Study of vertical breakwater reliability based on copulas

The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions. The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions, respectively. The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions, including the bivariate logistic Gumbel distribution, the bivariate lognormal distribution, and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously. We use the fully nested copulas to construct multivariate distributions taking into account related variables. Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater. We show that a bivariate model constructed by Frank copula gives the best reliability analysis, using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater, respectively. The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods. As copulas are suitable for constructing a bivariate or multivariate joint distribution, they have great potential in reliability analysis for other coastal structures.     

Analysis of Oblique Wave Interaction with a Comb-Type Caisson Breakwater

This study develops an analytical solution for oblique wave interaction with a comb-type caisson breakwater based on linear potential theory. The fluid domain is divided into inner and outer regions according to the geometrical shape of breakwater. By using periodic boundary condition and separation of variables, series solutions of velocity potentials in inner and outer regions are developed. Unknown expansion coefficients in series solutions are determined by matching velocity and pressure of continuous conditions on the interface between two regions. Then, hydrodynamic quantities involving reflection coefficients and wave forces acting on breakwater are estimated. Analytical solution is validated by a multi-domain boundary element method solution for the present problem. Diffusion reflection due to periodic variations in breakwater shape and corresponding surface elevations around the breakwater are analyzed. Numerical examples are also presented to examine effects of caisson parameters on total wave forces acting on caissons and total wave forces acting on side plates. Compared with a traditional vertical wall breakwater, the wave force acting on a suitably designed comb-type caisson breakwater can be significantly reduced. This study can give a better understanding of the hydrodynamic performance of comb-type caisson breakwaters.     

The efifect of wave breaking on surface wave imaging by Synthetic Aperture Radar

The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions (MTF) of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic (e.m.) wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.     

The effect of wave breaking on surface wave imaging by Synthetic Aperture Radar

The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions （MTF） of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic （e.m.） wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.     

Prediction of application scope of vertical fracture strike based on scattered wave fracture orientation function

Fracture system plays a very important role in the enrichment and accumulation of oil and gas in the reservoirs. Based on scattering wave information,Fracture Orientation Function( FOF) was built,which can be used to predict the fracture orientations. However,this method has only been verified by physical experiments without studies on the application scope. In this study,based on the linear sliding theory,FOF of the scattering wave was applied to the numerical simulation and the application scope was further studied according to fracture flexibility tensor. According to the fractures filled with gas and liquid,numerical simulation was conducted on the models with various fracture flexibilities. Numerical simulation results were used to inverse fracture orientation with the aid of the FOF of the scattering wave. The results show that it is workable to predict the vertical fracture orientation with the FOF of the scattering wave. Application of this method is more effective when the fractures are filled with gas than liquid. Moreover,the application scope can be predicted by the fracture flexibility.     

Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (ν=0.3−0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.     

The application of a numerical model to coastal surface water waves

Based on the Navier-Stokes Equations (NSE), numerical simulation with fine grids is conducted to simulate the coastal surface wave changes, including wave generation, propagation, transformation and interactions between waves and structures. This numerical model has been tested for the generation of the desired incident waves, including both regular and random waves. Some numerical results of this model are compared with available experimental data. In order to apply this model to actual cases, boundary conditions are considered in detail for different shoreline types (beach or breakwater, slope or vertical wall, etc. ). Finally, the utility of the model to a real coastal area is shown by applying it to a fishing port located in Shidao, Rongcheng, Shandong Province, P.R. China.     

Study on the breakwater caisson as oscillating water column facility

The Oscillating Water Column(OWC)wave energy convertor with the advantage of its simple geometrical construction and excellent stability is widely employed. Recently, perforated breakwaters have been often used as they can effectively reduce the wave reflection from and wave forces acting on the structures. Considering the similarity between the compartment of perforated caisson and the air chamber of OWC wave energy convertor, a new perforated caisson of breakwater is designed in this paper. The ordinary caisson is modified by installing facilities similar to the air chamber of OWC convener, but here they are utilized to dissipate the wave energy inside the caisson. Such an arrangement improves the stability of the caisson and reduces the construction cost by using the compartment of perforated caisson like using an air chamber. This innovation has both academic significance and important engineering value. For a new type of caisson, reliability analysis of the structure is necessary. Linear potential flow theory is applied to calculate the horizontal wave force acting on the caisson. The calculated results are compared with experimental data, showing the feasibility of the method. The Importance Sampling Procedure(ISP)is used to analyse the reliability of this caisson breakwater.     

Separation of up-going and down-going wave fields of vertical cable data

The vertical cable method for acquiring and processing pre-stack 3-D marine seismic data is based on the technology developed by the US Navy for antisubmarine warfare. In order to achieve the maximum utilization of vertical cable field data, a new separation method of the up-going and down-going wave fields of the vertical cable data processing was developed in this paper, which is different from the separation of the down-going and up-going wave fields of normal VSP data processing. In tests with synthetic modeling data andactual field data, this newly developed method performs well and is also computationally simpler without pre-assumption conditions.     

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.     

