Study on the Load Characteristics of Submerged Body Under Internal Solitary Waves on the Continental Shelf and Slope

Based on the high-quality observation data and the numerical simulation,the evolution characteristics of internal solitary waves(ISWs)and the load on the suspend submerged body are studied on the continental shelf and slope separately.The observed ISWs exhibit the first mode depression ISWs.The amplitudes of ISWs on the shelf and slope areas reach 50 m and 80 m,respectively.The upper layer velocity in the westward direction is about 0.8 m/s on the continental shelf and 0.9 m/s on the continental slope during the passing through of ISWs.The lower layer is dominated by the eastward compensating flow.In the vertical direction,the water in front of the wave flows downward,while the water behind the wave flows upward,and the maximum vertical velocity exceeds 0.2 m/s.Numerical simulation results show that the larger the amplitude of ISWs,the larger the load on the submerged body.The force on the submerged body by ISWs is dominated by the vertical force,and the corresponding maximum vertical forces on the continental shelf and slope are−25 kN and −27 kN.The submerged body is subjected to a large counterclockwise moment and the sudden change of the moment will also cause the submerged body to capsize.This paper not only gives a deeper understanding of the characteristics of ISWs from the deep continental slope to the shallow continental shelf,but also has a certain guiding value for the prediction of ISWs and for marine military activities.

Spatiotemporal variations of parameters of internal solitary waves in the northern South China Sea

The dynamic parameters for internal solitary waves(ISWs)derived from the extended Korteweg-de Vries(eKdV)equation play an important role in the understanding and prediction of ISWs.The spatiotemporal variations of the dynamic parameters of the ISWs in the northern South China Sea(SCS)were studied based on the reanalysis of long-term temperature and salinity datasets.The results for spectrum analysis show that there are definite geographical differences for the periodic variation of the parameters:in shallow water,all parameters vary with a wave period of one year,while in deep water wave components of the parameters at other frequencies exist.Using wavelet analysis,the wavelet power spectral densities in deep water exhibited an inter-annual variation pattern.For example,the wave component of the dispersion coefficient with a wave period of about half a year reached its power peak once every two years.Based on previous work,this inter-annual variation pattern was deduced to be caused by dynamic processes.In further work on the regulatory mechanisms,empirical orthogonal function(EOF)decomposition was performed.It was found that the modes of the dispersion coefficient have different geographical distributions,explaining the reason why the wave components in different frequencies appeared in different locations.The numerical simulation results confirm that the variations in the parameters of the ISWs derived from the eKdV equation could affect the waveforms significantly because of changes in the polarity of the ISWs.Therefore,the periodic variations of the dynamic parameters are related to the geographical location because of dynamic processes operating.

Experimental Study on the Variation of Optical Imaging Characteristics with Zenith Angle due to Internal Solitary Waves in Sunglint

Internal solitary waves(ISWs)change the roughness of the sea surface,thus producing dark and bright bands in optical images.However,reasons for changes in imaging characteristics with the solar zenith angle remain unclear.In this paper,the optical imaging pattern of ISWs in sunglint under different zenith angles of the light source is investigated by collecting optical images of ISWs through physical simulation.The experiment involves setting 10 zenith angles of the light source,which are divided into area a the optical images of ISWs in the three areas show dark-bright mode,single bright band,and bright-dark mode,which are consistent with those observed by optical remote sensing.In addition,this study analyzed the percentage of the dark and bright areas of the bands and the change in the relative gray difference and found changes in both areas under different zenith angles of the light source.The MODIS and ASAR images display a similar brightness-darkness distance of the same ISWs.Therefore,the relationship between the brightness-darkness distance and the characteristic half-width of ISWs is determined in accordance with the eKdV theory and the imaging mechanism of ISWs of the SAR image.Overall,the relationship between them in the experiment is almost consistent with the theoretical result.

