Joint Distribution of Wave Heights and Wavelengths and Distribution of Wave Steepness

A joint probability density is derived for wavelengths and wave heights. It is asymmetric and depends only on the spectral bandwidth epsilon defined by Cartwright and Longuet-Higgins (1956). After that a theoretical probability density for wave steepness is obtained. It tends to Rayleigh distribution as epsilon --> 0. A comparison between theoretical steepness distribution and laboratory experiment result shows good agreement.

Dependence of Wave Height Distribution on Spectral Width and Wave Steepness

In this paper experimental wind wave data are analyzed. It is found that differences in spectral width will give rise to differences in wave height distribution. The effect of spectral width on the distribution is mainly in the high wave range. The effect of wave steepness is in low, medium and high wave ranges. In the high wave range the effect of spectral width is comparable to that of wave steepness. Differences in spectral width in the observations may give rise to discrepancies in the result when wave steepness is the only parameter in the distribution.

The observed analysis on the wave spectra of Hurricane Juan (2003)

Hurricane Juan provides an excellent opportunity to probe into the detailed wave spectral patterns and spectral parameters of a hurricane system, with enough wave spectral observations around Juan＇s track in the deep ocean and shallow coastal water. In this study, Hurricane Juan and wave observation stations around Juan＇s track are introduced. Variations of wave composition are discussed and analyzed based on time series of one-dimensional frequency spectra, as well as wave steepness around Juan＇s track： before, during, and after Juan＇s passing. Wave spectral involvement is studied based on the observed one-dimensional spectra and two-dimensional spectra during the hurricane. The standardization method of the observed wave spectra during Hurricane Juan is discussed, and the standardized spectra show relatively conservative behavior, in spite of the huge variation in wave spectral energy, spectral peak, and peak frequency during this hurricane. Spectral widths＇ variation during Hurricane Juan are calculated and analyzed. A two-layer nesting WW3 model simulation is applied to simulate the one-dimensional and two-dimensional wave spectra, in order to examine WW3＇s ability in simulating detailed wave structure during Hurricane Juan.

On the Fifth-Order Stokes Solution for Steady Water Waves

This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear （1961）, confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.

Simplified Method for Calculating Standing Wave Pressure on Vertical Breakwater

Through numerical modeling, a kind of simplified calculating method for standing wave pressure on vertical face breakwater have been put forward. Not only the formulas proposed in this paper are simple in form and very easy in use, but also they possess continuity on the full range of standing wave. And more, the precision requiremennts of calculation can be satisfied to a certain extent in engineering practice.

Improvements on Mean Free Wave Surface Modeling

Some new results of the modeling of mean free surface of waves or wave set-up are presented. The stream function wave theory is applied to incident short waves. The limiting wave steepness is adopted as the wave breaker index in the calculation of wave breaking dissipation. The model is based on Roelvink (1993), but the numerical techniques used in the solution are based on the Weighted-Average Flux (WAF) method (Watson et al., 1992), with Time-Operator-Splitting (TOS) used for the treatment of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modeling wave set-up. The short wave (or incident primary wave) energy equation is solved by use of a traditional Lax-Wendroff technique. The present model is found to be satisfactory compared with the measurements conducted by Stive (1983).

Influence of impulse waves generated by rocky landslides on the pressure exerted on bank slopes

Rocky landslides on river banks can result in the generation of ultra-high waves,which may destroy structures on the opposite bank.Existing methods to calculate the pressure on bank slopes under the effect of impulse waves generated by landslides are,however,few and of low precision.Therefore,in this study,a three-dimensional physical model test was conducted by taking into account factors such as landslide geometry parameters and the bank slope angle.The model test section was generalized on the basis of a certain section of the Three Gorges reservoir area as a prototype,after which the wave parameters and wave pressure acting on the bank slope were measured.Subsequently,the magnitude,acting point,and distribution of the pressure of the impulse waves generated by the rocky landslide upon the bank slope were determined.The distribution curve of the impact pressure was similar to that calculated using theСНиПⅡ57-75 formula,and the experimental pulsating pressure value was close to the value calculated using the Subgrade formula.Based on the test results,a power function of the relative pulsating pressure steepness with respect to the reciprocal of the wave steepness,relative water depth,and slope ratio was proposed.The acting point of the maximum pulsating pressure was found to be located near the still water level.Finally,an empirical formula for calculating the envelope of the maximum pulsating pressure distribution curve was proposed.These formulas can serve as a theoretical basis for the prediction of impulse wave pressure generated owing to landslides on bank slopes.

