A Linear Theory for Wave Scattering by Double Slotted Barriers in Weak Steady Currents

Recent experimental results have shown that the presence of a steady current can significantly reduce the energy of transmitted waves. In this paper, a theory is developed to study the wave scattering by single or double vertical slotted barriers in the presence of a weak uniform current. The quasi-linear theory is based on an eigenfunction expansion method. Comparisons between theory and existing experimental results for both single slotted barrier and double slotted barriers show satisfactory agreements. In consideration of wave propagation in a weak current it is found that the friction factor used to characterize the head loss at the slotted barrier depends on both the geometry of the slotted barrier and the strength of the steady current.     

Scaled Boundary Finite Element Analysis of Wave Passing A Submerged Breakwater

The scaled boundary finite element method （SBFEM） is a novel semi-analytical technique combining the advantage of the finite element method （FEM） and the boundary element method （BEM） with its unique properties. In this paper, the SBFEM is used for computing wave passing submerged breakwaters, and the reflection coeffcient and transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater, a rigid submerged barrier breakwater and a trapezium submerged breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is obtained. Through comparison with the results using the dual boundary element method （DBEM）, it is found that the SBFEM can obtain higher accuracy with fewer elements. Many submerged breakwaters with different dimensions are computed by the SBFEM, and the changing character of the reflection coeffcient and the transmission coefficient are given in the current study.     

Experimental Research on Wave Transmission over Submerged Rubble Mound Breakwaters

This paper discusses some previous, and presents some new experimental results on wave transmission over submerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop a two-dimensional （2D） model as an improvement to the existing wave transmission coefficient models. Factors which affect wave transmission over stbmerged breakwaters are discussed through a series of laboratory experiments. Basic recommendations for evaluation and design of submerged rubble-monud breakwaters are presented. From the test results, a calculation formula of wave transmission coefficient is proposed.     

Hydrodynamic behavior of curtainwall-pile breakwaters

A numerical model is developed that can predict the interaction of regular waves normally incident upon a curtainwall-pile breakwater; the upper part of which is a vertical wall and the lower part consists of an array of vertical piles. The numerical model is based on an eigenfunction expansion method, and utilizes a boundary condition nearby the vertical piles that accounts for wave energy dissipation. Numerical solution comprises a finite number of terms, which is a superposition of propagating waves and a series of evanescent waves. The modeling is validated by comparison with previous experimental studies and overall agreement between measurement and calculation is fairly good. The numerical results are related to reflection, transmission, and dissipation coefficient; wave run-up, wave force, and wave overturning moment are also presented. Effect of porosity, relative draft, and relative water depth are discussed; the choice of suitable range of them is described. The relative draft is more effective for shallow water waves. Model shows decrease in relative draft and leads to reduction of relative wave force, overturning moment, and runup. It is shown that curtainwall-pile breakwaters can operate both effectively and efficiently in the range of relative draft between 0.15 and 0.75. The range 0.5 to 0.2 is also recommended for porosity.     

Interaction Between Waves and A Comb-Type Breakwater

The characteristics of wave transmission, reflection and energy dissipation of comb-type caisson breakwaters are studied through laboratory physical model tests. Regular and irregular waves, with a wide range of wave heights and periods and a constant water depth, are considered. Different dimensions of each portion of the comb-type caisson breakwater are tested. Empirical formulae for calculating the reduction coefficient k, which is the ratio of horizontal wave force on unit length of the comb-type breakwater to that on unit length of the vertical wall breakwater, and for calculating the reflection coefficient of waves k, are obtained from the measurements. The comb-type caisson breakwater has been found to be very efficient in dissipating incident wave energy and in reducing wave reflection, and has already been used for the construction of an island breakwater in the Dayao Bay of Dalian Port, Liaoning Province, China. Compared with the cost of a common caisson breakwater, about 24. 5% of the investm     

Experimental Study of Wave Attenuation in Trapezoidal Floating Breakwaters

A comprehensive experimental study was carried out on the regular wave attenuation with a trapezoidal pontoontype floating breakwater(FB) in deep water. The functionalities of two simple FB geometries consist of a rectangle and a trapezoid with the slope of 60° were investigated under the wave attack. A two-dimensional wave flume was used in the experiment; the incident, transmitted waves, mooring line forces and motion responses of the floating breakwaters were measured. Also the influence of the sea state conditions(incident wave height and wave period)and structural parameters(draught of the structure) were investigated using the trapezoidal FB. Our experimental results indicated that the trapezoidal FB significantly reduced the wave transmission and mooring line force when compared with rectangular FBs. A new formula was developed in order to predict the value of the transmission coefficient in trapezoidal FBs with the slope of 60°. Experimental data showed to be consistent with the results of the formula.     

