A Wave Superposition-Finite Element Method for Calculating the Radiated Noise Generated by Volumetric Targets in Shallow Water

A combined method of wave superposition and finite element is proposed to solve the radiation noise of targets in shallow sea.Taking the sound propagation of spherical sound source in shallow sea as an example,the radiation sound field of the spherical sound source is equivalent to the linear superposition of the radiation sound field of several internal point sound sources,and then the radiated noise induced by spherical sound source can be predicted quickly.The accuracy and efficiency of the method are verified by comparing with the numerical results of finite element method,and the rapid prediction of underwater radiated noise of cylindrical shell is carried out based on the method.The results show that compared with the finite element method,the relative error of the calculation results under different simulation conditions does not exceed 0.1%,and the calculation time is about 1/10 of the finite element method,so this method can be used to solve the radiated noise of shallow underwater targets.

Hydrodynamic Performance of An Integrated System of Breakwater and A Multi-Chamber OWC Wave Energy Converter

A multi-chamber oscillating water column wave energy converter(OWC-WEC)integrated to a breakwater is investigated.The hydrodynamic characteristics of the device are analyzed using an analytical model based on the linear potential flow theory.A pneumatic model is employed to investigate the relationship between the air mass flux in the chamber and the turbine characteristics.The effects of chamber width,wall draft and wall thickness on the hydrodynamic performance of a dual-chamber OWC-WEC are investigated.The results demonstrate that the device,with a smaller front wall draft and a wider rear chamber exhibits a broader effective frequency bandwidth.The device with a chamber-width-ratio of 1:3 performs better in terms of power absorption.Additionally,results from the analysis of a triplechamber OWC-WEC demonstrate that reducing the front chamber width and increasing the rearward chamber width can improve the total performance of the device.Increasing the number of chambers from 1 to 2 or 3 can widen the effective frequency bandwidth.

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.

Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.

LOCAL BIFURCATION OF STEADY ALMOST PERIODIC WATER WAVES WITH CONSTANT VORTICITY

In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal direction.Using conformal mappings,one can change the free boundary problem into a fixed boundary problem for some unknown functions with the boundary condition.By virtue of the Hilbert transform,the problem is equivalent to a quasilinear pseudodifferential equation for an almost periodic function of one variable.The bifurcation theory ensures that we can obtain an existence result.Our existence result generalizes and covers the recent result in[15].Moreover,our result implies a non-uniqueness result at the same bifurcation point.

Experimental observation on water entry of a sphere in regular wave

This paper presents a novel experiment to observe the whole water entry process of a free-falling sphere into a regular wave.A time-accurate synchronizing system modulates the moment elaborately to ensure the sphere impacting onto the water surface at the desirable wave phase.Four high-speed cameras focus locally to measure the high-precision size of the cavity evolution.Meanwhile,the aggregated field view of the camera array covers both the splash above the free surface and the entire cavity in the wave.The detailed methodologies are described and verified for the hardware set-up and the image post-processing.The theoretical maximum deviation is 1.7%on the space scale.The integral morphology of the cavity is captured precisely in the coordinate system during the sphere penetrates through the water at four representative wave phases and the still water.The result shows that the horizontal velocity of the fluid particle in the wave impels the cavity and changes the shape distinctly.Notably,the wave motion causes the cavity to pinch offearlier at the wave trough phase and later at the wave crest phase than in the still water.The wave motion influences the falling process of the sphere slightly in the present parameters.

Wave Radiation by a Floating Body in Water of Finite Depth Using an Exact DtN Boundary Condition

The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical surface to solve various types of fields,such as sound waves or electromagnetic waves,provided that the considered domain is infinite or unbounded in all directions.However,the substantial wave motion is considered in water of finite depth,that is,the fluid domain is bounded vertically but unbounded horizon-tally.Thus,the DtN boundary condition is given on an artificial cylindrical surface,which divides the water domain into an interior and exterior region.The boundary integral equation is adopted to implement the present model.In the case of a floating cylinder,the results of hydrodynamic coefficients of a chamfer box are discussed.

