Depression and elevation internal solitary waves in a two-layer fluid and their forces on cylindrical piles

Both large amplitude depression and elevation internal solitary waves (ISWs) were observed on the continental shelf of the northwest South China Sea (SCS) during the Wenchang Internal Wave Experiment. In this study, we investigate the characteristics of depression and elevation ISWs based on comparisons between observational results and internal wave theories. It is suggested that the large amplitude depression wave is better represented by the extended Korteweg-de Vries (EKdV) theory than by the KdV model, whereas the large amplitude elevation wave is in better agreement with the KdV equation than with the EKdV theory. Wave-induced forces on a supposed small-diameter cylindrical pile by depression and elevation waves are also estimated using the internal wave theory and Morison formula. The wave-induced force by elevation ISWs is rarely reported in the literature. It is found that the force induced by the elevation wave differs significantly from that by the depression wave, and the elevation wave generally produces greater force on the pile in the lower water column than the depression wave. These results show that ISWs in the study area can present a serious threat to ocean engineering structures, and should not be ignored in the design of oil platforms and ocean operations.     

A COMBINED REFRACTION-DIFFRACTION-DISSIPATION MODEL OF WAVE PROPAGATION

A numerical model based on the mild-slope equation of water wave propagation over complicated bathymetry,taking into account the combined effects of refraction,diffraction and dissipation due to wavebreaking is presented.Wave breaking is simulated by modifying the wave height probability density func-tion and the wave energy dissipation mechanism is parameterized according to that of the hydraulic jumpformulation.Solutions of the wave height,phase function,and the wave direction at every grid point areobtained by finite difference approximation of the governing equations,using Gauss-Seidel Iterative Method(GSIM)row by row.Its computational convenience allows it to be applied to large coast regions tostudy the wave transformation problem.Several case studies have been made and the results compare verywell with the experiment data and other model solutions.The capability and utility of the model forreal coast areas are illustrated by application to a shallow bay of northeast Australia.     

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-β 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.     

Numerical Study of the Secondary Circulations in Rip Current Systems

To investigate the mechanism of secondary circulations in rip current systems, and to explore the relationship between wave conditions and secondary circulation intensity, a series of numerical experiments is performed using coupled nearshore wave model and circulation model. In these experiments, the rip currents and secondary circulations generated above barred beaches with rip channels are simulated. A comparison experiment is conducted to investigate the formation and hydrodynamics of the secondary circulations. Model results indicate that the secondary circulations consist of alongshore flows driven by wave set-up near the shoreline, part of the feeder currents driven by the wave set-up over the bars, and onshore flows at the end of the rip channel driven by wave breaking and convection. The existence of the secondary circulation barely affects the rip current, but narrows and intensifies the feeder currents. Three groups of experiments of varying incident wave conditions are performed to investigate the relationship between wave conditions and secondary circulation intensity. The velocity of the alongshore flow of the secondary circulation is sensitive to the variation of the incident wave height and water depth. It is also found that the alongshore flow intensity is in direct proportion to the alongshore variation of the wave height gradient between the bars and the shoreline.     

Effects of wind input and wave dissipation formulations on the steady Ekman current solution

The effects of different wind input and wave dissipation formulations on the steady Ekman current solution are described. Two formulations are considered： one from the wave modeling （WAM） program proposed by Hasselmann and Komen and the other provided by Tsagareli and Babanin. The solution adopted for our study was presented by Song for the wave-modified Ekman current model that included the Stokes drift, wind input, and wave dissipation with eddy viscosity increasing linearly with depth. Using the Combi spectrum with tail effects, the solutions are calculated using two formulations for wind input and wave dissipation, and compared. Differences in the results are not negligible. Furthermore, the solution presented by Song and Xu for the eddy viscosity formulated using the K-Profile Parameterization scheme under wind input and wave dissipation given by Tsagareli and Babanin is compared with that obtained for a depth-dependent eddy viscosity. The solutions are further compared with the available well-known observational data. The result indicates that the Tsagareli and Babanin scheme is more suitable for use in the model when capillary waves are included, and the solution calculated using the K-Profile Parameterization scheme agrees best with observations.     

STATISTICAL PROPERTIES OF WAVE GROUPS DESCRIBED BY GROUP-INDUCED LONG WAVES

A new method using group-induced second-order long waves (GSLW) to describe wave groups is presented in this paper on the basis of the GSLW theory by Longuet- Higgins and Steward (1964) . In the method , the parabolic relationship between GSLW and the wave envelope is first deduced , and then the distribution function of GSLW amplitude is derived . Thus, the formulae in terms of the moments of GSLW and short wave spectra for the average time duration and the mean length of runs of wave heights exceeding a certain level can be derived . A new groupiness factor equivalent to half the mean wave number in wave groups is defined by taking into account the widths of spectra of GSLW and short waves . Compared with theoretical results of others , ours are closer to measured wave data .     

