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The main objective of this paper is to examine the influences of both the principal wave direction and the directional spreading parameter of the wave energy on the wave height evolution of multidirectional irregular waves over an impermeable sloping bottom and to propose an improved wave height distribution model based on an existing classical formula. The numerical model FUNWAVE 2.0, based on a fully nonlinear Boussinesq equation, is employed to simulate the propagation of multidirectional irregular waves over the sloping bottom. Comparisons of wave heights derived from wave trains with various principal wave directions and different directional spreading parameters are conducted. Results show that both the principal wave direction and the wave directional spread have significant influences on the wave height evolution on a varying coastal topography. The shoaling effect for the wave height is obviously weakened with the increase of the principal wave direction and with the decrease of the directional spreading parameter. With the simulated data, the classical Klopman wave height distribution model is improved by considering the influences of both factors. It is found that the improved model performs better in describing the wave height distribution for the multidirectional irregular waves in shallow water.

In the present study, the performance characteristics of a Savonius rotor type wave energy converter used in conjunction with a conventional double-buoy floating breakwater is investigated using physical model studies. The Savonius rotor type converter is suspended under the double-buoy floating breakwater to achieve wave attenuation while generating electricity, thereby enhancing the overall wave-elimination effect of the combination. The Savonius rotor is tested with different water submergence depths, and a reasonable relative submergence depth is determined within the scope of the research parameters. The hydrodynamics and energy capture performance of the combined breakwater with four different sizes of Savonius rotor under different wave conditions are studied, and the transmission coefficient of the experimental device is analyzed. The results show that when the optimal relative submergence depth is 0.65D, where D is the impeller diameter, there is a correspondence between the optimal performance of Savonius rotor with different rotor sizes and the wave period and wave height. The optimal energy capture efficiency of the wave energy converter reaches 17%–20.5%, and the transmission coefficient is reduced by 35%–45% compared with the conventional double-buoy breakwater.

Wave forces acting on a vertical cylinder at different locations on a slope beach in the near-shore region are investigated considering solitary waves as incoming waves. Based on the Reynolds-averaged Navier-Stokes equations and the k-e turbulence model, wave forces due to the interaction between the solitary wave and cylinder are simulated and analyzed with different incident wave heights and cylinder locations. The numerical results are first compared with previous theoretical and experimental results to validate the model accuracy. Then, the wave forces and characteristics around the cylinder are studied, including the velocity field, wave surface elevation and pressure. The effects of relative wave height, Keulegan-Carpenter (KC) number and cylinder locations on the wave forces are also discussed. The results show that the wave forces exerted on a cylinder exponentially increase with the increasing incident wave height and KC number. Before the wave force peaks, the growth rate of the wave force shows an increasing trend as the cylinder moves onshore. The cylinder location has a notable effect on the wave force on the cylinder in the near-shore region. As the cylinder moves onshore, the wave force on the cylinder initially increases and then decreases. For the cases considered here, the maximum wave force appears when the cylinder is located one cylinder diameter below the still-water shoreline. Furthermore, the fluid velocity peaks when the maximum wave force appears at the same location.

A structure scheme of a pile-based breakwater with integrated oscillating water column (OWC) energy conversion chamber was proposed, and four structure forms had been designed. Based on the physical test, the variations of the reflected wave height, the transmitted wave height, the air velocity at the outlet of the chamber, the air pressure and the wave height in the air chamber were studied under the conditions of different wave heights, periods, with or without elliptical front wall and the baffles on both sides of the chamber. Moreover, based on the results, the changes and relationship between the wave-eliminating effect and energy conversion effect of the scheme were analyzed. In general, it turns out, the transmission coefficients of the four structure forms are kept below 0.5. Furthermore, the transmission coefficients of the structural forms G2, G3, and G4 were all smaller than 0.4, and it is only 0.1 at its smallest. Thereinto, in general, the structure form G4 has the best wave-eliminating and energy conversion performance. At the same time, when the wave steepness is 0.066, the energy conversion and wave dissipation effect of the four structure forms is the best. The research results could be provided as the reference for the design structure selection of pile-based breakwater with integrated OWC energy conversion chamber.

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 (3D) 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.