Vibrating-Rocking Motion of Caisson Breakwater Under Breaking Wave Impact

The possible motions of a caisson breakwater under dynamic load excitation include vibrating, vibrating-sliding and vibrating-rocking motions. The models of vibrating motion and vibrating-sliding motion have been proposed in an early paper. In this paper, a model of vibrating-rocking motion of caisson breakwaters under breaking wave impact is presented, which can be used to simulate the histories of vibrating-rocking motion of caisson breakwaters. The effect of rocking motion on the displacement, rotation, sliding force and overturning moment of breakwaters is investigated. In case the overturning moment exceeds the stability moment of a caisson, the caisson may only rock. The caisson overturns only in case the rocking angle exceeds the critical angle. It is shown that the sliding force and overturning moment of breakwaters can be reduced effectively due to the rocking motion. It is proposed that some rocking motion should be allowed in breakwater design.     

Wave Interactions with Multiple Semi-Immersed Jarlan-Type Perforated Breakwaters

This study examines wave interactions with multiple semi-immersed Jarlan-type perforated breakwaters. A numerical model based on linear wave theory and an eigenfunction expansion method has been developed to study the hydrodynamic characteristics of breakwaters. The numerical results show a good agreement with previous analytical results and experimental data for limiting cases of double partially immersed impermeable walls and double and triple Jarlan-type breakwaters. The wave transmission coefficient C_T; reflection coefficient C_R, and energy dissipation coefficient C_E coefficients and the horizontal wave force exerted on the front and rear walls are examined. The results show that C_R reaches the maximum value when B/L = 0.46n while it is smallest when B/L=0.46n+0.24 (n=0, 1, 2,...). An economical triple semi-immersed Jarlan-type perforated breakwater can be designed with B/L = 0.25 and C_R and C_T ranging from 0.25 to 0.32 by choosing a relative draft d/h of 0.35 and a permeability parameter of the perforated front walls being 0.5 for an incident wave number kh nearly equal to 2.0. The triple semi-immersed Jarlan-type perforated breakwaters with significantly reduced C_R, will enhance the structure’s wave absorption ability, and lead to smaller wave forces compared with the double one. The proposed model may be used to predict the response of a structure in the preliminary design stage for practical engineering.     

VERIFICATION OF INTERNAL WAVES IN OFFSHORE AREAS BY MEANS OF CURRENT OBSERVATIONS

Based on the shear effect of internal wave currents in stratified fluid, the necessary condition for the possible existence of an internal wave and the sufficient condition under which there will be no internal wave are deduced starting from the continuity equation of incompressible fluid. The above two conditions are verified by the measured results from vertical current meter arraies at some observation stations in the Bohai Sea and the South Huanghai Sea. In the treatment of measured results, first of all, the tidal period components are separated from the measured currents by Fourier-analysis method, and then the internal wave currents of tidal period from the tidal period components in the light of some considerations. The analytical results of observed currents are well consistent with theoretical analysis. Furthermore, one can also deduce some features of internal waves therefrom. Consequently, it is concluded that the observation from a vertical current meter array is an important means to verif     

Verification of A Numerical Harbour Wave Model

A numerical model for wave propagation in a harbour is verified by use of physical models.The extended time-dependent mild slope equation is employed as the governing equation,and the model is solved by use of ADI method containing the relaxation factor.Firstly,the reflection coefficient of waves in front of rubble-mound breakwaters under oblique incident waves is determined through physical model tests,and it is regarded as the basis for simulating partial reflection boundaries of the numerical model.Then model tests on refraction,diffraction and reflection of waves in a harbour are performed to measure wave height distribution.Comparative results between physical and numerical model tests show that the present numerical model can satisfactorily simulate the propagation of regular and irregular waves in a harbour with complex topography and boundary conditions.     

Wave interaction with one or two rows of closely spaced rectangular cylinders

Experimental results are reported on the wave reflection from and transmission through one row or two rows of closely spaced rectangular cylinders. An empirical expression is proposed for the friction factor which models the head loss due to closely spaced rectangular cylinders. Algebraic expressions are presented to calculate the reflection and transmission coefficients of regular waves for a single slotted wall or double slotted walls. The model is validated by the published and present experimental results. The proposed method can be used for the preliminary design of slotted-wall breakwaters.     

Hydraulic performance and wave loadings of perforated/slotted coastal structures: A review

This paper reviews recent progress in the study of perforated/slotted breakwaters, with an emphasis on two main groups of such breakwaters: (1) perforated/slotted breakwaters with impermeable back walls, and (2) perforated/slotted breakwaters without a back-wall. The methods commonly used to simulate the interactions between such structures and various linear/nonlinear waves are summarized. The transmission and reflection characteristics of perforated/slotted breakwaters in these two groups are reviewed extensively. Several methods for calculating wave forces on perforated caissons are also reviewed. Some recent works published in Chinese journals, which are generally not well-known to non-Chinese researchers, are reviewed with a hope that these works can be beneficial to other researchers working in this area.     

An experimental study of wave scattering by a vertical slotted barrier in the presence of a current

In coastal waters, tidal currents and surface waves co-exist. In this study, the influence of a steady current on the scattering of waves by a vertical slotted barrier is investigated experimentally in a wave flume. The separation of the incident and reflected waves is carried out by a two-point method that takes into account the effects of the current. Results show that currents significantly increase the wave-energy loss by the barrier and remarkably reduce the wave transmission through the barrier. It is suggested that the tidal currents should be taken into consideration in an economical design of slotted breakwaters.     