Study of the ability of SWOT to detect sea surface height changes caused by internal solitary waves

Surface Water and Ocean Topography(SWOT)is a next-generation radar altimeter that offers high resolution,wide swath,imaging capabilities.It has provided free public data worldwide since December 2023.This paper aims to preliminarily analyze the detection capabilities of the Ka-band radar interferometer(KaRIn)and Nadir altimeter(NALT),which are carried out by SWOT for internal solitary waves(ISWs),and to gather other remote sensing images to validate SWOT observations.KaRIn effectively detects ISW surface features and generates surface height variation maps reflecting the modulations induced by ISWs.However,its swath width does not completely cover the entire wave packet,and the resolution of L2/L3 level products(about 2 km)cannot be used to identify ISWs with smaller wavelengths.Additionally,significant wave height(SWH)images exhibit blocky structures that are not suitable for ISW studies;sea surface height anomaly(SSHA)images display systematic leftright banding.We optimize this imbalance using detrending methods;however,more precise treatment should commence with L1-level data.Quantitative analysis based on L3-level SSHA data indicates that the average SSHA variation induced by ISWs ranges from 10 cm to 20 cm.NALTs disturbed by ISWs record unusually elevated SWH and SSHA values,rendering the data unsuitable for analysis and necessitating targeted corrections in future retracking algorithms.For the normalized radar cross section,Ku-band and four-parameter maximum likelihood estimation retracking demonstrated greater sensitivity to minor changes in the sea surface,making them more suitable for ISW detection.In conclusion,SWOT demonstrates outstanding capabilities in ISW detection,significantly advancing research on the modulation of the sea surface by ISWs and remote sensing imaging mechanisms.

Shoaling Internal Solitary Waves and the Formation of Boluses

An internal solitary wave of elevation in a two-layer density stratified system of an incompressible, viscous and homogeneous fluid was studied. The run-up of a wave of elevation encountering different slopes was investigated numerically based on solving the continuity, Navier-Stokes and convective-diffusion equations within the Boussinesq approximation. The commercial software COMSOL Multiphysics was used to conduct the numerical simulations. For gradual shoals, a bolus formed that transported dense fluid up the shoal. The bolus disappeared when it reached its maximum height on the slope due to the draining of the dense fluid. Various shoal angles were simulated to detect the critical angle above which a bolus does not form. An angle of 30 or less resulted in the formation of a bolus. In addition, the simulations demonstrated that the size of the bolus induced by shallower slopes was larger and that the vertical height traveled by the bolus was insensitive to the slope of the shoal.

Loads and Dynamic Response Characteristic on FPSO Under Internal Solitary Waves

According to the established prediction model of internal solitary wave loads on FPSO in the previous work,the lumped mass model and the movement equations of finite displacement in time domain,the dynamic response model of interaction between internal solitary waves and FPSO with mooring lines were established.Through calculations and analysis,time histories of dynamic loads of FPSO exerted by internal solitary waves,FPSO’s motion and dynamic tension of mooring line were obtained.The effects of the horizontal pretension of mooring line,the amplitude of internal solitary wave and layer fluid depth on dynamic response behavior of FPSO were mastered.It was shown that the internal solitary waves had significant influence on FPSO,such as the large magnitude horizontal drift and a sudden tension increment.With internal solitary wave of −170 m amplitude in the ocean with upper and lower layer fluid depth ratio being 60:550,the dynamic loads reached 991.132 kN(horizontal force),18067.3 kN(vertical force)and−5042.92 kN·m(pitching moment).Maximum of FPSO’s horizontal drift was 117.56 m.Tension increment of upstream mooring line approached 401.48 kN and that of backflow mooring line was−140 kN.Moreover,the loads remained nearly constant with different pretension but increased obviously with the changing amplitude and layer fluid depth ratio.Tension increments of mooring lines also changed little with the pretension but increased rapidly when amplitude and layer fluid depth ratio increased.However,FPSO’s motion increased quickly with not only the horizontal pretension but also the amplitude of internal solitary wave and layer fluid depth ratio.