Estimation and Prediction of Typhoons and Wave Overtopping in Qingdao,China

This study aims to estimate and predict the impact of climate change on typhoons and wave overtopping during typhoon progresses in Qingdao, China. The SWAN wave model is used to simulate wave elements. The scale coefficients of wave overtopping are estimated using an empirical prediction formula. A total of 75 tropical cyclones affected Qingdao from 1949 to 2019. These tropical cyclones can be grouped into eight categories according to typhoon tracks. Typhoon wind speed during Track G is projected to decrease, and those of the other seven typhoon progresses will increase by 0.35% – 0.75% in 2025, 0.69% – 1.5% in 2035, and 1.38% – 3.0% in 2055. The significant wave height and wave overtopping outside the bay are greater than those inside the bay. Among the 506 typical points selected, the maximum values of the significant wave height and wave overtopping inside the bay are mainly distributed in the range of 0 – 2 m and 0 – 60 m~3 km~(-1) s~(-1), respectively. The increments of the significant wave height and wave overtopping of Track F are most obvious. The significant wave height of Track F will increase by 50.5% in 2025, 51.8% in 2035, and 53.4% in 2055. In the 2℃ scenario, the maximum value of wave overtopping of Track F will increase by 21.9% in 2025, 24.3% in 2035, and 29.5% in 2055. In the 4℃ scenario, the maximum value of wave overtopping of Track F will increase by 21.9% in 2025, 24.3% in 2035, and 29.5% in 2055.     

Parameterized first-guess spectrum method for retrieving directional spectrum of swell-dominated waves and huge waves from SAR images

A method to retrieve ocean wave spectra from SAR images, named Parameterized First-guess Spectrum Method (PFSM), was proposed after interpretation of the theory to ocean wave imaging and analysis of the drawbacks of the retrieving model generally used. In this method, with additional information and satellite parameters, the separating wave-number is first calculated to determine the maximum wave-number beyond which the linear relation can be used. The separating wave-number can be calculated using the additional information on wind velocity and parameters of SAR satellite. And then the SAR spectrum can be divided into SAR spectrum of wind wave and of swell according to the result of separating wave-number. The portion of SAR spectrum generated by wind wave, is used to search for the most suitable parameters of ocean wind wave spectrum, including propagation direction of ocean wave, phase speed of dominating wave and the angle spreading coefficient. The swell spectrum is acquired by directly inversing the linear relation of ocean wave spectrum to SAR spectrum given the portion of SAR spectrum generated by swell. We used the proposed method to retrieve the ocean wave spectrum from ERS-SAR data from the South China Sea and compared the result with altimeter data. The agreement indicates that the PFSM is reliable.     

Experimental Investigation of Wave Load and Run-up on the Composite Bucket Foundation Influenced by Regular Waves

In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the interaction between the wave field and the composite bucket foundation(CBF) becomes complicated. In this study, the hydrodynamic characteristics, including wave pressure, load, upwelling, and run-up, around the arc transition of a CBF influenced by regular waves are investigated through physical tests at Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China. The distributions of the wave pressures and upwelling ratios around the CBF are described, and the relationship between the wave load and the wave parameters is discussed. New formulae based on the velocity stagnation head theory with linear wave theory and the second-order Stokes wave theory for wave kinematics are proposed to estimate the wave run-up. Moreover, the multiple regression method with nonlinear technology is employed to deduce an empirical formula for predicting run-up heights. Results show that the non-dimensional wave load increases with the increase in the values of the wave scattering parameter and relative wave height. The wave upwelling height is high in front of the CBF and has the lowest value at an angle of 135? with the incoming wave direction. The performance of the new formulae proposed in this study is compared using statistical indices to demonstrate that a good fit is obtained by the multiple regression method and the analytical model based on the velocity stagnation head theory is underdeveloped.     

Modification on Lynett and Liu＇s model for internal solitary wave propagation over variable bathymetry

A two-dimensional, depth-integrated model proposed by Lynett and Liu （2002） was checked carefully, and several misprints in the model were corrected after detailed examination on both the theory and the numerical program. Several comparisons were made on wave profile, system energy and maximum wave amplitude. It is noted that the modified model can simulate the propagation of the internal solitary waves over variable bathymetry more reasonably to a certain degree, and the wave profiles obtained based on the modified model can better fit the experiment data reported by Helfrich （1992） than those from original model.     