Numerical Modelling of Double Slit Caisson Breakwater Integrated Oscillating Water Column Wave Energy Converter with Modal Superposition Method

Oscillating water column wave energy converter is a power generation device in which ocean waves excite the oscillation of the water surface in an air chamber, which generates fluctuations in air pressure and rotate air turbine generator(s). The oscillation of the fluid in the air chamber is a fluid oscillation phenomenon with a natural period, similar to fluid oscillation in a container such as sloshing. Previous research has shown that for an oscillating water column with a single air chamber submerged in water, the oscillation characteristics can be modeled as a one-degree-of-freedom oscillation system that takes only a single oscillation mode into account. However, a double-slit breakwater integrated oscillating water column wave energy converter using two water columns of the breakwater separated by slit walls, has been verified to have two resonance periods. In this study, the free oscillating motion of the oscillating water column wave energy converter using the double-slit breakwater is modeled by modal superposition method including the first-order and second-order modes of vertical motion of the two water surfaces. The result from the simulation is similar to the result of the free vibration experiment.

Effect of particle composition and consolidation degree on the wave-induced liquefaction of soil beds

The wave-induced liquefaction of seabed is responsible for causing damage to marine structures.Particle composition and consolidation degree are the key factors affecting the pore water pressure response and liquefaction behavior of the seabed under wave action.The present study conducted wave flume experiments on silt and silty fine sand beds with varying particle compositions.Furthermore,a comprehensive analysis of the differences and underlying reasons for liquefaction behavior in two different types of soil was conducted from both macroscopic and microscopic perspectives.The experimental results indicate that the silt bed necessitates a lower wave load intensity to attain the liquefaction state in comparison to the silty fine sand bed.Additionally,the duration and development depth of liquefaction are greater in the silt bed.The dissimilarity in liquefaction behavior between the two types of soil can be attributed to the variation in their permeability and plastic deformation capacity.The permeability coefficient and compression modulus of silt are lower than those of silty fine sand.Consequently,silt is more prone to the accumulation of pore pressure and subsequent liquefaction under external loading.Prior research has demonstrated that silt beds with varying consolidation degrees exhibit distinct initial failure modes.Specifically,a dense bed undergoes shear failure,whereas a loose bed experiences initial liquefaction failure.This study utilized discrete element simulation to examine the microscopic mechanisms that underlie this phenomenon.

Spatiotemporal characteristics of water exchange between the Andaman Sea and the Bay of Bengal

A high-resolution customized numerical model is used to analyze the water transport in the three major water passages between the Andaman Sea(AS)and the Bay of Bengal,i.e.,the Preparis Channel(PC),the Ten Degree Channel(TDC),and the Great Channel(GC),based on the daily averaged simulation results ranging from 2010 to 2019.Spectral analysis and Empirical Orthogonal Function(EOF)methods are employed to investigate the spatiotemporal variability of the water exchange and controlling mechanisms.The results of model simulation indicate that the net average transports of the PC and GC,as well as their linear trend,are opposite to that of the TDC.This indicates that the PC and the GC are the main inflow channels of the AS,while the TDC is the main outflow channel of the AS.The transport variability is most pronounced at surface levels and between 100 m and 200 m depth,likely affected by monsoons and circulation.A 182.4-d semiannual variability is consistently seen in all three channels,which is also evident in their second principal components.Based on sea level anomalies and EOF analysis results,this is primarily due to equatorial winds during the monsoon transition period,causing eastward movement of Kelvin waves along the AS coast,thereby affecting the spatiotemporal characteristics of the flow in the AS.The first EOF of the PC flow field section shows a split at 100 m deep,likely due to topography.The first EOF of the TDC flow field section is steady but has potent seasonal oscillations in its time series.Meanwhile,the first EOF of the GC flow field section indicates a stable surface inflow,probably influenced by the equatorial Indian Ocean’s eastward current.

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.

NONLINEAR WATER WAVE PROPAGATING OVER UNEVEN BOTTOMS

Various types of wave group solutions of the weakly nonlinear waves may exist over uneven bottoms. In this paper, the variation of the zeroes of the dispersive and nonlinear terms,and the wave group solution in the third-order evolution equations are described for the case of mild and locally fastvarying water depths.

A THIRD GENERATION SHALLOW WATER WAVE NUMERICAL MODEL-YE-WAM

This paper pnesents a third gneration shallow Whter disode spedtal wave nbotal medeIYE-WAM based on the spedtal action balance equation. The mode accounts for all edevan effectsof currents on waves, incuding tmpotally and spatialy varying depth and current inded refraction,sttalning and fequency shift and also explidtly takeS into aanunt all source terms, speclally adePth-limited breaking dheipation. In addition, an energy forcing scheme is propond and applied to themode’s open boundaries to areUn for the propagution of sedIs into the study spstem The upwinddiffeIenng scheme and a standard hybrid diffdrencing scheme for the propagaion terrn and a simpleEuler method for the source teme are employed.

