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.

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.

Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain(a nonintegrable system)and compares the simulation results with the theoretical results in fluid(an integrable system).Three stages(the pre-in-phase traveling stage,the central-collision stage,and the post-in-phase traveling stage)are identified to describe the nonlinear interaction processes in the granular chain.The nonlinear scattering effect occurs in the central-collision stage,which decreases the amplitude of the incident solitary waves.Compared with the leading-time phase in the incident and separation collision processes,the lagging-time phase in the separation collision process is smaller.This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage.We next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular chain.The space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave amplitude.The results are reversed in the fluid.An increase in solitary wave amplitude leads to decreased attachment,detachment,and residence times for granular chains and fluid.For the immediate time-phase shift,leading and lagging phenomena appear in the granular chain and the fluid,respectively.These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

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.

Submarine Trenches and Wave-Wave Interactions Enhance the Sediment Resuspension Induced by Internal Solitary Waves

Internal solitary waves(ISWs)are nonlinear fluctuations in nature that could cause significant interactions between seawater and the seabed.ISWs have been proven to be an adequate cause of sediment resuspension in shallow and deep-sea environments.In the South China Sea,ISWs have the largest amplitude globally and directly interact with the seabed near the Dongsha slope in the northern South China Sea.We analyzed the water profile and high-resolution multibeam bathymetric data near the Dongsha slope and revealed that submarine trenches have a significant impact on the sediment resuspension by ISWs.Moreover,ISWs in the zone of the wave-wave interaction enhanced sediment mixing and resuspension.The concentration of the suspended particulate matter inside submarine trenches was significantly higher than that outside them.The concentration of the suspended particulate matter near the bottoms of trenches could be double that outside them and formed a vast bottom nepheloid layer.Trenches could increase the concentration of the suspended particulate matter in the entire water column,and a water column with a high concentration of the suspended particulate matter was formed above the trench.ISWs in the wave-wave interaction zone near Dongsha could induce twice the concentration of the bottom nepheloid layer than those in other areas.The sediment resuspension caused by ISWs is a widespread occurrence all around the world.The findings of this study can offer new insights into the influence of submarine trench and wave-wave interaction on sediment resuspension and help in geohazard assessment.

Optical remote sensing image characteristics of large amplitude convex mode-2 internal solitary waves:an experimental study

A series of experiments are designed to propose a new method to study the characteristics of convex mode-2internal solitary waves(ISWs)in optical remote sensing images using a laboratory-based optical remote sensing simulation platform.The corresponding wave parameters of large-amplitude convex mode-2 ISWs under smooth surfaces are investigated along with the optical remote sensing characteristic parameters.The mode-2 ISWs in the experimentally obtained optical remote sensing image are produced by their overall modulation effect on the water surface,and the extreme points of the gray value of the profile curve of bright-dark stripes appear at the same location as the real optical remote sensing image.The present data extend to a larger range than previous studies,and for the characteristics of large amplitude convex mode-2 ISWs,the experimental results show a second-order dependence of wavelength on amplitude.There is a close relationship between optical remote sensing characteristic parameters and wave parameters of mode-2 ISWs,in which there is a positive linear relationship between the bright-dark spacing and wavelength and a nonlinear relationship with the amplitude,especially when the amplitude is very large,there is a significant increase in bright-dark spacing.

Two Kinds of Waves Causing the Resuspension of Deep-Sea Sediments:Excitation and Internal Solitary Waves

The resuspension of marine sediments plays a key role in the biogeochemical cycle and marine ecology system.Internal solitary waves are considered to be important driving forces of the resuspension of bottom sediments.In this paper,the movement of turbidity currents,the generation and the effects on the bottom bed of internal solitary waves and excitation waves are studied by flume tests and numerical simulations,and the sediment resuspension are analyzed.The results show that the excitation wave can lead to the resuspension of the bottom sediments under all the conditions,while the internal solitary wave can lead to the resuspension of the sediment only under some special conditions,such as high amplitude or large underwater slope.Under the experimental conditions,the change in the near-bottom velocity caused by the excitation wave is close to three times that of the internal solitary wave.