Acoustic numerical simulation for VTI media

The generality to anisotropy of the earth media can be proved by a lot of research and observation, which is shown by the elastic parameters of the seismic wave changes with the direction of propagation. Actually, computational efficiency is very low, when simulating on the elastic anisotropie media, for the complicated and multi-parameters computation, which becomes a disadvantage to the succeeding migration and imaging pro-cedure. Using acoustic approximation in the VT[ media is an advisable simplification for the elastic wave simu-lation in that setting S-velocity into zero can greatly reduce the computational amount as well as get the same simulation effect. The authors get an acoustic approximation formula, then gain an anisotropic wave equation with 2-order in time and 4-order in space by inverse Fourier transformation, and dispel with the dispersion by adopting the high order finite difference operator in space and remove the edge reflection using the absorption attenuation boundary. Finally, the feasibility and effectiveness of this algorithm can be proved by the snaps and synthetic records.     

Numerical simulation and preliminary analysis on ocean waves during Typhoon Nesat in South China Sea and adjacent areas

Using the wave model WAVEWATCH III(WW3), we simulated the generation and propagation of typhoon waves in the South China Sea and adjacent areas during the passage of typhoon Nesat(2011). In the domain 100°–145°E and 0°–35°N, the model was forced by the cross-calibrated multi-platform(CCMP) wind fi elds of September 15 to October 5, 2011. We then validated the simulation results against wave radar data observed from an oil platform and altimeter data from the Jason-2 satellite. The simulated waves were characterized by fi ve points along track using the Spectrum Integration Method(SIM) and the Spectrum Partitioning Method(SPM), by which wind sea and swell components of the 1D and 2D wave spectra are separated. There was reasonable agreement between the model results and observations, although the WW3 wave model may underestimate swell wave height. Signifi cant wave heights are large along the typhoon track and are noticeably greater on the right of the track than on the left. Swells from the east are largely unable to enter the South China Sea because of the obstruction due to the Philippine Islands. During the initial stage and later period of the typhoon, swells at the fi ve points were generated by the propagation of waves that were created by typhoons Haitang and Nalgae. Of the two methods, the 2D SPM method is more accurate than the 1D SIM which overestimates the separation frequency under low winds, but the SIM method is more convenient because it does not require wind speed and wave direction. When the typhoon left the area, the wind sea fractions decreased rapidly. Under similar wind conditions, the points located in the South China Sea are affected less than those points situated in the open sea because of the infl uence of the complex internal topography of the South China Sea. The results reveal the characteristic wind sea and swell features of the South China Sea and adjacent areas in response to typhoon Nesat, and provide a reference for swell forecasting and offshore structural designs.     

Comparison of retrieving methods of ocean wave periods from satellite altimeter with buoy measurements

For validating the results of retrieved mean wave period, four empirical algorithms established previously are introduced. Based on the data of over five years derived from TOPEX satellite altimeter for the entire East China Sea, ocean wave periods were calculated and statistical comparison among them was performed. The retrieved mean wave period obtained with our new distribution parameters showed better agreement with the wave period TB measured by buoy than that calculated by other three algorithms. The difference between the mean values of and that of TB is 0.16 s and the RMSE (root mean square error) of is the lowest value (0.48).     

Wave interaction with a partially reflecting vertical wall protected by a submerged porous bar

This study gives an analytical solution for wave interaction with a partially reflecting vertical wall protected by a submerged porous bar based on linear potential theory. The whole study domain is divided into multiple sub-regions in relation to the structures. The velocity potential in each sub-region is written as a series solution by the separation of variables. A partially reflecting boundary condition is used to describe the partial reflection of a vertical wall. Unknown expansion coefficients in the series solutions are determined by matching velocity potentials among different sub-regions. The analytical solution is verified by an independently developed multi-domain boundary element method(BEM) solution and experimental data. The wave run-up and wave force on the partially reflecting vertical wall are estimated and examined, which can be effectively reduced by the submerged porous bar. The horizontal space between the vertical wall and the submerged porous bar is a key factor, which affects the sheltering function of the porous bar. The wave resonance between the porous bar and the vertical wall may disappear when the vertical wall has a low reflection coefficient. The present analytical solution may be used to determine the optimum parameters of structures at a preliminary engineering design stage.     

The Fractional Power Law of Wind Wave Growth in Deep Water for Short Fetch

Combining the 3/2 power law proposed by Toba with the significant wave energy balance equation for wind waves, wave growth in deep water for short fetch is investigated. It is found that the variations of wave height and period with fetch have the form of power function with fractional exponents 3/8 and 1/4 respectively. Using these exponents in the power functions and through data fitting, the concise wind wave growth relations for short fetch are obtained.     

