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 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.

Multi-Parameter Influence Analysis of Interaction Between Internal Solitary Wave and Fixed Submerged Body

To obtain the interaction characteristics between Internal solitary waves(ISWs)and submerged bodies,a three-dimensional numerical model for simulating ISWs was established in the present study based on the RANS equation.The velocity entrance method was adopted to generate the ISWs.First,the reliability of this numerical model was validated by comparing it with theoretical and literature results.Then,the influence of environmental and navigation parameters on interactions between ISWs and a fixed SUBOFF-submerged body was studied.According to research,the hydrodynamic performance of the submerged body has been significantly impacted by the ISWs when the body is nearing the central region of the wave.Besides,the pitching moment(y')will predominate when the body encounters the ISWs at a certain angle between 0°and 180°,and the lateral force is larger than the horizontal force.Additionally,the magnitude of the force acting on the body is mostly affected by the wave amplitude.The variation of the vertical force is the main way that ISWs affect the hydrodynamic performance of the bodies.The investigations and findings discussed above can serve as a guide to forecast how ISWs will interact with submerged bodies.

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.

Spatial and temporal variation process of seabed dynamic response induced by the internal solitary wave

Internal solitary wave(ISW)is often accompanied by huge energy transport,which will change the pore water pressure in the seabed.Based on the two-dimensional Biot consolidation theory,the excess pore water pressure in seabed was simulated,and the spatiotemporal distribution characteristics of excess pore water pressure was studied.As the parameters of both ISW and seabed can affect the excess pore water pressure,the distribution of pore water pressure showed both dissipation and phase lag.And parametric studies were done on these two phenomena.Due to influenced by the phase lag of excess pore water pressure,the penetration depth under the site of northern South China Sea with total water depth 327 m,induced by typical internal solitary wave increased by 26.19%,53.27%and 149.86%from T_(0)to T_(0.5)in sand silt,clayey silt and fine sand seabed,respectively.That means the effect of ISW on seabed will be underestimated if we only take into accout the penetration depth under ISW trough,especially for fine sand seabed.In addition,the concept of“amplitude-depth ratio”had been introduced to describe the influence of ISW on seabed dynamic response in the actual marine environment.In present study,it is negatively correlated with the excess pore water pressure,and an ISW with smaller amplitude-depth ratio can wide the range of lateral impacts.Our study results help understand the seabed damage induced by the interaction between ISW and seabed.

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.

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.

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.

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.

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.

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.

Mooring observations of internal solitary waves in the deep basin west of Luzon Strait

A total of 137 internal solitary waves （ISWs） are captured during a field experiment conducted in the deep basin west of the Luzon Strait （LS） from March to August, 2010. Mooring observations reveal that a fully developed ISW owns a maximum westward velocity of more than 1.8 m/s and an amplitude of about 200 m. The ISWs in the South China Sea （SCS） are most active in July, which may be due to the strong stratification in summer. Most of the ISW episodes are detected around and after the 1st or 15th lunar day, indicating that the ISW in the SCS is triggered by astronomic tides. Half part of the observed ISWs were detected around 19：00 local time, which can be explained by the fact that type-a ISWs emerged in the evening at roughly the same time each day. The propagation direction of the ISWs and the astronomic tides in the LS show that the area south of the Batan Island is probably the main source region of the type-a ISWs, while the area south of Itbayat Island and south of the Batan Island is likely the main source region of the type-b ISWs observed at the mooring. Moreover, for the resonance of semidiurnal internal tides emitting from the double ridges in the LS, the underwater ridge south of the Itbayat Island and south of the Batan Island is believed to favor the generation of the energetic ISWs.

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.

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: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.

Numerical Model of Internal Solitary Wave Evolution on ImpermeableVariable Seabed in A Stratified Two-Layer Fluid System

In the present study a numerical model developed by Lynett and Liu （2002） is modified to include density difference in a stratified two-layer fluid in a three-dimensional internal wave domain. The internal solitary wave （ISW） in the model is assumed to be weakly nonlinear and weakly dispersive, and the viscosity effects at all boundaries are ignored. The governing equations based on the Navier-Stokes and Euler equations are solved for internal solitary wave propagation over variable seabed topography. Theoretical formulations are established, from which analytical solutions are obtained, in addition to numerical results. Wave profiles from previous experimental studies are compared with the numerical results from the present analytical solutions. Numerical models developed on the basis of the present analytical solutions are better than those developed by Lynett and Liu （2002）. The results of numerical modeling agree well with the experimental data.