Application of the monitoring and early warning system for internal solitary waves:Take the second natural gas hydrates production test in the South China Sea as an example

Internal solitary waves(ISWs) contain great energy and have the characteristics of emergency and concealment. To avoid their damage to offshore engineering, a new generation of monitoring and early warning system for ISWs was developed using technologies of double buoys monitoring, intelligent realtime data transmission, and automatic software identification. The system was applied to the second natural gas hydrates(NGHs) production test in the Shenhu Area, South China Sea(SCS) and successfully provided the early warning of ISWs for 173 days(from October 2019 to April 2020). The abrupt changes in the thrust force of the drilling platform under the attack of ISWs were consistent with the early warning information, proving the reliability of this system. A total of 93 ISWs were detected around the drilling platform. Most of them occurred during the spring tides in October–December 2019 and April 2020, while few of them occurred in winter. As suggested by the theoretical model, the full-depth structure of ISWs was a typical current profile of mode-1, and the velocities of wave-induced currents can reach 80 cm/s and30 cm/s, respectively, in the upper ocean and near the seabed. The ISWs may be primarily generated from the interactions between the topography and semidiurnal tides in the Luzon Strait, and then propagate westward to the drilling platform. This study could serve as an important reference for the early warning of ISWs for offshore engineering construction in the future.

Deformation and Stress Analysis of the Deepwater Steel Lazy Wave Riser Subjected to Internal Solitary Waves

The dynamic response of the steel lazy wave riser(SLWR)subjected to the internal solitary wave is a key to assessing its application feasibility.The innovation of this paper is to study the dynamic response properties of the SLWR with large deformation characteristics under internal wave excitation.A numerical scheme of the SLWR is constructed using the slender-rod theory,and the internal solitary wave(ISW)with a two-layer seawater model is simulated by the extended Korteweg-deVries equation.The finite element method combined with the Newmark-βmethod is applied to discretize the equations and update the time integration.The ISW excitation combined with vessel motion on the dynamic deformation and stress of the SLWR is investigated,and extensive simulations of the ISW parameters,including the interface depth ratio and density difference,are carried out.Case calculation reveals that the displacement of the riser in the lower interface layer increases significantly under the ISW excitation,and the stresses at a part of both ends grow evidently.Moreover,the mean value of riser responses under a combination of vessel motion and ISW coincides with the ISW-induced ones.Furthermore,the dynamic responses along the whole riser,including the displacement amplitudes,bending moment amplitudes,and stress amplitudes,almost increase with the increase in interface depth ratios and density differences.

Reconstructions of time-evolving sound-speed fields perturbed by deformed and dispersive internal solitary waves in shallow water

The high-fidelity reconstruction of sound speeds is crucial for predicting acoustic propagation in shallow water where internal solitary waves(ISWs)are prevalent.Mapping temperatures from time series to spatial fields is an approach widely used to reproduce the sound speed perturbed by deformed internal waves.However,wave-shape distortions are inherent in the modeling results.This paper analyzes the formation mechanism and dynamic behavior of the distorted waveform that is shown to arise from the mismatch between the modeled and real propagation speeds of individual solitons within an ISW packet.To mitigate distortions,a reconstruction method incorporating the dispersion property of an ISW train is proposed here.The principle is to assign each soliton a real speed observed in the experiment.Then,the modeled solitons propagate at their intrinsic speeds,and the packet disperses naturally with time.The method is applied to reconstruct the sound speed perturbed by ISWs in the South China Sea.The mean and median of the root-mean-square error between the reconstructed and measured sound speeds are below 2 m/s.The modeled shape deformations and packet dispersion agree well with observations,and the waveform distortion is reduced compared with the original method.This work ensures the high fidelity of waveguide-environment reconstructions and facilitates the investigation of sound propagation in the future.