Nonlinear Numerical Analysis of Vortex-Induced Vibration of A Three-Dimensional Deepwater Steep Wave Riser with Large Deformation Features

The cross-flow(CF)vortex-induced vibration(VIV)of a deepwater steep wave riser(SWR)subjected to uniform or shear flow loads is investigated numerically.The model is based on a three-dimensional(3D)nonlinear elastic rod theory coupled with a wake oscillator model.In this numerical simulation,the nonlinear motion equations of the riser with large deformation features are established in a global coordinate system to avoid the transformation between global and local coordinate systems,and are discretized with the time-domain finite element method(FEM).A wakeoscillator model is employed to study the vortex shedding,and the lift force generated by the wake flow is described in a van der Pol equation.A Newmark-βiterative scheme is used to solve their coupling equation for the VIV response of the SWR.The developed model is validated against the existing experimental results for the VIV response of the top-tension riser(TTR).Then,the numerical simulations are executed to determine VIV characteristics of the SWR.The effects of both flow velocity and the spanwise length of the flow field on the drag coefficient in the inline(IL)direction and the lift coefficient in the CF direction are investigated systematically.The results indicate that compared with TTR,the low frequency and multi-modal vibration are the main components of the SWR due to the large deformation and flexible characteristics.For shear flow,the multi-frequency resonance dominates the VIV response of the SWR,especially at the hang-off segment.

Nonlinear Dynamic Analysis and Fatigue Study of Steep Wave Risers Under Irregular Loads

As a reliable alternative option for traditional steel catenary risers(SCRs),steep wave risers(SWRs)have been widely applied to deepwater oil and gas production.However,the nonlinear dynamic analysis of SWRs is more complicated than that of traditional SCRs due to their special configuration and significant geometric nonlinearity.Moreover,SWRs are highly susceptible to fatigue failure under the combined excitation of irregular waves and top floater motions(TFMs).In this study,considering irregular waves and TFMs,a numerical SWR model with an internal flow is constructed based on the slender rod model and finite element method.The Newmark-βmethod is adopted to solve the dynamic behavior of SWR.Moreover,the Palmgren-Miner rule,a specified S-N curve,and rainflow counting method are applied to estimate the fatigue damage.An efficient numerical computation procedure,i.e.,DRSWR,is programmed with MATLAB in this study.Calculation results are compared with those of OrcaFlex to verify the accuracy of the DRSWR.The nonlinear dynamic response and fatigue damage of an SWR under the combined excitation of irregular waves and TFMs are obtained,and a comprehensive parametric analysis is then conducted.The analysis results show that the buoyancy section undergoes the highest level of stress and fatigue damage under the combined excitation of irregular waves and TFMs.An internal flow with high velocity and high density produces a high level of fatigue damage.The buoyancy factor and length of the buoyancy section should be set moderately to reconcile the reduction of the top tension with increased fatigue life.These results are expected to provide some reference significance for the engineering design of SWR.

Nonlinear Analysis of Bidirectional Vortex-Induced Vibration of A Deepwater Steep Wave Riser Subjected to Oblique Currents

An improved three-dimensional(3D)time-domain couple model is established in this paper to simulate the bidirectional vortex-induced vibration(VIV)of a deepwater steep wave riser(SWR)subjected to oblique currents.In this model,the nonlinear motion equations of the riser are established in the global coordinate system based on the slender rod theory with the finite element method.Van der Pol equations are used to describe the lift forces induced by the x-and y-direction current components,respectively.The coupled equations at each time step are solved by a Newmark-βiterative scheme for the SWR VIV.The present model is verified by comparison with the published experimental results for a top-tension riser.Then,a series of simulations are executed to determine the influences of the oblique angle/velocity of the current,different top-end positions and the length of the buoyancy segment on the VIV displacement,oscillating frequency as well as hydrodynamic coefficients of the SWR.The results demonstrate that there exists a coupled resonant VIV corresponding to x-direction and y-direction,respectively.However,the effective frequency is almost identical between the vibrations at the hang-off segment along x and y directions.The addition of the buoyancy modules in the middle of the SWR has a beneficial impact on the lift force of three segments and simultaneously limits the VIV response,especially at the decline segment and the hang-off segments.Additionally,the incident current direction significantly affects the motion trajectory of the SWR which mainly includes the fusiform and rectangle shapes.