Large-scale interceptors constitute the main structure of offshore self-driven floating marine litter collection devices, and the structural stability of such interceptors under the action of waves directly influences the overall safety of the device. When the ratio of the diameter of a horizontal cylinder in such interceptors to the incident wavelength is larger than 0.25, the wave force can be calculated by using the diffraction theory, by considering the problem as that of the interaction between the waves and a partially immersed large-scale horizontal cylinder. In this study, an analytical approach to calculate the wave force on a partially immersed large-scale horizontal cylinder was formulated by using the stepwise approximation method. Physical model tests were conducted to investigate the effects of different factors (wave height, period, and immersion depth) on the wave force on a large-scale horizontal cylinder under conditions involving short-period waves. The results show that both horizontal and vertical wave forces on the cylinder increase as the wave height (immersion depth) increases in most cases. The vertical wave force decreases with the decrease of the period. For the horizontal wave force, it increases with the decrease of the period when the wavelength is larger than the diameter of the cylinder and decreases with the decrease of the period when the wavelength is smaller than the diameter of the cylinder.

Interstitial flows in breakwater cores and seabeds are a key consideration in coastal and marine engineering designs and have a direct impact on their structural safety. In this paper, a unified fully coupled model for wave-permeable breakwater-porous seabed interactions is built based on an improved N-S equation. A numerical wave flume is constructed, and numerical studies are carried out by applying the finite difference method. In combination with a physical model test, the accuracy of the numerical simulation results is verified by comparing the calculated and measured values of wave height at measurement points and the seepage pressure within the breakwater and seabed. On this basis, the characteristics of the surrounding wave field and the internal flow field of the pore structure, as well as the evolution process of the fluctuating pore water pressure inside the breakwater and seabed, are further analyzed. The spatial distribution of the maximum fluctuating pore water pressure in the breakwater is compared between two cases by considering whether the seabed is permeable, and then the effect of seabed permeability on the dynamic pore water pressure in the breakwater is clarified. This study attempts to provide a reference for breakwater design and the protection of nearby seabeds.

This paper proposes an equation to calculate breaking wave induced wave set-up and set-down along reef flat. The mathematical equation was derived based on the theory of radiation stress and the conservation of wave energy. The equation is primarily determined by several physical variables including the breaking wave index, the stable wave index, the attenuation coefficient of wave energy flux, and the flow velocity in the re-stabilization zone. A series of laboratory experiments were carried out to calibrate the theoretical equations. Specifically, the breaking wave index, the stable wave index, and the velocity over the reef flat were measured in the laboratory. The attenuation coefficient of wave energy flux in our theoretical equation was determined by calibration by comparing with the laboratory measured wave height. Furthermore, it has been put forward that the velocity based on cnoidal wave theory could be used to determine the velocity over the reef flat if there is no velocity measurement available. Overall, the proposed equation can provide satisfactory prediction of wave set-up and set-down along the reef flat.

Based on potential flow theory, a dissipative semi-analytical solution is developed for the wave resonance in the narrow gap between a fixed floating box and a vertical wall by using velocity potential decompositions and matched eigenfunction expansions. The energy dissipation near the box is modelled in the potential flow solution by introducing a quadratic pressure loss condition on the gap entrance. Such a treatment is inspired by the classical local head loss formula for the sudden change of cross section in channel flow, where the energy dissipation is assumed to be proportional to the square of local velocity for high Reynolds number flows. The dimensionless energy loss coefficient is calibrated based on experimental data. And it is found to be insensitive to the incident wave height and wave frequency. With the calibrated energy loss coefficient, the resonant wave height in gap and the reflection coefficient are calculated by the present dissipative semi-analytical solution. The predictions are in good agreement with experimental data. Case studies suggest that the maximum relative energy dissipation occurs near the resonant frequency, which leads to the minimum reflection coefficient. The horizontal wave forces on the box and the vertical wall attain also maximum values near the resonant frequency, while the vertical wave force on the box decreases abruptly there to a small value.

The interaction between structure and wave is a typical phenomenon in naval architecture and ocean engineering. In this paper, numerical simulation is carried out to study the interaction between a two-dimensional submerged, fixed, horizontal rigid plate and solitary wave with our in-house meshless particle CFD solver MLParticle-SJTU. First, the in-house CFD solver is verified by experimental results conducted at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology. During the verification, the plate is submerged under water and the solitary wave with a given amplitude is generated by a piston-type wave maker. Free surface elevation of the wave and the pressure impacting on the plate is recorded and compared with experimental data respectively. The predicted pressure and surface elevation agree well with the experimental results. Then in order to further investigate factors affecting wave-structure interaction, wave height, submerged depth and plate length are analyzed.

Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which considers nonlinear interactions between waves and the arc-plate breakwater, has been constructed by using the velocity wavegenerating method, the volume of fluid (VOF) method and the finite volume method. The results show that the relative width, relative height and relative submergence of the breakwater are three main influencing factors and have significant influence on wave energy dissipation of the lower arc-plate open breakwater. The transmission coefficient is found to decrease with the increasing relative width, and the minimum transmission coefficient is 0.15 when the relative width is 0.45. The reflection coefficient is found to vary slightly with the relative width, and the maximum reflection coefficient is 0.53 when the relative width is 0.45. The transmission and reflection coefficients are shown to increase with the relative wave height for approximately 85% of the experimental tests when the relative width is 0.19−0.45. The transmission coefficients at relative submergences of −0.04, −0.02 and 0 are clearly shown to be greater than those at relative submergences of 0.02 and 0.04, while the reflection coefficient exhibits the opposite relationship. After the wave interacts with the lower arc-plate breakwater, the wave energy is mainly converted into transmission, reflection and dissipation energies. The wave attenuation performance is clearly weakened for waves with greater heights and longer periods.

An offshore shoal or bar refracts ocean surface waves and causes wave focusing/defocusing on the adjacent beach. Wave focal patterns characterized by alongshore variations in wave height, wave angle, and breaking location induce alongshore non-uniformities of wave setup and nearshore circulation, e.g., rip currents and alongshore currents, in the surfzone. A simplified analytic model for nearshore circulation generated by focused/defocused waves on a planar beach is developed and theoretical solutions are obtained using transport stream function and perturbations in alongshore distributions of wave height and wave angle at the breaker line. The analytic model suggests that alongshore currents are strongly affected by a pair of counter-rotating vortices generated shoreward of the wave focal zone. The vortices are persistent, and their strengths depend on the amplitudes of alongshore variations in wave height and wave angle. The alongshore gradient in wave height tends to intensify the vortices while the convergence of wave angle tends to weaken the vortices. Divergent flows associated with the vortices in the surfzone are intense, strengthening alongshore currents in the downstream of the wave focal zone and weakening alongshore currents or causing flows reversal in the upstream. Alongshore currents are modulated by rip currents associated with the wave focusing/defocusing patterns.

The extraordinary transmission (ET) phenomenon is examined for waves propagating through gaps of vertical thin barriers in channels with a hypersingular boundary element method model on the linear potential theory, and an estimate formula based on small gap approximation for predicting the number of ET frequencies is proposed. Numerical computations are carried out to examine the influences of barrier number, barrier interval, gap size, gap position and barrier arrangement on extraordinary transmission and wave height in the channel. It shows that all of those factors evidently affect the extraordinary transmission frequencies. The contours of wave amplitude show that very high waves can be excited in the basins between barriers at the extraordinary transmission frequencies. Proper arrangement of barriers in a channel can avoid the occurrence of ET phenomenon and reduce wave height in the channel.

To evaluate the trapped wave energy and energy loss, the problem of wave scattering by twin fixed vertical surfacepiercing plates over a stepped bottom is numerically simulated using the open source package OpenFOAM and the associated toolbox waves2Foam. The volume of fluid (VOF) method was employed to capture the free surface in the time domain. The validation of the present numerical model was performed by comparing with both the analytical and experimental results. The effects of the spacing between two plates and the configuration of stepped bottom on the hydrodynamic characteristics, such as reflection and transmission coefficients, viscous dissipation ratio, and relative wave height between the plates (termed as trapped wave energy), were examined. Moreover, the nonlinear effects of the incident wave height on the hydrodynamic characteristics were addressed as well. The results show that the step configuration can be tuned for efficient-performance of wave damping, and the optimum configurations of the step length B, the step height h1 and the spacing b, separately equaling λ/4, 3h/4, and 0.05h (λ and h are the wavelength and the water depth, respectively), are recommended for the trapping of wave energy.

In this paper, we establish a generalized extreme Value-Pareto distribution model and derive an analytical expression of Weibull–Pareto distribution model. Based on a data sample of 26-year wave height, we adopt the new model to estimate the design wave height for 500, 700 and 1000-year return periods. Results show that the design wave height from Weibull–Pareto distribution is between that of the Weibull distribution and that of the Pearson-III distribution. For the 500-year return period design wave height, the results from the new model is 1.601% lower than those from the Weibull distribution and 1.319% higher than those from the Pearson-III distribution. The Weibull–Pareto distribution innovatively considers the fractal features, extreme-value statistics and the truncated data in the derivation process. Therefore, it is a more holistic and practical model for estimating the design parameters in marine and coastal environments.

