Experimental Researches on Reflective and Transmitting Performances of Quarter Circular Breakwater Under Regular and Irregular Waves

A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater （QCB） in comparison with those of semi-circular breakwater （SCB）. Based on regular wave tests, the reflection and transmission characteristics of QCB are analyzed and a few influencing factors are investigated. Then, the wave energy dissipation as wave passing over the breakwater is discussed based on the hydraulic coefficients of QCB and SCB. In irregular wave experiments, the reflection coefficients of QCB and their spectrums are studied. Finally, the comparisons between the experimental results and numerical simulations for QCB under regular and irregular wave conditions are presented.

Reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core

The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.

Impact Pressure of Incident Regular Waves and Irregular Waves on the Subface of Open-Piled Structures

This paper presents the results of comparison of impact pressures on open-plied structures induced by regular waves and irregular waves in a laboratory channel. Regular waves with wave heights ranging from 0.1～0.2 m and periods ranging from 1.0～2.0 s are tested. The target spectrum for the irregular wave is JONSWAP spectrum. Irregular waves with significant wave heights in the range of 0.10～0.25 m and peak periods in the range of 1.0～2.0 s are tested. The relative clearance s/H 1/3(H) is between -0.1 and 0.4, s being the subface level of structure model above the still water level. Time series of impact pressure are analyzed to indicate whether the property of impact pressures induced by the regular wave significantly deviates from that by the irregular wave. The distribution of the impact pressure along the underside of the structure is compared for different types of incident waves. The effects of wave parameters, structure dimension and structure clearance on the impact pressure are also discussed.

RANSE Simulation of High-speed Planning Craft in Regular Waves

This paper presents a study on the numerical simulation of planing crafts sailing in regular waves. This allows an accurate estimate of the seas keeping performance of the high speed craft. The simulation set in six-degree of freedom motions is based on the Reynolds averaged Navier Stokes equations volume of fluid （RANSE VOF） solver. The trimming mesh technique and integral dynamic mesh method are used to guarantee the good accuracy of the hydrodynamic force and high efficiency of the numerical simulation. Incident head waves, oblique waves and beam waves are generated in the simulation with three different velocities （Fn =1.0, 1.5, 2.0）. The motions and sea keeping performance of the planing craft with waves coming from different directions are indicated in the flow solver. The ship designer placed an emphasis on the effects of waves on sailing amplitude and pressure distribution of planing craft in the configuration of building high speed crafts.

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

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

Numerical Prediction of Regular Wave Breaking on Very Gentle Slopes

Regular wave deformation and breaking on very gentle slopes is calculated by Mixed-Eulerian-Lagrangian procedure. The velocity potentials and their normal derivatives on the boundary are calculated through the mixed 0-1 boundary element method. The wave elevation and the potentials of Lime-stepping integration are determined by the 2nd-order Taylor expansion at the nodes of free surface boundary elements. During calculation the x-coordinates of the free surface element nodes are supposed to remain unchanged, i.e. the partial derivatives of wave elevation and potentials with respect to x are considered as zero. The numerical results of asymmetric parameters of breaking waves are verified by experimental study. It is shown that when the wave asymmetry is weak, the maximum horizontal velocity of water particales occurs at the wave peak and, the average ratio of this maximum velocity to wave celerity is 0.96. However, when the wave asymmetry is strong, the maximum horizontal velocity of water particles occurs just before the wave crest, and the average ratio of the maximum velocity to wave celerity is about 0.98. The numerical results also show that the asymmetry of wave profiles affects the value of the wave breaking index (H/d) (b), that is, when the asymmetric characteristics are weak, the value of wave breaking index coincides with that given by Goda; on the contrary, when the asymmetry of wave profiles is notable, the value of wave breaking index is close to Nelson's result. The experimental study gives the same conclusions.

FORCES ON CYLINDERS IN COEXISTING FIELD OF REGULAR WAVES AND CURRENTS

Based on the linear wave theory, the lift force on the cylinder under the action of both regular waves and currents related to inline force and the resultant force has been investigated. The relationship between the hydrodynamic coefficients of resultant force Cf, of drag force Cd, of inertia force Cm and of lift force CL and the redefined KC number is reported. It is indicated that in a certain region of KC number, the influence of lift force on the resultant force can not be ignored.