Time-Domain Nonlinear Wave-Current Interaction with A Steep Wave Riser Considering Internal Flow Effect

The nonlinear dynamic response induced by the wave-current interaction on a deepwater steep wave riser(SWR)is numerically investigated based on a three-dimensional(3 D)time-domain finite element method(FEM).The governing equation considering internal flow is established in the global coordinate system.The whole SWR consists of three segments:the decline segment,buoyancy segment and hang-off segment,in which the buoyancy segment is wrapped by several buoyancy modules in the middle section,leading to the arch bend and sag bend.A Newmark-β iterative scheme is adopted for the accurate analysis to solve the governing equation and update the dynamic response at each time step.The proposed method is verified through the published results for the dynamic response of steel catenary riser(SCR)and static configuration of steel lazy wave riser(SLWR).Simulations are executed to study the influence of wave height,current velocity/direction,internal flow density/velocity and top-end pressure on the tension,configuration and bending moment of the SWR.The results indicate that the influence of the current on the configuration and mechanical behavior of the SWR is greater than that of the wave,especially in the middle section.With increasing current velocity,the suspending height of the middle section drops,meanwhile,its bending moment decreases accordingly,but the tension increases significantly.For a fixed external load,the increasing internal flow density induces the amplification of the tension at the hang-off segment and the mitigation at the decline segment,while the opposite trend occurs at the bending moment.

Numerical method for wave height distribution within the artificial harbor with water depth of steep variation

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半潜船波浪诱导运动与载荷预报数值方法比较研究

Numerical simulation tools based on potential-flow theory and/or Morison’s equation are widely used for predicting the hydrodynamic responses of floating offshore wind platforms.In general,these simplified approaches are used for the analysis under operational conditions,albeit with a carefully selected approach to account for viscous effects.Nevertheless,due to the limit hydrodynamic modelling to linear and weakly nonlinear models,these approaches severely underpredict the low-frequency nonlinear wave loads and dynamic responses of a semisubmersible.They may not capture important nonlinearities in severe sea states.For the prediction of wave-induced motions and loads on a semisubmersible,this work systematically compares a fully nonlinear viscous-flow solver and a hybrid model combining the potential-flow theory with Morison-drag loads in steep waves.Results show that when nonlinear phenomena are not dominant,the results obtained by the hybrid model and the high-fidelity method show reasonable agreement,while larger discrepancies occur for highly nonlinear regular waves.Specifically,regular waves with various steepness over different frequencies are focused in the present study,which supplements the understanding in applicability of these two groups of method.

On the parameterization of drag coefficient over sea surface

Six parameterization schemes of roughness or drag coefficient are evaluated on the basis of the data from six experiments. They present great consistency with measurement when friction velocity u＊〈0.5 m/s （ap- proximately corresponding to 10 m wind speed U10〈 12 m/s） and large deviation from measurement when u＊≥0.5 m/s （approximately U10 ≥ 12 m/s）. In order to improve the deviation, a new parameterization of drag coefficient is derived on the basis of the similarity theory, Charnock relationship and Toba 3/2 power law. Wave steepness and wind-sea Reynolds number are considered in the new parameterization. Then it is test- ed on the basis of the measurements and shows significant improvement when u＊≥0.5 m/s. Its standard errors are much smaller than the ones of the other six parameterizations. However, the new parameteriza- tion still needs more tests especially for high winds.

Wind speed scaling and the drag coefficient

Wind speed scaling in similarity law in wind-generated waves and the drag coefficient are studied. In analyzing the data in the wind wave channel, it is found that the u＊ scaling greatly reduces the scatter in the U10 scaling. The u＊ scaling has much less scatter than the scaling using other wind speeds. The friction velocity seems to play a distinctive role in wave growth. The result is important in the applications of the similarity law and in wave modeling. In theory it gives an insight into the mechanism of wind wave interaction. It is found that wave steepness is important in influencing the drag coefficient. The variability of the coefficients in the currently widely used drag form can be explained by the differences in wave steepness in the observations. A drag coefficient model with wind speed and wave steepness as parameters is proposed. An explanation for Kahma＇s result that the u, scaling does not reduce the scatter in the U10 scaling is given.

浮体升沉和纵摇运动对甲板上浪载荷影响数值研究（英文）

In this paper,the influence of heave and pitch motions on green water impact on the deck is numerically investigated.The vessel motions are determined using a potential theory based method and provided as input to finite volume based CFD computations of green water phenomenon.A dynamic mesh approach is adopted to determine instantaneous body positioning in the fluid domain.Detailed validation studies with published experimental results for 2D and 3D fixed vessel cases are initially performed to validate the present numerical approach before studying the moving vessel problem.The results show that inclusion of heave and pitch motion changes the disturbed wave field near the bow which influences the free surface as well as the impact loading due to green water.The effect of wave steepness on green water impact is also investigated and it is seen that the present numerical method is capable of capturing green water load.It is observed that the effects of vessel motions on green water load are not negligible and one should consider this effect too.The incorporation of vessel motions in the vertical plane affects the green water loading on the deck.