The PDFs (probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA (2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship's manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.

Wave energy is an important type of marine renewable energy. A wave energy converter (WEC) moored with two floating bodies was developed in the present study. To analyze the dynamic performance of the WEC, an experimental device was designed and tested in a tank. The experiment focused on the factors which impact the motion and energy conversion performance of the WEC. Dynamic performance was evaluated by the relative displacements and velocities of the oscillator and carrier which served as the floating bodies of WEC. Four factors were tested, i.e. wave height, wave period, power take-off (PTO) damping, and mass ratio (R M) of the oscillator and carrier. Experimental results show that these factors greatly affect the energy conversion performance, especially when the wave period matches R M and PTO damping. According to the results, we conclude that: (a) the maximization of the relative displacements and velocities leads to the maximization of the energy conversion efficiency; (b) the larger the wave height, the higher the energy conversion efficiency will be; (c) the relationships of energy conversion efficiency with wave period, PTO damping, and R M are nonlinear, but the maximum efficiency is obtained when these three factors are optimally matched. Experimental results demonstrated that the energy conversion efficiency reached the peak at 28.62% when the wave height was 120 mm, wave period was 1.0 s, R M was 0.21, and the PTO damping was corresponding to the resistance of 100 Ω.

A series of physical tests are conducted to examine the characteristics of the wave loading exerted on circular-front breakwaters by regular waves. It is found that the wave trough instead of wave crest plays a major role in the failure of submerged circular caissons due to seaward sliding. The difference in the behavior of seaward and shoreward horizontal wave forces is explained based on the variations of dynamic pressure with wave parameters. A wave load model is proposed based on a modified first-order solution for the dynamic pressure on submerged circular-front caissons under a wave trough. This wave loading model is very useful for engineering design. Further studies are needed to include model uncertainties in the reliability assessment of the breakwater.

The interaction between waves and porous breakwater has an important theoretical significance and great application value of engineering. In this paper, the tests of the core material’s influence in rubble mound breakwater on wave propagation are carried out. The relations among the transmitted wave height, incident wave element, and breakwater width are discussed. The calculation formula is obtained. The test results show that different core materials have obvious influence on wave propagation.

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.

Attenuations of solitary wave over a patch of submerged canopy are experimentally investigated. The submerged canopy is modeled by a group of circular cylinder array. The decay coefficients of different wave heights in two water depths along the wave flume are measured for six canopy models, including two canopy heights and three styles of arrangements. The relationships among the decay coefficient, and the dimensionless wave height, submergence ratio, relative height and arrangement of the canopy are experimentally studied. 2D PIV technique is employed to measure the representative flow field inside the canopy. A four-deck flow structure is proposed for wave flow field over shallow submerged canopy. The characteristics of shear flow inside the aligned canopy region are discussed.

This paper introduces a newly developed Unmanned Wave Glide Vehicle (UWGV), which is driven only by extracting energy from gravity waves, and presents a comprehensive study on the propulsion performance of the UWGV’s propulsor―Wave Glide Propulsor (WGP) in a regular wave. By simplifying the WGP as six 2D tandem asynchronous flapping foils (TAFFs), a CFD method based on Navier–Stokes equations was first used to analyze the hydrodynamic performance of TAFFs with different parameters of non-dimensional wave length m and non-dimensional wave height n. Then, a series of hydrodynamic experiments were performed. The computational results agree well with the experimental results when n≤0.07 and both of them show the thrust force and input power of the WGP are larger at smaller m or larger n. By analyzing the flow field of TAFFs, we can see that a larger m is beneficial to the forming, merging and shredding of the TAFFs’ vortices; as TAFFs are arranged in tandem and have the same motions, the leading edge vortex and wake vortex of the TAFFs are meaningful for improving the thrust force of their adjacent ones.

The modified versions of the linear theoretical model of Longuet-Higgins (1983) are derived in this work and also compared with the laboratory experiments carried out in MARINTEK. The main feature of modifications is to replace the mean frequency in the formulation with the peak frequency of the wave spectrum. These two alternative forms of joint distributions are checked in three typical random sea states characterized by the initial wave steepness. In order to further explore the properties of these models, the associated marginal distributions of wave heights and wave periods are also researched with the observed statistics and some encouraging results are obtained.

Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device (CCD) camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.