Experimental study on the variation of optical remote sensing imaging characteristics of internal solitary waves with wind speed

Optical remote sensing has been widely used to study internal solitary waves(ISWs).Wind speed has an important effect on ISW imaging of optical remote sensing.The light and dark bands of ISWs cannot be observed by optical remote sensing when the wind is too strong.The relationship between the characteristics of ISWs bands in optical remote sensing images and the wind speed is still unclear.The influence of wind speeds on the characteristics of the ISWs bands is investigated based on the physical simulation experiments with the wind speeds of 1.6,3.1,3.5,3.8,and 3.9 m/s.The experimental results show that when the wind speed is 3.9 m/s,the ISWs bands cannot be observed in optical remote sensing images with the stratification of h_(1)∶h_(2)=7∶58,ρ_(1)∶ρ_(2)=1∶1.04.When the wind speeds are 3.1,3.5,and 3.8 m/s,which is lower than 3.9 m/s,the ISWs bands can be obtained in the simulated optical remote sensing image.The location of the band’s dark and light extremum and the band’s peak-to-peak spacing are almost not affected by wind speed.More-significant wind speeds can cause a greater gray difference of the light-dark bands.This provided a scientific basis for further understanding of ISW optical remote sensing imaging.

Unveiling three-dimensional sea surface signatures caused by internal solitary waves:insights from the surface water ocean topography mission

Internal solitary waves(ISW),characterized by large amplitude and long propagation distance,are widespread in global oceans.While remote sensing images have played an essential role in studying ISWs,they mainly exploit two-dimensional image information.However,with the launch of the surface water ocean topography(SWOT)satellite on December 16,2022,a unique opportunity has emerged to capture wide-swath three-dimensional ISW-induced sea surface information.In this study,we examine ISWs in the Andaman Sea using data from the Ka-band Radar Interferometer(KaRIN),a crucial sensor onboard SWOT.KaRIN not only provides backscattering satellite images but also employs synthetic aperture interferometry techniques to retrieve wide-swath two-dimensional sea surface height measurements.Our observations in the Andaman Sea revealed the presence of ISWs characterized by dark-bright strips and surface elevation solitons.The surface soliton has an amplitude of 0.32 m,resulting in an estimation of ISW amplitude of approximately 60 m.In contrast to traditional two-dimensional satellite images or nadir-looking altimetry data,the SWOT mission’s capability to capture threedimensional sea surface information represents a significant advancement.This breakthrough holds substantial promise for ISW studies,particularly in the context of ISW amplitude inversion.

Interaction between internal solitary waves and the seafloor in the deep sea

Internal solitary wave(ISW),as a typical marine dynamic process in the deep sea,widely exists in oceans and marginal seas worldwide.The interaction between ISW and the seafloor mainly occurs in the bottom boundary layer.For the seabed boundary layer of the deep sea,ISW is the most important dynamic process.This study analyzed the current status,hotspots,and frontiers of research on the interaction between ISW and the seafloor by CiteSpace.Focusing on the action of ISW on the seabed,such as transformation and reaction,a large amount of research work and results were systematically analyzed and summarized.On this basis,this study analyzed the wave–wave interaction and interaction between ISW and the bedform or slope of the seabed,which provided a new perspective for an in‐depth understanding of the interaction between ISW and the seafloor.Finally,the latest research results of the bottom boundary layer and marine engineering stability by ISW were introduced,and the unresolved problems in the current research work were summarized.This study provides a valuable reference for further research on the hazards of ISW to marine engineering geology.