Performance of hemi-cylindrical and rectangular submerged breakwaters

A parametric experimental study is conducted to compare the reflection and transmission characteristics of submerged hemi-cylindrical and rectangular rigid and water-filled flexible breakwater models. The results show that, for the rigid breakwaters, rectangular models are more effective than hemi-cylindrical ones in terms of reduction of transmitted waves. As for the flexible breakwaters, the hemi-cylindrical models may give better wave reflection than rectangular ones. However, the energy loss induced by the rectangular breakwaters is much larger and more significant to result in an overall better efficiency in terms of reduction in wave transmission. The effects of internal pressure show that the lowest pressurized flexible models considered in this work are the most effective in the reduction of the transmitted wave height. Higher wave reflection, lower wave transmission and higher energy loss are obtained consistently at the lower submergence depth ratio.     

Simplified analytical solutions for wave interaction with absorbing-type caisson breakwaters

Simplified analytical solutions are presented to model the interaction of linear waves with absorbing-type caisson breakwaters, which possess one, or two, perforated or slotted front faces which result in one, or two, interior fluid regions (chambers). The perforated/slotted surfaces are idealized as thin porous plates. Energy dissipation in the interior fluid region(s) inside the breakwater is modelled through a damping function. Under the assumption of potential flow and linear wave theory a boundary-value problem may then be formulated to describe wave interaction with the idealized structure. A solution to this simplified problem may be obtained by an eigenfunction expansion technique and an explicit analytical expression may be obtained for the reflected wave height. Using the experimental work of previous authors, damping coefficients are determined for both single and double chamber absorbing-type caisson breakwaters. Based on the damping for a single perforated-wall breakwater, a methodology is proposed to enable the estimation of the damping coefficients for a breakwater with two chambers. The theoretical predictions of the reflection coefficients for the two-chamber structures using the present model are compared with those obtained from laboratory experiments by other authors. It is found that the inclusion of the damping in the interior fluid region gives rise to improved agreement between theory and experiment.     

Wave interactions with multiple-row curtainwall-pile breakwaters

In this study, a mathematical model has been developed that can compute various hydrodynamic characteristics of a multiple-row curtainwall-pile breakwater. To examine the validity of the developed model, laboratory experiments have been conducted for double- and triple-row breakwaters with various combinations of drafts of curtain walls, porosities between piles, and distances between rows. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. As a whole, the transmission coefficient decreases with an increase in relative water depth, whereas the reflection coefficient, normalized run-up and force exhibit an opposite trend in their variations. With fixed values of the draft of the curtain wall and the porosity of lower perforated part of the first row of a double-row breakwater, as these values of the second row increase and decrease, respectively, the transmission coefficient decreases, as expected. On the other hand, their effects on wave reflection, run-up, and wave force change with the relative depth. As for the distance between the rows, the transmission coefficient becomes a maximum when it is about one half of the wave length, suggesting that this condition should be avoided to achieve the advantage of the breakwater in reducing wave transmission. It is shown that for prototype breakwaters, on an average, the transmission coefficient would be smaller than 0.3 for wave periods less than 6.0 s, and it would be about 0.45 even for the wave period of 9.0 s, although there would be a variation depending on the geometry of the breakwater. It is also shown that wave transmission is significantly reduced by multiple-row breakwaters compared with a single-row breakwater, while the difference between double-row and triple-row breakwaters is marginal. Finally, engineering monograms are provided for double-row breakwaters to be used in practical engineering applications of the breakwaters.     

Investigation of Π-type breakwaters performance under regular and irregular waves

In this paper, performance of solid and perforated Π-type breakwaters was investigated experimentally. Both regular and irregular waves were used during testing. Four depths of immersions were selected for each breakwater and wave type. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy-dissipation characteristics were determined. The results of the experimental study were evaluated and some empirical expressions based on the results were suggested to define the transmission, reflection and energy-dissipation coefficients for different immersion depths of solid and perforated breakwaters under regular and irregular waves. Moreover, performance of solid and perforated Π-type breakwaters were compared with that of solid and perforated U-type breakwaters investigated by Günaydın and Kabdaşlı [2006. Performance of solid and perforated U-type breakwaters under regular and irregular waves. Ocean Engineering 31, 1377–1405]. These comparisons showed that the most reasonable model and wave type are selected to determine requiring performance parameters.     

Experiments on wave transmission coefficients of floating breakwaters

To find a simple, inexpensive, and effective type of floating breakwater for deep-sea aquaculture, we studied three types of structures: the single box, the double box, and the board net. We conducted two-dimensional physical model tests in a wave-current flume in the laboratory to measure the wave transmission coefficients of the three types of breakwaters under regular waves with or without currents. Based on the initial comparison of the wave transmission coefficients, we proposed the use of the board-net floating breakwater for use with fish cages; we then conducted detailed experiments to examine how wave transmission coefficients are affected by several factors, including the width of the board, the row number of the net, the rigidity of the board, and the current velocity. The experimental results show that the board-net floating breakwater, which is a simple and inexpensive type of structure, can effectively protect fish and fish cages and may be adopted for aquaculture engineering in deep-water regions.