Global air-sea surface carbon-dioxide transfer velocity and flux estimated using ERS-2 data and a new parametric formula

Using data from the European remote sensing scatterometer （ERS-2） from July 1997 to August 1998, glob- al distributions of the air-sea CO2 transfer velocity and flux are retrieved. A new model of the air-sea CO2 transfer velocity with surface wind speed and wave steepness is proposed. The wave steepness （6） is re- trieved using a neural network （NN） model from ERS-2 scatterometer data, while the wind speed is directly derived by the ERS-2 scatterometer. The new model agrees well with the formulations based on the wind speed and the variation in the wind speed dependent relationships presented in many previous studies can be explained by this proposed relation with variation in wave steepness effect. Seasonally global maps of gas transfer velocity and flux are shown on the basis of the new model and the seasonal variations of the transfer velocity and flux during the 1 a period. The global mean gas transfer velocity is 30 cm/h after area-weighting and Schmidt number correction and its accuracy remains calculation with in situ data. The highest transfer velocity occurs around 60°N and 60°S, while the lowest on the equator. The total air to sea CO2 flux （calcu- lated by carbon） in that year is 1.77 Pg. The strongest source of CO2 is in the equatorial east Pacific Ocean, while the strongest sink is in the 68°N. Full exploration of the uncertainty of this estimate awaits further data. An effectual method is provided to calculate the effect of waves on the determination of air-sea CO2 transfer velociW and fluxes with ERS-2 scatterometer data.

四分之一圆非越浪型穿孔防波堤稳定性研究中的多元非线性回归分析

Breakwaters have been built throughout the centuries for the coastal protection and the port development,but changes occurred in their layout and criteria used for the design.Quarter circle breakwater(QBW)is a new type evolved having advantages of both caisson type and perforated type breakwaters.The present study extracts the effect of change in the percentage of perforations on the stable conditions of seaside perforated QBW by using various physical models.The results were graphically analyzed using dimensionless parameters and it was concluded that there is a reduction in dimensionless stability parameter with an increase in steepness of the wave and change in water depth to the height of breakwater structure.Multiple non–linear regression analysis was done and the equation for the best fit curve with a higher regression coefficient was obtained by using Excel statistical software—XLSTAT.

Numerical study on roll dynamics of damaged ship in beam waves and calm water

Computational fluid dynamics is used to study the roll dynamics of a damaged ship in beam waves with various steepnesses and in calm water.The wave-making method,which combines the velocity-inlet boundary and momentum source with the fifth-order Stokes theory,is employed for wave generation.The SST k-ωturbulence model with a modification to the turbulent viscosity in Reynolds stress is adopted to prevent the over-production of turbulence in the numerical wave tank.The lateral drift restrained model with a combined dynamic mesh strategy is utilized to deal with the coupled heave-sway-roll motions of the ship.First,benchmarking tests are performed,including wave generation and roll response of the damaged ship in regular beam waves.Then,the effects of incident wave steepness on the roll response of the damaged ship are analyzed.For different wave steepnesses,the ship roll motion is dominated by the first-order harmonic component.The second-order component increases with the increase of wave steepness.Finally,the roll hydrodynamic coefficients for different parts of the damaged ship are investigated with different rolling parameters.The added moment of inertia for the whole damaged ship is mainly attributed to the external hull composition and changes slightly with the change of roll amplitude and frequency.The added moment of inertia for the compartments could be negative in particular cases.The damping coefficients of the whole damaged ship and external hull increase with the increase of roll amplitude and frequency,while that of the compartments appears complicated with the change of roll amplitude and frequency.

An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion

In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. （2003）, the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. （2007）＇s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly varying topography and wave breaking, the present model is applied to study： （1） wave refraction and diffraction over a submerged elliptic shoal on a slope （Berkhoff et al., 1982）; （2） Bragg reflection of monochromatic waves from the sinusoidal ripples （Davies and Heathershaw, 1985）; （3） wave transformation near a shore attached breakwater （Watanabe and Maruyama, 1986）. Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models （REF/DIF model and FUNWAVE model） show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.