of one anticyclonic eddy (AE) and one cyclonic eddy (CE) propagated across the mooring array. Observations revealed that the amplitude, propagation direction, and speed of the transbasin ISWs were significantly modulated by the eddy pair. When the moorings were covered by the southern portion of the AE, the ISW amplitudes decreased by as much as 67% because of the thermocline deepening along the wave direction and the energy divergence along the wave front. When the moorings were covered by the northern portions of both eddies, the amplitude of ISWs also decreased but to a relatively smaller degree. ISWs propagated the fastest inside the southern portion of the AE, where both the thermocline deepening and eddy currents enhanced the propagation speed of ISWs. Under the influence of the AE (CE) core, ISWs propagated more northward (southward) than usual. The observational results reported here highlight the importance of resolving mesoscale eddies in circulation–internal wave coupled models to accurately predict kinematic characteristics of ISWs.

<p>In this paper, we used the seismic oceanography method to study the structural characteristics of internal solitary waves (ISWs) near the Strait of Gibraltar in the Mediterranean Sea, South China Sea and offshore Central America.</p><p>The ISWs near the Strait of Gibraltar are the first mode depressional type, mostly medium amplitude and large amplitude internal solitary waves. The maximum vertical amplitude is up to 74.5m, and the amplitude increases with depth，the propagation velocity increases with amplitude. It can be determined that the "true" maximum amplitude position is near the pycnocline. After correction, the maximum half-height-width can reach 1721.8m, but there is somewhat different from the theoretical result，which may be related to the development stability of ISWs. As the solitary wave packet continuously moves eastward, the overall wave width becomes larger, and the vertical velocity becomes smaller. In this paper, seismic oceanography is applied to the analysis of ISWs in the Mediterranean Sea, which further proves the feasibility of using seismic oceanography to study the movement of sea water.</p><p>We reprocess some multi-channel seismic (MCS) data which is acquired recently in the Dongsha region of the northeastern South China Sea and we obtain new seismic oceanography data. The research suggest that there are the mode-2 internal solitary wave(ISWs) not just the mode-1 ISWs and a special reflection pattern (hair-like reflection configuration )usually above sand dunes in the seismic images. In new seismic oceanography data, there are some mode-1 ISWs with amplitudes less than 50m and wavelength of 1~5 km and the biggest mode-1 ISWs have the amplitude about 45m. The internal solitary waves packets are not prototypical rank-ordered ISW packets, their soliton amplitudes are smaller than 40. The mode-2 ISWs is well-shaped and its’ amplitude is approximate 30m, the vertical structure height is about 200m.The reflection configuration of water column above sand dunes usually include weak reflection layer-maybe called turbulent bottom boundary layer, and there is hair reflection configuration that must not appear. Whether there will be hair reflection configuration or not may depend on the angle between the seismic line and the sand dunes.</p><p>In the region offshore Central America, there are lots of mode-2 ISWs revealed from seismic oceanography data. We combine seismic data with hydrographic data to study the features of ISWs in these different regions. The preliminary results show the phase velocity in SCS is the largest, that in the Strait of Gibraltar is the second and that offshore Central America is the last. The phase velocity depends on the amplitude of ISW. Usually the mode-1 depressional ISW has the largest phase velocity, while the mode-1 elevation ISW is the second, and the mode-2 ISW is the last. The location of the maximum amplitude from the characteristic function is consistent with the pycnocline as shown from floating frequency curve. The polarity of ISW is consistent with nonlinear parameter of alpha. Seismic data in global continental margins will provide more and more key evidence to increase our understanding of ISW evolution in the ocean.</p>

We investigated the stability of the bottom boundary layer (BBL) beneath periodic internal solitary waves (ISWs) of depression over a flat bottom through two-dimensional direct numerical simulations. We explored the convective versus absolute/global nature of the BBL instability in response to changes in Reynolds number, and the sensitivity of the instability to seeding noise in the front of the ISW – spanning laboratory to geophysical scales. The BBL was laminar at $Re_{ISW}=90$ and convectively unstable at $Re_{ISW}=300$ . At laboratory-scale $Re_{ISW}=300$ , the convective wave packet was periodically amplified by each successive ISW, until vortex shedding occurred. The associated noise-amplification behaviour potentially explains the discrepancies of the critical $Re_{ISW}$ between the lock–release laboratory experiments and our Dubreil–Jacotin–Long-initialized numerical simulations as the result of the difference in background noise. Instability energy decreased under the front shoulder of the ISW, analogous to flow relaminarization under a favourable pressure gradient. At geophysical-scale $Re_{ISW}=900$ , the BBL was initially convectively unstable, and then the instability tracked with the ISW, appearing phenomenologically similar to a global instability. The simulated initial convective instability at both $Re_{ISW}=300$ and $Re_{ISW}=900$ is in agreement with local linear stability analysis which predicts that the instability group speed is always lower than the ISW celerity. Increased free stream perturbations in front of the ISW and larger $Re_{ISW}$ shift the location of vortex shedding (and enhanced bed shear stress) beneath the wave, closer to the ISW trough, thereby potentially changing the location of maximum sediment resuspension, in agreement with field observations at higher $Re_{ISW}$ .