In this paper, a wave generating approach for long-crest irregular waves in a numerical tank by our in-house solver naoe-FOAM-SJTU is presented. The naoe-FOAM-SJTU solver is developed using an open source tool kit, OpenFOAM. Reynolds-averaged Navier-Stokes (RANS) equations are chosen as governing equations and the volume of fluid (VOF) is employed to capture the two phases interface. Incoming wave group is generated by imposing the boundary conditions of the tank inlet. A spectrum based correction procedure is developed to make the measured spectrum approaching to the target spectrum. This procedure can automatically adjust the wave generation signal based on the measured wave elevation by wave height probe in numerical wave tank. After 3 to 4 iterations, the measured spectrum agrees well with the target one. In order to validate this method, several wave spectra are chosen and validated in the numerical wave tank, with comparison between the final measured and target spectra. In order to investigate a practical situation, a modified Wigley hull is placed in the wave tank with incoming irregular waves. The wave-induced heave and pitch motions are treated by Fourier analysis to obtain motion responses, showing good agreements with the measurements.

In the design process of berm breakwaters, their front slope recession has an inevitable rule in large number of model tests, and this parameter being studied. This research draws its data from Moghim’s and Shekari’s experiment results. These experiments consist of two different 2D model tests in two wave flumes, in which the berm recession to different sea state and structural parameters have been studied. Irregular waves with a JONSWAP spectrum were used in both test series. A total of 412 test results were used to cover the impact of sea state conditions such as wave height, wave period, storm duration and water depth at the toe of the structure, and structural parameters such as berm elevation from still water level, berm width and stone diameter on berm recession parameters. In this paper, a new set of equations for berm recession is derived using the M5' model tree as a machine learning approach. A comparison is made between the estimations by the new formula and the formulae recently given by other researchers to show the preference of new M5' approach.

This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.

Simulation of solitary wave run-up on a vertical circular cylinder is carried out in a viscous numerical wave tank developed based on the open source codes OpenFOAM. An incompressible two-phase flow solver naoe-FOAM-SJTU is used to solve the Reynolds-Averaged Navier-Stokes (RANS) equations with the SST k-ω turbulence model. The PISO algorithm is utilized for the pressure-velocity coupling. The air-water interface is captured via Volume of Fluid (VOF) technique. The present numerical model is validated by simulating the solitary wave run-up and reflected against a vertical wall, and solitary wave run-up on a vertical circular cylinder. Comparisons between numerical results and available experimental data show satisfactory agreement. Furthermore, simulations are carried out to study the solitary wave run-up on the cylinder with different incident wave height H and different cylinder radius a. The relationships of the wave run-up height with the incident wave height H, cylinder radius a are analyzed. The evolutions of the scattering free surface and vortex shedding are also presented to give a better understanding of the process of nonlinear wave-cylinder interaction.

A new method of treating maximum wave height as a random variable in reliability analysis of breakwater caissons is proposed. The maximum wave height is expressed as the significant wave height multiplied by the so-called wave height ratio. The proposed wave height ratio is a type of transfer function from the significant wave height to the maximum wave height. Under the condition of a breaking wave, the ratio is intrinsically nonlinear. Therefore, the probability density function for the variable cannot be easily defined. In this study, however, it can be derived from the relationship between the maximum and significant waves in a nonbreaking environment. Some examples are shown to validate the derived probability density function for the wave ratio parameter. By introducing the wave height ratio into reliability analysis of caisson breakwater, the maximum wave height can be used as an independent and primary random variable, which means that the risk of caisson failure during its lifetime can be evaluated realistically.

A new load surface based approach to the reliability analysis of caisson-type breakwater is proposed. Uncertainties of the horizontal and vertical wave loads acting on breakwater are considered by using the so-called load surfaces, which can be estimated as functions of wave height, water level, and so on. Then, the first-order reliability method (FORM) can be applied to determine the probability of failure under the wave action. In this way, the reliability analysis of breakwaters with uncertainties both in wave height and in water level is possible. Moreover, the uncertainty in wave breaking can be taken into account by considering a random variable for wave height ratio which relates the significant wave height to the maximum wave height. The proposed approach is applied numerically to the reliability analysis of caisson breakwater under wave attack that may undergo partial or full wave breaking.