Experimental Investigation of the Response of Monopiles in Silty Seabed to Regular Wave Action

Excessive displacement responses of monopiles affect the serviceability of offshore structures.Related to complicated pile−seabed−wave interactions,the actual behavior of monopiles in silty seabed under periodic wave action remains unclear,and relevant studies in the literature are limited.A series of experiments were conducted in a wave flume containing single piles in silty seabed with relative density of 0.77 subjected to regular waves.Two stages of wave loading were applied successively,accompanied by data recording which included pore water pressure,water surface elevation,pile head displacement,and pile strain.Development of pile-head displacement and pore pressure in silty seabed was the main focus,but the effects of pile diameter,pile type,and pile stiffness were also investigated.The experimental results indicate that,in silty seabed,piles of large diameter or with fins accelerate soil liquefaction,resulting in strengthened soil which allows a higher upper boundary of pore pressure.Using fins at deeper locations led to a quick failure of the piles,but the opposite result was observed with an increase in fin dimensions.Once pile-head displacement entered its rapid development period,the wave load calculated via the pile moment was an overestimation,especially for the piles of large diameter.

Experimental Study of Dissolved Oxygen Transport by Regular Waves Through a Perforated Breakwater

The perforated breakwater is an environmentally friendly coastal structure, and dissolved oxygen concentration levels are an important index to denote water quality. In this paper, oxygen transport experiments with regular waves through a vertical perforated breakwater were conducted. The oxygen scavenger method was used to reduce the dissolved oxygen concentration of inner water body with the chemicals Na2SO3 and COC12. The dissolved oxygen concentration and wave parameters of 36 experimental scenarios were measured with different perforated arrangements and wave conditions. It was found that the oxygen transfer coefficient through wave surface, K1α1, is much lower than the oxygen transport coefficient through the perforated breakwater, K2α2. If the effect of K1α1 is not considered, the dissolved oxygen concentration computation for inner water body will not be greatly affected. Considering the effect of a permeable area ratio a, relative location parameter of perforations 6 and wave period T, the aforementioned data of 30 experimental scenarios, the dimensional analysis and the least squares method were used to derive an equation of K2α2 （K2α2=0.0042aσ56δ2T1）. It was validated with 6 other experimental scenarios data, which indicates an approximate agreement. Therefore, this equation can be used to compute the DO concentration caused by the water transport through perforated breakwater.

Experimental Study on Coupled Motions of Mother Ship Launching and Recovering of Human-Occupied Vehicle in Regular Waves

The launching and recovery process of a human-occupied vehicle(HOV)faces more complex wave effects than other types of submersible operations.However,due to the nonlinearity between the HOV and its mother ship,difficulties occur in theoretically simulating their coupled motion and hydrodynamics.The coupled motion responses and the load under different regular wave conditions are investigated experimentally in this study.The optimized design of the experimental scheme simulated the launching and recovery process of the mother ship and HOV in regular waves.The attitude sensor performed synchronous real-time measurement of the coupled motion between the mother ship and HOV as well as obtained the load data on the coupled motion under different cable lengths.The results show that models in heading waves mainly lead to the vertical motion of the hoisting point.In beam waves,the transverse and vertical motions of the hoisting point occur in a certain frequency of waves.Under the heading and beam wave conditions,the longer the hoisting cable is,the greater the movement amplitude of the submersible is.Moreover,compared with the condition of the beam waves,the hoisting submersible has less influence on the mother ship under the condition of the heading waves.The findings provide theoretical support for the design optimization of the launching and recovery operation.

