Wave Pressure Acting on V-Shaped Floating Breakwater in Random Seas

Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwater is solved using the finite-depth Green function and boundary element method, in which the Green function is solved by integral method. The Response-Amplitude Operator(RAO) of wave pressure is acquired according to the Longuet-Higgins' wave model and the linear Bernoulli equation. Furthermore, the wave pressure's response spectrum is calculated according to the wave spectrum by discretizing the frequency domain. The wave pressure's characteristic value corresponding to certain cumulative probability is determined according to the Rayleigh distribution of wave heights. The numerical results and field test results are compared, which indicates that the wave pressure calculated in random seas agrees with that of field measurements. It is found that the bigger angle between legs will cause the bigger pressure response, while the increase in leg length does not influence the pressure significantly. The pressure at the side of head sea is larger than that of back waves. When the incident wave angle changes from 0? to 90?, the pressure at the side of back waves decreases clearly, while at the side of head sea, the situation is more complicated and there seems no obvious tendency. The concentration of wave energy around low frequency(long wavelength) will induce bigger wave pressure, and more attention should be paid to this situation for the structure safety.     

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.     

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.     

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 …     

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.     

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.     

Dynamic visual simulation of marine vector field based on LIC——a case study of surface wave field in typhoon condition

Line integral convolution(LIC) is a useful visualization technique for a vector field. However, the output image produced by LIC has many problems in a marine vector field. We focus on the visual quality improvement when LIC is applied in the ocean steady and unsteady flow field in the following aspects. When a white noise is used as the input in a steady flow field, interpolation is used to turn the discrete white noise into continuous white noise to solve the problem of discontinuity. The "cross" high-pass filtering is used to enhance the textures of streamlines to be more concentrated and continuity strengthened for each streamline. When a sparse noise is used as the input in a steady flow field, we change the directions of background sparse noise according to the directions of vector field to make the streamlines clearer and brighter. In addition, we provide a random initial phase for every streamline to avoid the pulsation effect during animation. The velocities of vector field are encoded in the speed of the same length streamlines so that the running speed of streamlines can express flow rate. Meanwhile, to solve the problem of obvious boundaries when stitching image, we change the streamline tracking constraints. When a white noise is used as an input in an unsteady flow field, double value scattering is used to enhance the contrast of streamlines; moreover, the "cross" high-pass filtering is also adopt instead of two-dimensional high-pass filtering. Finally, we apply the above methods to a case of the surface wave field in typhoon condition. Our experimental results show that applying the methods can generate high-quality wave images and animations. Therefore, it is helpful to understand and study waves in typhoon condition to avoid the potential harm of the waves to people's lives and property.     

Directional spectrum of wind waves: Part I—model and derivation

A new model on the directional spectrum of wind waves for deep water is proposed based on the statistics of wind waves. This model contains three parameters: the wave age, the inverse spectral bandwidth and the local spectral-peak angular frequency. The inverse spectral bandwidth is a robust parameter for describing the spectral steepness of wind waves. Using the inverse spectral bandwidth parameter, the proposed model can well describe various observations obtained from the open ocean and laboratory tank.     

Directional Spectrum of Wind Waves: Part Ⅰ- Model and Derivation

1　Introduction　Numerousinvestigationsondeepwaterwindwavespectrumhavebeen performed (Phillips ,195 8;Bretschneider,195 9;PiersonandMoscowitz ,196 4;Hasselmannetal.,1973;Donelanetal.,1985 ;Ban ner ,1990 ;Wenetal.,1999) .Ondimensionalground ,Phillips (195 8)suggestedthattheequilibriumfre quencyspectrumofwindwavesfordeepwatershouldbe proportionaltoω- 5,andthecorrespondingwavenumberspectrumshouldbe proportionaltok- 4,whereωistheangularfrequencyandkisthewavenumber.Forfully developedwindwaves…     

Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas

Some approximate formulas, based on the internal- wave directional spectral model established by Schott and Willebrand (1973), of vertically standing wavemode eigenfunctions and a dispersion relation of internal waves in shallow seas are presented. An optimization method to estimate internal wave directional spectra is described and the confidence interval expression of the estimates is established. The GM spectral model of oceanic internal waves cannot be used in shallow seas (01 bers, 1983). Internal waves in shallow seas have two origins: oceanic (those generated in and propagating from the deep sea and ocean) and local (Phillips, 1977). As both reveal obvious propagation orientations, it is important to investigate the directional properties of the internal wave field. Though cross correlation function or cross-spectrum analyses can reveal the directional properties in some degree (Fang et al., 1984, and Fang, 1987), internal- wave directional spectrum analysis can further estimate the main propagation directions of wave components with different modenumbers and frequencies. So the latter is a more effective analysis tool. Because internal- wave directional spectrum analysis requires high quality data and long computer time, there are very few study reports so far on this subject. Among them. Schott and Willebrands' (1973) work is noteworthy. On the supposition, of linearization, they derived an internal- wave directional spectrum model. Internal-wave directional-spectra in shallow seas are investigated in the present study with their work as reference. Project supported by the National Natural Science Foundation of China.     

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 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.     

Swells of the East China Sea

Over the past few decades, an increasing number of marine activities have been conducted in the East China Sea, including the construction of various marine structures and the passage of large ships. Marine safety issues are paramount and are becoming more important with respect to the likely increase in size of ocean waves in relation to global climate change and associated typhoons. In addition, swells also can be very dangerous because they induce the resonance of floating structures, including ships. This study focuses on an investigation of swells in the East China Sea and uses hindcast data for waves over the past 5 years in a numerical model, WAVEWATCH III (WW3), together with historical climate data. The numerical calculation domain covers the entire North West Pacific. Next, swells are separated and analyzed using simulated wave fields, and both the characteristics and generation mechanisms of swells are investigated.     

THE WAVE GROUPING EFFECT ON WAVE FORCES ON A VERTICAL BREAKWATER

Linear wave theory and Longuet-Higgins and Steward's (1964) group-induced second-order longweve (GSLW) theory ware used in this study on the grouping effect on wave forces acting on a verticalbreakwater. The calculated variance of total wave pressure on the vertical breakwater was closer tothe measured value if the wave grouping effect was considered.     

A new modulation transfer function for ocean wave spectra retrieval from X-band marine radar imagery

When imaging ocean surface waves by X-band marine radar,the radar backscatter from the sea surface is modulated by the long surface gravity waves. The modulation transfer function(MTF) comprises tilt,hydrodynamic,and shadowing modulations. A conventional linear MTF was derived using HH-polarized radar observations under conditions of deep water. In this study,we propose a new quadratic polynomial MTF based on VV-polarized radar measurements taken from heterogeneous nearshore wave fields. This new MTF is obtained using a radar-observed image spectrum and in situ buoy-measured wave frequency spectrum. We validate the MTF by comparing peak and mean wave periods retrieved from X-band marine radar image sequences with those measured by the buoy. It is shown that the retrieval accuracies of peak and mean wave periods of the new MTF are better than the conventional MTF. The results also show that the bias and root mean square errors of the peak and mean wave periods of the new MTF are 0.05 and 0.88 s,and 0.32 and 0.53 s,respectively,while those of the conventional MTF are 0.61 and 0.98 s,and 1.39 and 1.48 s,respectively. Moreover,it is also shown that the retrieval results are insensitive to the coefficients in the proposed MTF.     