A New Method for In-Situ Measurement of Internal Solitary Waves Based on the Stimulated Raman Scattering in Optical Fibers

In-situ measurement of internal solitary waves(ISWs)is complicated in the ocean due to their randomness.At present,the ISWs are mainly detected by the chain structure of conductivity-temperature-depth systems(CTDs)or temperature sensors.The high cost limits the spatial resolution,which ultimately affects the measuring accuracy of the ISW amplitude.In this paper,we developed an experimental measurement system for detecting ISWs based on the stimulated Raman scattering in distributed optical fibers.This system has the advantages of high precision,low cost,and easy operation.The experimental results show that the system is consistent with CTDs in the measurement of vertical ocean temperature variation.The spatial resolution of the system can reach 1.0 m and the measuring accuracy of temperature is 0.2℃.We successfully detected 3 ISWs by the system in the South China Sea and two optical remote sensing images collected on May 18,2021,the same day of two detected ISWs,verify the occurrence of the measured ISWs.We used the image pairs method to calculate the phase velocity of ISW and the result is 1.71 ms^(-1).By extracting the distances between wave packets,it can be found that the semi-diurnal tide generates the detected ISWs.The impact of the tidal current velocity on the ISW in amplitude is undeniable.Undoubtedly,the system has a great application prospect for detecting ISWs and other dynamic phenomena in the ocean.

Linear analysis of the dynamic response of a riser subject to internal solitary waves

The flow field induced by internal solitary waves(ISWs)is peculiar wherein water motion occurs in the whole water depth,and the strong shear near the pycnocline can be generated due to the opposite flow direction between the upper and lower layers,which is a potential threat to marine risers.In this paper,the flow field of ISWs is obtained with the Korteweg-de Vries(Kd V)equation for a two-layer fluid system.Then,a linear analysis is performed for the dynamic response of a riser with its two ends simply supported under the action of ISWs.The explicit expressions of the deflection and the moment of the riser are deduced based on the modal superposition method.The applicable conditions of the theoretical expressions are discussed.Through comparisons with the finite element simulations for nonlinear dynamic responses,it is proved that the theoretical expressions can roughly reveal the nonlinear dynamic response of risers under ISWs when the approximation for the linear analysis is relaxed to some extent.

On the Generation and Evolution of Internal Solitary Waves in the Andaman Sea

Internal solitary waves(ISWs)are ubiquitous in the Andaman Sea,as revealed by synthetic aperture radar images;however,their generation mechanisms and corresponding influencing factors remain unknown.Based on a nonhydrostatic two-dimensional model,the generation of ISW packets along the transect of a channel lying between Batti Malv Island and Car Nicobar Island is investigated.Moreover,the influences of topographic characteristics,seasonal stratifications,and tidal forcings are analyzed through a series of sensitivity runs.The simulation results indicate that bidirectional rank-ordered ISW packets are generated by the nonlinear steepening of internal tides.An east-west ISW asymmetry is observed,which is attributed to distinct topographic characteristics.The surrounding sills can also generate internal wave beams,which modulate the intensity of ISWs.However,the topographic structure of the west flank of the ridge mainly contributes to the suppression of westward ISWs,which decreases the modulating effect of internal wave beams.During the spring tide,the generation of ISWs is enhanced.During the neap tide,ISWs are weak,and the east-west ISW asymmetry is less obvious.Moreover,seasonal stratification only has a minor effect on the generation and evolution of ISWs.

SOLITARY WAVES IN STRATIFIED FLUIDS AND THEIR INTERACTION

A systematic procedure is proposed for obtaining solutions for soli- tary waves in stratified fluids. The stratification of the fluid is assumed to be expo- nential or linear. Its comparison with existing results for an exponentially stratified fluid shows agreement, and it is found that for the odd series of solutions the direc- tion of displacement of the streamlines from their asymptotic levels is reversed when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be rehed upon to provide the answers to the interaction problem.

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 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: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 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.