The effect of a seasonal stratification variation on the load exerted by internal solitary waves on a cylindrical pile

On the basis of Morison＇s empirical formula and modal separation method in estimating the force and torque exerted by internal solitary waves （ISWs） on a cylindrical pile, it is found that the loads exerted by the ISWs change largely in different seasons at the same site of the continental shelf in the South China Sea （SCS） even under the condition that the amplitudes of ISWs are the same. Thus, the effect of a seasonal water stratification variation on the force and torque exerted by the ISWs is investigated, and a three-parameter stratification model is employed. It is shown that the loads exerted by the ISWs depend largely on the wa- ter stratification. The stronger the water stratification, the larger the force and the torque; when the depth where the maximum thermocline appears is deepened, the force decreases but the torque increases; when the width of the thermocline is narrowed, the force increases but the torque decreases. The seasonal varia- tion of the force and the torque exerted by the ISWs in four seasons in the SCS is thus explained. Key words： internal solitary waves, force, torque, water stratification, South China Sea

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea:Ⅰ.Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models, i. e. , the problem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal waters at high radar frequency bands （ X-band and C-band）, the impact of the ocean surface mixed layer turbulence and the significance of strat- ified oceanic model on SAR remote sensing of internal solitary waves are proposed. In the north of the South China Sea by utilizing some observed data of background field the nonlinearity coefficient, the dispersion coefficient, the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately. Through simulations of internal tide transfor- mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of internal wave field are obtained. The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m, but the maximum current speeds take place at depth 20 m in this area of the sea （about 20°30＇N, 114°E） in August. It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation. The obtained results provide the possibility for the simulation of SAR signatures of internal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.

A study of internal solitary waves observed on the continental shelf in the northwestern South China Sea

Based on in-situ time series data from the acoustic Doppler current profiler （ADCP） and thermistor chain in Wenchang area, a sequence of internal solitary wave （ISW） packets was observed in September 2005, propagating northwest on the continental shelf of the northwestern South China Sea （SCS）. Corresponding to different stratification of the water column and tidal condition, both elevation and depression ISWs were observed at the same mooring location with amplitude of 35 m and 25 m respectively in different days. Regular arrival of the remarkable ISW packets at approximately the diurnal tidal period and the dominance of diurnal internal waves in the study area, strongly suggest that the main energy source of the waves is the diurnal tide. Notice that the wave packets were all riding on the troughs and shoulders of the internal tides, they were probably generated locally from the shelf break by the evolution of the internal tides due to nonlinear and dispersive effects.

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea:Ⅱ.Simulation of SAR signatures of internal solitary waves

A new model developed from the full-spectrum model of Lyzenga and Bennett （ 1988 ） is built up by us preliminarily through considering the impact of the ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves. In the partial differential equation of the action spectral density of the surface gravity-capillary waves the source function representing the contribution of the turbulence is added besides the usual source function representing the contribution of the wind. The source function is determined by applying the κ - ε model and adopting the Nasmyth spectrum of oceanic turbulence （ Nasmyth, 1970; Oakey, 1982; Fan, 2002） on the basis of the previous simulation results of internal tide transformation obtained in the companion paper （Fan et al. ,2008）. Either under relatively high wind speed, or under low wind speed, our model predicts significant large modulations of radar backscatter at all three bands （ L, C and X bands） for both VV and HH polarization. These results prove that considering the impact of ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves is reasonable and appropriate for settlement of the well-known problem of contemporary radar imaging models.

Study on characteristics of internal solitary waves in the Malacca Strait based on Sentinel-1 and GF-3 satellite SAR data

The study of the characteristics of internal solitary waves happened in the Malacca Strait is an urgent problem for submarine, ship navigation and marine engineering. Based on SAR remote sensing data obtained from the high spatial resolution Sentinel-1 and GF-3, the internal solitary wave characteristics of the Malacca Strait are investigated. By use of 20 Sentinel-1 SAR images from June 2015 to December 2016 and 24 GF-3 images from April2018 to March 2019, the spatial distribution characteristics of internal solitary wave s are statistically analyzed. It is found that the internal solitary waves are usually in the form of wave packets and single solitary waves, and the maximum crest length of the leading wave can reach 39 km. The amplitude and group velocity of internal solitary wave s can be calculated by the inversion model of high-order nonlinear Schrodinger(NLS) equation, and the calculated amplitude of the internal solitary wave s and the propagation group velocity of the wave packets range from 4.7 m to 23.9 m and 0.12 m/s to 0.40 m/s, respectively. The range of phase velocity of single internal solitary waves obtained by Kd V equation is 0.26 m/s to 0.60 m/s. In general, the amplitude and the velocity of internal solitary wave s in Malacca strait are related to the topography.