Influence of Headland Breakwaters on Morphological Processes at Longfengtou Beach in Haitan Bay,Facing the Taiwan Strait

Breakwaters can be used as artificial headlands in beach nourishment to mitigate coastal erosion. Longfengtou Beach, located on the southwest coast of Haitan Bay facing the Taiwan Strait on the northeast, suffers severe erosion, where the monsoon causes significant season hydrodynamic variations. Headland breakwaters are intended to be employed to mitigate coastal erosion. A 2D sediment transport model is established using MIKE21 based on current-wave coupling and calibrated by measured data. Summer and winter wave conditions are chosen as characteristic weak and strong waves respectively. The numerical results of suspended sediment concentration and seasonal morphological evolution are compared under the conditions with and without the headland breakwaters. Sediment transport in summer can be regarded as mainly determined by current field, while in winter wave effect is strong enough to change current field. The northern breakwater, nearly perpendicular to the ebb current direction, obstructs the currents and decreases velocity of the ebb currents, and confines the water carrying sediments within the protection area during the flood period. The southern breakwater also breaks the waves in advance and significantly reduces the hydrodynamic effects during the flood period and maintains high suspended sediment concentration in the protection area. In general, two headland breakwaters decrease the erosion near the beach and enlarge the deposition area, which play a significant role in prevention of sediment loss in nearshore area and mitigate coastal erosion.     

Crest-height distribution of nonlinear random waves

The wave crest is an important factor for the design of both fixed and floating marine structures. Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage. Many empirical and theoretical distribution functions for wave crest heights have been proposed, but there is a lack of agreement between them. It is of significance to develop a better new nonlinear wave crest height distribution model. The progress in the research of wave crest heights is reviewed in this paper. Based on Stokes’ wave theory, an approximate nonlinear wave crest-height distribution formula with simple parameters is derived. Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail. The new crest-height distribution model agrees well with observations. Also, the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.     

Hydrodynamic conditions in front of a vertical wall with an overhanging horizontal cantilever slab

Transforming wave heights from offshore to the shoreline is the first step of any coastal engineering work. Wave breaking is analyzed to understand hydrodynamic conditions. For vertical breakwaters and sea walls, wave reflection is an important process that affects the determination of the wave height. Many of the design formulas presented in the literature depend on empirical studies based on the structures tested. In this study, the hydrodynamic conditions in front of a vertical wall with an overhanging horizontal cantilever slab with a foreshore slope of 1/20 are determined experimentally under regular wave conditions to assess the applicability of the formulas of Goda (2000) for predicting the nearshore wave height and breaker index equation (Goda, 2010). The selection of wave measurements used to determine the design wave height, the reflection coefficients, and wave breaking is also analyzed, and the reflection equations are derived from the dataset covering different breaker types. Small-scale tests show that the incident wave height is a good representative of the design wave height and that the values predicted by Goda are in good agreement with actual measurements. However, the predicted H_max values are overestimated. In addition, the inception of the wave breaking point is postponed because of the reflection and/or turbulence left over from preceding waves, which is an effect of the vertical wall. At higher water levels, the effect of the vertical wall on the inception point becomes more significant.     

Wave uplift force on horizontal panels: a laboratory study

Accurate estimation of wave uplift force is essential to the designs of reliable coastal and marine structures. We presents a series of laboratory work here on the impact of regular waves on horizontal panels, from which an empirical formula to estimate accurately the wave uplift force on panels is established. The laboratory measurements show that the wave uplift force depends mainly on the incident wave height, the wave period, the wave length, the panel width, and the clearance between the subsurface of the panel and the still water level. Among these factors, the impact of the panel width on uplift forces is relatively complicated. Result shows that the relative panel width(i.e., the ratio of panel width to wave length) plays a more important role in estimating the wave uplift force. Based on our comprehensive laboratory measurements, we further developed an empirical formula to compute wave uplift force on horizontal panels through dimensionless analysis. Compared with other empirical formulas, this formula uses dimensionless variables of clear physical meanings, thus can describe the interaction between waves and the panels in a better way. In addition, the efficiency of the formula to estimate wave uplift force on horizontal panels is verified against existing works. Therefore, the findings in this study shall be useful for understanding the mechanism of wave uplift force on horizontal panels and numerical model validation.