Based on one-year wave field data measured at the south part of the radial sand ridges of the Southern Yellow Sea, the wave statistical characteristics, wave spectrum and wave group properties are analyzed. The results show that the significant wave height (H1/3) varies from 0.15 to 2.22 m with the average of 0.59 m and the mean wave period (Tmean) varies from 2.06 to 6.82 s with the average of 3.71 s. The percentage of single peak in the wave spectra is 88.6 during the measurement period, in which 36.3% of the waves are pure wind waves and the rest are young swells. The percentage with the significant wave height larger than 1 m is 12.4. The dominant wave directions in the study area are WNW, W, ESE, E and NW. The relationships among the characteristic wave heights, the characteristic wave periods, and the wave spectral parameters are identified. It is found that the tentative spectral model is suitable for the quantitative description of the wave spectrum in the study area, while the run lengths of the wave group estimated from the measured data are generally larger than those in other sea areas.

In order to study the mechanism of flow-sediment movement, it is essential to obtain measured data of water hydrodynamic and sediment concentration process with high spatial and temporal resolution in the bottom boundary layer (BBL). Field observations were carried out in the northwest Caofeidian sea area in the Bohai Bay. Near 2 m isobath (under the lowest tidal level), a tripod system was installed with AWAC (Acoustic Wave And Current), ADCP (Acoustic Doppler Current Profilers), OBS-3A (Optical Backscatter Point Sensor), ADV (Acoustic Doppler Velocimeters), etc. The accurate measurement of the bottom boundary layer during a single tidal period was carried out, together with a long-term sediment concentration measurement under different hydrological conditions. All the measured data were used to analyze the characteristics of wave-current-sediment movement and the BBL. Analysis was performed on flow structure, shear stress, roughness, eddy viscosity and other parameters of the BBL. Two major findings were made. Firstly, from the measured data, the three-layer distribution model of the velocity profiles and eddy viscosities in the wave-current BBL are proposed in the observed sea area; secondly, the sediment movement is related closely to wind-waves in the muddy coast area where sediment is clayey silt: 1) The observed suspended sediment concentration under light wind conditions is very low, with the peak value generally smaller than 0.1 kg/m3 and the average value being 0.03 kg/m3; 2) The sediment concentration increases continuously under the gales over 6–7 in Beaufort scale, under a sustained wind action. The measured peak sediment concentration at 0.4 m above the seabed is 0.15–0.32 kg/m3, and the average sediment concentration during wind-wave action is 0.08–0.18 kg/m3, which is about 3–6 times the value under light wind conditions. The critical wave height signaling remarkable changes of sediment concentration is 0.5 m. The results show that the suspended load sediment concentration is mainly influenced by wave-induced sediment suspension.

In using the PGCEVD (Poisson-Gumbel Compound Extreme Value Distribution) model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution (P-III) model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.

Based on rigid kinematics theory and lumped mass method, a mathematical model of the two net cages of grid mooring system under waves is developed. In order to verify the numerical model, a series of physical model tests have been carried out. According to the comparisons between the simulated and the experimental results, it can be found that the simulated and the experimental results agree well in each wave condition. Then, the forces on the mooring lines and the floating collar movement are calculated under different wave conditions. Numerical results show that under the same condition, the forces on the bridle ropes are the largest, followed by forces on the main ropes and the grid ropes. The horizontal and the vertical float collar motion amplitudes increase with the increase of wave height, while the relationship of the horizontal motion amplitude and the wave period is indistinct. The vertical motion amplitude of the two cages is almost the same, while on the respect of horizontal motion amplitude, cage B (behind cage A, as shown in Fig. 4) moves much farther than cage A under the same wave condition. The inclination angle of the floating system both in clockwise along y axis and the counter one enlarges a little with the increase of wave height.

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.

In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, were used to calculate the wave height transformation and the mean water level change around a submerged breakwater. The numerical solution is verified with experimental data. The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall. In contrast to cases without a seawall, the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall. Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater. We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.

The wave transmission characteristics and wave induced pressures on twin plate breakwater are investigated experimentally in regular and random waves. A total of twenty pressure transducers are fixed on four surfaces of twin plate to measure the wave induced dynamic pressures. The spatial distribution of dynamic wave pressure is given along the surface of the twin plate. The uplift wave force obtained by integrating the hydrodynamic pressure along the structure is presented. Discussed are the influence of different incident wave parameters including the relative plate width B/L, relative wave height Hi/a and relative submergence depth s/a on the non-dimensional dynamic wave pressures and total wave forces. From the investigation, it is found that the optimum transmission coefficient, Kt occurs around B/L = 0.41∼0.43, and the twin plate breakwater is more effective in different water depths. The maximum of pressure ratio decreases from 1.8 to 1.1 when the relative submergence depth of top plate is increased from −0.8 to +0.8.