Estimation of wave forces on large compliant platforms

Compliant offshore structures such as spars, tension leg platforms (TLPs) and semi-submersibles have been dramatically improved in recent years due to their capability for deep water operation. Waves are the most important environmental phenomenon affecting these offshore structures. Estimation of wave forces is vital in offshore structure design. For large compliant offshore plat-forms, Morrison's equation is not valid anymore and usually diffraction theory is used. In this research, by using the finite difference method, a detailed analysis of the first-order diffraction of monochromatic waves on a large cylinder as a structural element is per-formed to solve the radiation and diffraction potentials. The results showed that the developed model is a reliable tool to estimate the wave forces and hydrodynamic coefficients on large structure elements when wave diffraction and radiation are considered.     

A study on the Antarctic circumpolar wave mode-A coexistence system of standing and traveling wave

The Antarctic circumpolar wave （ACW） has become a focus of the air-sea coupled Southern Ocean study since 1996, when it was discovered as an air-sea coupled interannual signal propagating eastward in the region of the Antarctic Circumpolar Current （ACC）. In order to analyze the mechanism of discontinuity along the latitudinal propagation, a new idea that ACW is a system with a traveling wave in the Southern Pacific and Atlantic Ocean and with a concurrent standing wave in the southern Indian Ocean is proposed in this paper. Based on the ideal wave principle, the average wave parameters of ACW is achieved using a non-linear approximation method, by which we find that the standing part and the traveling part possess similar radius frequency, proving their belonging to an integral system. We also give the latitudinal distribution of wave speed with which we could tell the reason for steady propagation during the same period. The spatial distribution of the propagation reveals complex process with variant spatial and temporal scales--The ENSO scale oscillation greatly impacts on the traveling process, while the result at the south of Australia indicates little connection between the Indian Ocean and the Pacific, which may be blocked by the vibration at the west of the Pacific. The advective effect of ACC on the propagation process should be examined clearly through dynamical method.     

NONLINEAR INERTIA—GRAVITY INTERNAL WAVE IN STRATIFIED FLUID

Based on the fundamental equations of geophysical fluid dynamics and on the consequence of verticaldensity stratification,travelling wave coordinates are used in this work to study the geometric topologicalstructures of nonlinear permanent wave in phase plane.Rigorous mathematical mechanics demonstratethat the solution of permanent solitary wave does not exist.Hamilton functions and "action-angle" varia-bles are used to express the travelling wave system in the simplest form and the analytic solution of the nonlinear inertia-gravity internal wave is 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.     

基于Barnes滤波原理的降水场客观分析及尺度分离

基于Barnes滤波原理（又称高斯加权客观分析）,在进行网格点插值的同时,通过选择适当的滤波参数C、G滤去原始场中的短波噪音,使分析结果平稳光滑;另外可通过它构成一带通滤波器,根据实际需要分离出影响天气过程的各种次天气尺度,达到尺度分离的目的。以全国160个国家基准代表站1954—2006年共53a的年平均降水场为例作实例分析,并同用Grads内插函数（Oacres函数）、九点平滑函数（Smth9函数）的绘图结果进行对比分析,结果表明客观分析结果同Grads内插平滑分析结果基本相似,都能反映出我国53a年平均降水场从东南向西北逐渐递减的趋势且与实际情况相符,降水场高值中心位于长江流域及以南的华南等地区,低值中心位于黄河流域以北的广大西部地区。取不同的参数C和G得到的尺度分离后的带通滤波值,既抑止了长波,又抑制了短波,达到较好的尺度分离效果。     

Numerical simulation of 3-D wave crests

1　Introduction　Anefficientwaytostudywaveforceonoffshorestructuresisthroughphysicalandnumericalwavesim ulation .Althoughmanysimulationsof 2 Dregularorirregularwaveshavesuccessfullybeencarriedoutinlaboratorythroughwindandwavegenerator ,itisstillratherdifficulttosimulate 3 Drandomwavesinlabo ratory .Therefore ,numericalsimulationiswidelyusedinsuchstudies (Baietal.,2 0 0 0 ;Zhuetal.,1999) .Tobuildlargeoffshorestructureslikemarineairports ,itisofinteresttostudytheeffectof 3 Dwaves .Goda(1994 …     

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 .     

A relationship between wave steepness and wave age for wind waves in deep water

Studying the relationship between wave steepness and wave age is important for describing wind wave growth with energy balance equation of significant waves. After invoking the dispersion rela- tion of surface gravity wave in deep water, a new relationship between wave steepness and wave age is revealed based on the “3/2-power law” (Toba, 1972), in which wave steepness is a function of wave age with a drag coefficient as a parameter. With a given wave age, a larger drag coefficient would lead to larger wave steepness. This could be interpreted as the result of interaction between wind and waves. Comparing with previous relationships, the newly proposed one is more consistent with observational data in field and laboratory.     

CALCULATIONS OF WAVE BREAKING PROBABILITY AND DISTRIBUTION OF BREAKING WAVE HEIGHTS IN DEEP WATER

lareODUcrI0NThephenomenonofbreakingwavesintheoasnoocurswheneveramomentahiyhighcrestmecheSanunstablecondition.It0ccursintendtimhy,andtheoccurrencefre-qUencydePendsonthescastate.ManystudAshaddricaniedoutontheoccurmcefre-qUencyofbrmkingwavesindeepweter.0chiandTsai(l983),LongueHiggins(l975)andVanD0mandPamn(l975)nadstheptalictonofbrmkingwavesoccurrenceindeePwater,usingabaskingcriterionforindividualwavesbasedonthewavesmpness.ThecriterioncanbeexpmeedintennSofthewaVehdghtHandperiodTasH>PgT'(…