ON A NEW ALGORITHM OF CONSTRUCTING SOLITARY WAVE SOLUTIONS FOR SYSTEMS OF NONLINEAR EVOLU-TION EQUATIONS IN MATHEMATICAL PHYSICS

According to the improved sine-cosine method and Wu-elimination method, a new algorithm to construct solitary wave solutions for systems of nonlinear evolution equations is put forward. The algorithm has some conclusions which are better than what the hyperbolic function method known does and simpler in use. With the aid of MATHEMATICA, the algorithm can be carried out in computer.

The Solitary Waves of the Barotropic Quasi-Geostrophic Model with the Large-scale Orography

Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive perturbation method, then the solitary waves are obtained. The results show that the orography is essential factor exciting solitary Rossby waves in a flow without shear.

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.

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.

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.

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.

Influence of dissipation on solitary wave solution to generalized Boussinesq equation

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations,and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary waves.The dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in detail.The influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied,and the critical values that can describe the magnitude of the dissipation effect are,respectively,found for the two cases of b_3<0 and b_3>0 in the equation.The results show that,when the dissipation effect is significant(i.e.,r is greater than the critical value in a certain situation),the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution;when the dissipation effect is small(i.e.,r is smaller than the critical value in a certain situation),the traveling wave solution to the equation appears as the oscillation attenuation solution.By using the hypothesis undetermined method,all possible solitary wave solutions to the equation when there is no dissipation effect(i.e.,r=0)and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained;in particular,when the dissipation effect is small,an approximate solution of the oscillation attenuation solution can be achieved.This paper is further based on the idea of the homogenization principles.By establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper,and by investigating the asymptotic behavior of the solution at infinity,the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained,which is an infinitesimal amount that decays exponentially.The influence of the dissipation coefficient on the amplitude,frequency,period,and energy of the bounded traveling wave solution of the equation is also discussed.