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.

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.

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.

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.

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.

Ion acoustic solitary waves in an adiabatic dusty plasma:Roles of superthermal electrons,ion loss and ionization

We investigate propagation of dust ion acoustic solitary wave(DIASW)in a multicomponent dusty plasma with adiabatic ions,superthermal electrons,and stationary dust.The reductive perturbation method is employed to derive the damped Korteweg-de Vries(DKdV)equation which describes DIASW.The result reveals that the adiabaticity of ions significantly modifies the basic features of the DIASW.The ionization effect makes the solitary wave grow,while collisions reduce the growth rate and even lead to the damping.With the increases in ionization cross sectionΔσ/σ_(0),ion-to-electron density ratioδ_(ie)and superthermal electrons parameterκ,the effect of ionization on DIASW enhances.

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.

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.

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.

Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide

The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.

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.

Solitary Wave Solutions of a Generalized Derivative Nonlinear Schrdinger Equation

With the aid of a class of nonlinear ordinary differential equation （ODE） and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Sehrodinger equation （GDNLSE） have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given.

A new model for algebraic Rossby solitary waves in rotation fluid and its solution

A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space.Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves,the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves,the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.

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.

Optical Solitary Waves in Fourth-Order Dispersive Nonlinear Schroedinger Equation with Self-steepening and Self-frequency Shift

Abstract By making use of the generalized sine-Gordon equation expansion method, we lind cnoidal periodic wave solutions and fundamental bright and dark optical solitary wave solutions for the fourth-order dispersive and the quintic nonlinear Schroedinger equation with self-steepening, and self-frequency shift. Moreover, we discuss the formation conditions of the bright and dark solitary waves.

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

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.

New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov-Kuzentsov equation

In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.

Dynamic Responses of Top Tensioned Riser Under Combined Excitation of Internal Solitary Wave, Surface Wave and Vessel Motion

An investigation on the dynamic response of a top tensioned riser （TTR） under combined excitation of internal solitary wave, surface wave and vessel motion is presented in this paper. The riser is idealized as a tensioned slender beam with dynamic boundary conditions. The KdV-mKdV equation is chosen to simulate the internal solitary wave, and the vessel motion is analysed by using the method proposed by Sexton. Using finite element method, the governing equation is solved in time domain with Newmark-13 method. The computation programs for solving the differential equations in time domain are compiled and numerical results are obtained, including dimensionless displacement and stress. The action of internal solitary wave on the riser is like a slow powerful impact, and is much larger than those of surface wave and vessel motion. When the riser is under combined excitation, it vibrates at frequencies of both surface wave and vessel motion, and the vibration is dominated by internal solitary wave. As the internal solitary wave crest passes by the centre of the riser, the maximum displacement and stress along the riser occur. Compared to the lower part, the displacement and stress of the riser in the upper part are much larger.