Hydrodynamic Coefficient Investigation on a Partial Permeable Stepped Breakwater Under Regular Waves

Traditional breakwater takes the advantage of high protection performance and has been widely used.However,it contributes to high wave reflection in the seaside direction and poor water exchange capacity between open seawater and an inside harbor.Consequently,a partially permeable stepped breakwater(PPSB)is proposed to ensure safety and good water exchange capacity for an inside harbor,and a 3-D computational fluid dynamics(CFD)mathematical model was used to investigate the hydrodynamic coefficients using Reynolds-Averaged Navier-Stokes equations,Re-Normalization Group(RNG)k-εequations,and the VOF technique.A series of experiments are conducted to measure the wave heights for validating the mathematical model,and a series of dimensionless parameters considering wave and PPSB effects were presented to assess their relationships with hydrodynamic coefficients,respectively.With the increase in the reciprocal value of PPSB slope,incident wave steepness and permeable ratio below still water level(SWL),the wave reflection coefficient decreases.The wave transmission coefficient decreases with an increase in the reciprocal value of the PPSB slope and incident wave steepness;however,it increases with the increase in the permeable ratio below SWL.With increases in the reciprocal value of the PPSB slope,permeable ratio below SWL and incident wave steepness for relatively high wave period scenarios,the wave energy dissipation coefficient increases;however,it decreases slightly with increases in the incident wave steepness for the smallest wave period scenarios.Furthermore,simple prediction formulas are conducted for predicting the hydrodynamic coefficients and they are well validated with the related data.

Experimental observation on water entry of a sphere in regular wave

This paper presents a novel experiment to observe the whole water entry process of a free-falling sphere into a regular wave.A time-accurate synchronizing system modulates the moment elaborately to ensure the sphere impacting onto the water surface at the desirable wave phase.Four high-speed cameras focus locally to measure the high-precision size of the cavity evolution.Meanwhile,the aggregated field view of the camera array covers both the splash above the free surface and the entire cavity in the wave.The detailed methodologies are described and verified for the hardware set-up and the image post-processing.The theoretical maximum deviation is 1.7%on the space scale.The integral morphology of the cavity is captured precisely in the coordinate system during the sphere penetrates through the water at four representative wave phases and the still water.The result shows that the horizontal velocity of the fluid particle in the wave impels the cavity and changes the shape distinctly.Notably,the wave motion causes the cavity to pinch offearlier at the wave trough phase and later at the wave crest phase than in the still water.The wave motion influences the falling process of the sphere slightly in the present parameters.

Numerical Investigation of Run-ups on Cylinder in Steep Regular Wave

The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylinder by solving the Navier-Stokes equations. A numerical wave tank is established based on the open-source package to simulate the wave scattering induced by a vertical cylinder. The VOF method is applied to capture the large deformation and breaking of the free surface. The numerical model is validated by experimental results. The relative wave run-ups on the front face and the back face along the centerline of a cylinder are analyzed. The changes of the relative run-ups with the wave steepness, the relative diameter and the relative depth are studied. It is found that the relative run-ups on the front face and the back face of the cylinder depend mainly on the wave steepness and the relative diameter, while the dependence on the relative depth is weak. The empirical formulae are proposed to calculate the relative run-ups in terms of the wave steepness of incident regular waves and the relative diameter of a cylinder.

Applying Finite Difference Method to Simulate the Performance of a Perforated Breakwater Under Regular Waves

Using a discretized finite difference method, a numerical model was developed to study the interaction of regular waves with a perforated breakwater. Considering a non-viscous, non-rotational fluid, the governing equations of Laplacian velocity potential were developed, and specific conditions for every single boundary were defined. The final developed model was evaluated based on an existing experimental result. The evaluated model was used to simulate the condition for various wave periods from 0.6 to 2 s. The reflection coefficient and transmission coefficient of waves were examined with different breakwater porosities, wave steepnesses, and angular frequencies. The results show that the developed model can suitably present the effect of the structural and hydraulic parameters on the reflection and transmission coefficients. It was also found that with the increase in wave steepness, the reflection coefficient increased logarithmically, while the transmission coefficient decreased logarithmically.

Performance Evaluation of Bottom-Standing Submerged Breakwaters in Regular Waves Using the Meshless Singular Boundary Method

In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. Both the single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. Only the impermeable breakwaters are considered in this study. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with the appropriate mixed-type boundary conditions, and it is solved numerically using the ISBM. The numerical results are presented in terms of the hydrodynamic quantities of reflection and transmission coefficients. The values are first validated against the data of previous studies, computed, and discussed for a variety of structural conditions, including the height, width, and spacing of breakwater submergence. An excellent agreement is observed between the ISBM results and those of other methods. The breakwater width is found to feature marginal effects compared with the height. The present method is shown to accurately predict the resonant conditions at which the maximum reflection and transmission occur. The trapezoidal breakwaters are found to generally present a wide spectrum of reflections, suggesting that they would function better than the rectangular breakwaters. The dual breakwater systems are confirmed to perform much better than single structures.