Study on the propagation velocity of internal solitary waves in the Andaman Sea using Terra/Aqua-MODIS remote sensing images

The Andaman Sea has been a classic study region for internal solitary waves(ISWs)for several decades,and extraordinarily large ISWs are characteristic of the Andaman Sea in the Indian Ocean.This paper presents results on the estimation of the propagation velocity of ISWs in the Andaman Sea that were tracked using 195 image pairs acquired by MODIS National Aeronautics and Space Administration(NASA)Terra/Aqua satellites between January 2014 and December 2018.A total of 562 ISWs were identified during the period,and the results of the propagation velocity distribution of ISWs in the Andaman Sea are presented.The estimated propagation velocity of ISWs agrees well with the theoretical results derived from the Korteweg-de Vries(KdV)equation using monthly climatology stratification data and local bathymetry.The ISW propagation velocity decreases as they propagate from deep to shallow water;the maximum propagation velocity of 3.27 m/s was estimated on the western side of the Nicobar Islands and minimum speed of 0.54 m/s occurred in the shallow water region of the southeastern Andaman Sea.The results show that the ISW propagation characteristics differ in the northern,central,and southern regions of the Andaman Sea.In the northern Andaman Sea,the velocity of ISWs propagating westward was greater than that of ISWs propagating eastward at the same water depth.In the central Andaman Sea,the propagation velocity of the ISWs differed over a small area at a depth of 2500 m,and the velocity of ISWs in the deep mixing layer in winter was higher than that in the shallow mixing layer in spring.Monthly variations in ISW propagation velocity were analyzed in the southern Andaman Sea,and the velocity of ISWs differed greatly in shallow water and was not significantly different in deep water.Water depth and monthly stratification play vital roles in controlling the phase speed of ISWs in the Andaman Sea.This study will provide a basis for the propagation and prediction of ISWs in the Andaman Sea.

Mooring observed mode-2 internal solitary waves in the northern South China Sea

The mode-2 internal solitary waves(ISWs)generated by mode-2 internal tide(IT)are identified by mooring observations in the northern South China Sea(SCS)from 2016 to 2017.Two mode-2 ISWs with a re-appearance period of 24.9 h observed on 29 and 30 July 2016 are characterized by type-b ISWs.They occurred when the isotherms compressed obviously in the vertical direction.Modal decomposition of IT horizontal currents shows that the vertical compression of the isotherms is mainly caused by diurnal mode-2 IT.The analysis of the role of the density stratification reveals that a deeper and thinner pycnocline is favorable for generation of mode-2 ISWs rather than pycnocline intensity.By comparing the mode-2 nonlinear,dispersion coefficients and the Ursell numbers calculated based on the stratification associated with different kinds of ITs with the observation results,it is shown that the diurnal mode-2 IT plays a crucial role in the generation of the mode-2 ISWs.When the diurnal mode-2 IT interacts with the semidiurnal IT and causes a deeper and thinner pycnocline,the mode-2 ISWs are easily excited.