Relationship between wave steepness and wave age in the course of wind wave growth

It is traditionally assumed that the relationship between wave steepness and wave age is independent of the wind wave growth state. In fact, the traditional relationship can not describe the whole course of wind wave growth. This paper assumes that the relationship between wave steepness and wave age changes with the variety of dimensionless fetch. Based on the relationship proposed by Hou and Wen (1990), a new relationship in the course of wind wave growth is revealed. Comparisons between the present study and other previous relationships show that this new relationship explains better the observations than the other existing relationships.In the case of small fetch, wave age value increases more quickly than other models while it is in opposition to that in the case of large fetch. The result in present paper can clearly reflect the whole course of wind wave growth, it is an improvement for traditional results.     

Climatology of Wind-Seas and Swells in the China Seas from Wave Hindcast

The wind-sea and swell climates in the China Seas are investigated by using the 27-yr Integrated Ocean Waves for Geophysical and other Applications(IOWAGA)hindcast data.A comparison is made between the significant wave height from the IOWAGA hindcasts and that from a jointly calibrated altimetry dataset,showing the good performance of the IOWAGA hindcasts in the China Seas.A simple but practical method of diagnosing whether the sea state is wind-sea-dominant or swell-dominant is proposed based on spectral partitioning.Different from the characteristics of wind-seas and swells in the open ocean,the wave fields in the enclosed seas such as the China Seas are predominated by wind-sea events in respect of both frequencies of occurrences and energy weights,due to the island sheltering and limited fetches.The energy weights of wind-seas in a given location is usually more significant than the occurrence probability of wind-sea-dominated events,as the wave energy is higher in the wind-sea events than in the swell events on average and extreme wave heights are mostly related to wind-seas.The most energetic swells in the China Seas(and other enclosed seas)are‘local swells’,having just propagated out of their generation areas.However,the swells coming from the West Pacific also play an important role in the wave climate of the China Seas,which can only be revealed by partitioning different swell systems in the wave spectra as the energy of them is significantly less than the‘local swells’.     

Ocean wave diffraction in near-shore regions observed by Synthetic Aperture Radar

Observation and analysis of ocean wave diffraction in near-shore and near-island region was performed with Synthetic Aperture Radar (SAR) data, using an optimized retrieval method named parameterized first-guess spectrum retrieval method. The results retrieved from ERS-SAR and ENVISAT-ASAR images showed that, in the region sheltered by land jut, the energy of long waves is reduced by 10%-20% and that the propagation direction of long waves is changed due to the effect of topography. In the shadow zone behind the island, ocean wave can propagate along the seashore instead of perpendicular to the coastline, as shown by SAR images.     

A preliminary study on the intensity of cold wave storm surges of Laizhou Bay

Dike failure and marine losses are quite prominent in Laizhou Bay during the period of cold wave storm surges because of its open coastline to the north and flat topography. In order to evaluate the intensity of cold wave storm surge, the hindcast of marine elements induced by cold waves in Laizhou Bay from 1985 to 2004 is conducted using a cold wave storm surge–wave coupled model and the joint return period of extreme water level, concomitant wave height, and concomitant wind speed are calculated. A new criterion of cold wave storm surge intensity based on such studies is developed. Considering the frequency of cold wave, this paper introduces a Poisson trivariate compound reconstruction model to calculate the joint return period, which is closer to the reality. By using the newly defined cold wave storm surge intensity, the ‘cold wave grade' in meteorology can better describe the severity of cold wave storm surges and the warning level is well corresponding to different intensities of cold wave storm surges. Therefore, it provides a proper guidance to marine hydrological analysis, disaster prevention and marine structure design in Laizhou Bay.     

Propagation of internal waves up continental slope and shelf

In a two-dimensional and linear framework, a transformation was developed to derive eigensolutions of internal waves over a subcritical hyperbolic slope and to approximate the continental slope and shelf. The transformation converts a hyperbolic slope in physical space into a flat bottom in transform space while the governing equations of internal waves remain hyperbolic. The eigensolutions are further used to study the evolution of linear internal waves as it propagates to subcritical continental slope and shelf. The stream function, velocity, and vertical shear of velocity induced by internal wave at the hyperbolic slope are analytically expressed by superposition of the obtained eigensolutions. The velocity and velocity shear increase as the internal wave propagates to a hyperbolic slope. They become very large especially when the slope of internal wave rays approaches the topographic slope, which is consistent with the previous studies.