Analytical study of the effect of the geometrical parameters during the interaction of regular wave-horizontal plate-current

The present work is an analytical study of the influence of geometrical parameters, such as length, thickness and immersion of the plate, on the reflection coefficient of a regular wave for an immersed horizontal plate in the presence of a uniform current with the same direction as the propagation of the incident regular wave. This study was performed using the linearized potential theory with the evanescent modes while searching for complex roots to the dispersion equation that are neither pure real nor pure imaginary. The results show that the effects of the immersion and the relative length on the reflection coefficient of the plate are accentuated by the presence of the current, whereas the plate thickness practically does not have an effect if it is relatively small.

COMPARISON OF SCOURS IN FRONT OF VERTICAL BREAKWATERS DUE TO REGULAR AND IRREGULAR WAVES

In this paper the scours of sand bed due to regular and irregular waves in front of vertical breakwaters, such as scouring patterns, scouring mechanisms, etc., are investigated. Thereby, the scours under the action of the two kinds of waves are compared connected.

NUMERICAL SIMULATION OF TWO-DIMENSIONAL OVERTOPPING AGAINST SEAWALLS ARMORED WITH ARTIFICIAL UNITS IN REGULAR WAVES

A new mathematical model for the overtopping against seawalls armored with artificial units in regular waves was established. The 2-D numerical wave flume, based on the Reynolds Averaged Navier-Stokes （RANS） equations and the standard κ-ε turbulence model, was developed to simulate the turbulent flows with the free surface, in which the Volume Of Fluid （VOF） method was used to handle the large deformation of the free surface and the relaxation approach of combined wave generation and absorbing was implemented. In order to consider the effects of energy dissipation due to the armors on a slope seawall, a porous media model was proposed and implemented in the numerical wave flume. A series of physical model experiments were carried out in the same condition of the numerical simulation to determine the drag coefficient in the porous media model in terms of the overtopping discharge. Compared the computational value of overtopping over the seawall with the experimental data, the values of the effective drag coefficient was calibrated for the layers of blocks at different locations along the seawalls.

Numerical Prediction of Added Resistance and Vertical Ship Motions in Regular Head Waves

The numerical prediction of added resistance and vertical ship motions of one ITTC （Intemational Towing Tank Conference） S-175 containership in regular head waves by our own in-house unsteady RANS solver naoe-FOAM-SJTU is presented in this paper. The development of the solver naoe-FOAM-SJTU is based on the open source CFD tool, OpenFOAM. Numerical analysis is focused on the added resistance and vertical ship motions （heave and pitch motions） with four very different wavelengths （ 0.8Lpp 〈 2 〈 1.5L ） in regular head waves. Once the wavelength is near the length of the ship model, the responses of the resistance and ship motions become strongly influenced by nonlinear factors, as a result difficulties within simulations occur. In the paper, a comparison of the experimental results and the nonlinear strip theory was reviewed and based on the findings, the RANS simulations by the solver naoe-FOAM-SJTU were considered competent with the prediction of added resistance and vertical ship motions in a wide range of wave lengths.

Oxygen transfer characteristics of bubbly jet in regular waves

The dissolved oxygen level is an important index of the water environment,and in this paper,the oxygen transfer of the bubbly jet in regular waves is investigated numerically and experimentally.The Reynolds-averaged Navier-Stokes equations,the re-normalisation group k-e equations,and the volume of fluid(VOF)technique are used along with a 2-D CFD model to simulate the wave and bubble motions as well as the turbulence,and a dissolved oxygen transport equation is used to model the oxygen transfer behavior both through the bubbly interface and the wave surface.A series of experiments are conducted to validate the mathematical model,with good agreement.In addition,a group of dimensionless parameters are defined from the wave parameter and the aeration parameter,and their relationships with the total oxygen transfer coefficient are explored.Furthermore,the dimensional analysis and the least squares methods are used to derive simple prediction formulas for the total oxygen transfer coefficient,and they are validated with the related experimental data.