A 2D-numerical modeling of the generation and propagation of internal solitary waves in the Luzon Strait

The wide presence of internal solitary waves （ISWs） in the northern South China Sea （SCS） has been confirmed by both Synthetic Aperture Radar （SAR） images and in situ observations.These ISWs are believed being generated over the varying topography in the Luzon Strait.They typically propagate westwards into the SCS with a diurnal or semidiurnal period.Their generation sites are,however,not yet solidly identified.To obtain a clear picture of the ISWs,we designed numerical experiments to analyze the generation and propagation of the ISWs in the Luzon Strait using a 2-dimensional non-hydrostatic model.The model current is forced by barotropic or baroclinic currents imposed at open boundaries.The experiments show that the tidal current serves as a kind of triggering force for the ISWs over the submarine ridges in the strait.Under the forcing of tidal currents,depressions are formed near the ridges.The ISWs then split from the depressions through a process different from lee-wave generation mechanism.The appearance of the ISWs is influenced by the strength and period of the forcing current： the ISWs are more likely to be generated by a stronger tidal current.That is why the ISWs in the Luzon Strait are frequently observed during spring tide.Compared with diurnal tidal current,the ISWs generated by semidiurnal tidal current with the same amplitude is much more energetic.It is partly because that the wave beams in diurnal frequency have a larger angle with the vertical direction,thus are more likely to be reflected by the topography slope.The impact of the Kuroshio to the ISWs is also analyzed by adding a vertical uniform or shear current at boundaries.A vertically uniform current may generate ISWs directly.On the other hand,a vertically shear current,which is more realistic to represent the Kuroshio branch,seems to have little influence on the generation process and radiating direction of the ISWs in the Luzon Strait.

A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea

A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow.One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained.The model simulations describe the generation and propagation of internal waves well.When the strength of imposed barotropic tides and the water stratification stay unchanged,the steepness of the sill slope can control both(a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves,and(b) the amplitude of the internal solitary waves generated.If the steepness of the sill is asymmetric,the nonlinear internal solitary waves may be induced on the steeper side of the sill.These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.

Remote sensing survey and research on internal solitary waves in the South China Sea-Western Pacific-East Indian Ocean(SCS-WPAC-EIND)

Internal solitary waves(ISWs)are common mesoscale dynamic processes in the ocean that are spread throughout the world’s oceans.The South China Sea(SCS),Western Pacific(WPAC)and Indian Ocean(EIND)(SCS-WPACEIND)are areas where ISWs frequently occur.In particular,in the northern part of the South China Sea,Sulu Sea,Celebes Sea,Andaman Sea,Lombok Strait and northeastern part of Taiwan Island,ISWs exist almost year-round.Remote sensing is an important technique to carry out investigations and research on ISWs on a large scale.In particular,optical sensors represented by the Moderate Resolution Imaging Spectroradiometer(MODIS)can observe ISWs for a long time and on a large scale,while SAR sensors such as Sentinel-1 A/B can compensate for the deficiencies in optical sensors and comprehensively observe ISWs.Based on many years of remote sensing surveys of ISWs,this paper uses MODIS and Sentinel-1 satellite remote sensing images of more than 70000 scenes from 2010 to 2020 to carry out survey studies of ISWs in the SCS-WPAC-EIND.The survey systematically gives the temporal and spatial distribution characteristics of ISWs in the SCS-WPAC-EIND and focuses on the analysis of the ISW characteristics in main areas in the SCS-WPAC-EIND,thereby providing basic data for further research on ISWs.

Effects of Tidal Currents on Nonlinear Internal Solitary Waves in the South China Sea

The propagation and fission process of internal solitary waves （ISWs） with amplitudes of about 170 m are simulated in the northeast of the South China Sea （NSCS） by using the generalized Korteweg-de Vries （KdV） equation under continuous stratification. More attention is paid to the effects of the ebb and flood background currents on the fission process of ISWs. This kind of background current is provided by the composed results simulated in terms of monthly mean baroclinic circulation and barotropic tidal current. It is found that the obtained relation of the number of fission solitons to the water depth and stratification is roughly in accordance with the fission law derived by Djordjevic and Redekopp in 1978; however, there exists obvious difference between the effects of the ebb and flood background currents on the wave-lengths of fission solitons （defined as the distance between two neighboring peaks of ISWs）. The difference in nonlinearity coefficient a between the ebb and flood background currents is a main cause for the different wave-lengths of fission solitons.