Wave Numerical Model for Shallow Water

The history of forecasting wind waves by wave energy conservation equation Is briefly described. Several currently used wave numerical models for shallow water based on different wave theories are discussed. Wave energy conservation models for the simulation of shallow water waves are introduced, with emphasis placed on the SWAN model, which takes use of the most advanced wave research achievements and has been applied to several theoretical and field conditions. The characteristics and applicability of the model, the finite difference numerical scheme of the action balance equation and its source terms computing methods are described in detail. The model has been verified with the propagation refraction numerical experiments for waves propagating in following and opposing currents; finally, the model is applied to the Haian Gulf area to simulate the wave height and wave period field there, and the results are compared with observed data.

Numerical Study of Air Chamber for Oscillating Water Column Wave Energy Convertor

Oscillating Water Column （OWC） wave energy converting system is one of the most widely used facilities all over the world. The air chamber is utilized to convert the wave energy into the pneumatic energy. The numerical wave tank based on the two-phase VOF model is established in the present study toinvestigate the operating performance of OWC air chamber. The RANS equations, standard k-ε turbulence model and dynamic mesh technology are employed in the numerical model. The effects of incident wave conditions and shape parameters on the wave energy converting efficiency are studied and the capability of the present numerical wave tank on the corresponding engineering application is validated.

WATER WAVES IN AN ELASTIC VESSEL

Linear and nonlinear analyses of water waves in an elastic vessel are carried out to study the dramatic phenomena of Dragon Wash as well as related controllable experiments. It is proposed that the capillary edge waves are generated by parametric resonance, which is shown to be a possible mechanism for both rectangular an circular vessels. For circular vessel, the normal geometric resonance is also operating, thus greatly. enhance the dramatic effect. The mechanism of nonlinear mode-mode interaction is proposed far the generation of axisymmetric low-frequency gravity waves by the high-frequency external excitation. A simple model system is studied numerically to demonstrate explicitly this interaction mechanism.

Study on the Interaction of Water Waves with Semi-Circular Breakwater

The present study investigates the interaction of steep waves with semi-circular breakwater with the complex plane's Cauchy boundary integral theorem. The boundary integral method is used to transform the calculation in fluid domain into its boundary alone. In the calculation the computation domain is moved with the propagation of waves. A numerical solution is obtained for incident Stokes waves passing the submerged obstacles. This method has been extended to the calculation of wave run-up on a slope for estimating wave overtopping.

THEORY OF WATER WAVES IN AN ELASTIC VESSEL

Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Based on this new finding, a theory of parametric resonance is developed in detail to explain the on- set of the prominent circumferential capillary waves. Numerical computation is also carried out and the results agree generally with the experiments. Analysis and nu- merical computation are also presented to explain the generation of axisymmetric low-frequency gravity waves by tile high-frequency external excitation.

Analysis on Shock Wave Speed of Water Hammer of Lifting Pipes for Deep-Sea Mining

Water hammer occurs whenever the fluid velocity in vertical lifting pipe systems for deep-sea mining suddenly changes. In this work, the shock wave was proven to play an important role in changing pressures and periods, and mathematical and numerical modeling technology was presented for simulated transient pressure in the abnormal pump operation. As volume concentrations were taken into account of shock wave speed, the experiment results about the pressure-time history, discharge-time history and period for the lifting pipe system showed that： as its concentrations rose up, the maximum transient pressure went down, so did its discharges; when its volume concentrations increased gradually, the period numbers of pressure decay were getting less and less, and the corresponding shock wave speed decreased. These results have highly coincided with simulation results. The conclusions are important to design lifting transporting system to prevent water hammer in order to avoid potentially devastating consequences, such as damage to components and equipment and risks to personnel.

The patterns of surface capillary-gravity short-crested waves with uniform current fields in coastal waters

A fully three-dimensional surface gravitycapillary short-crested wave system is studied as two progressive wave-trains of equal amplitude and frequency, which are collinear with uniform currents and doubly-periodic in the horizontal plane, are propagating at an angle to each other. The first- and second-order asymptotic analytical solutions of the short-crested wave system are obtained via a perturbation expansion in a small parameter associated with the wave steepness, therefore depicting a series of typical three-dimensional wave patterns involving currents, shallow and deep water, and surface capillary waves, and comparing them with each other.