Hydrodynamic Performance of Air-Filled Wave Attenuator for Wave Control:Experimental Study

Numerous types of floating breakwaters have been proposed,tested and commercialized in the past decades.The majority of these breakwaters are made of solid bodies;hence,they are relatively bulky and are not readily to be rapidly installed at the targeted sites when immediate wave protection of the coastal and offshore facilities is needed.Furthermore,the application of these hard floating structures at the recreational beaches is rather unlikely due to potential deadly marine traffic collision.To overcome these problems,a flexible air-filled wave attenuator(AFWA)has been developed in the present study.This floating breakwater is made of flexible waterproof membrane materials.The main body consists of a rectangular air-filled prism and is ballasted by sandbags located around the floating module.The objective of this study is to evaluate the wave transmission,wave reflection,energy dissipation,motion responses and mooring forces of the AFWA under the random wave actions using physical modelling.The test model located in a 20 m long wave flume was subjected to a range of wave heights and periods.The wave profiles in the vicinity of the test model were measured using wave probes for determination of wave transmission,reflection and energy loss coefficients.The motion responses in terms of heave,surge and pitch,and wave forces acting on the mooring lines were measured using a motion tracking system and load cells,respectively.The experimental results reveal that the AFWA is effective in attenuating up to 95%in the incoming wave height and has low-wave-reflection properties,which is commendable for floating breakwaters.

Floating periodic pontoons for broad bandgaps of water waves

The narrow attenuation bands of traditional marine structures have long been a challenge in mitigating water waves.In this paper,a metastructure(MS)composed of floating periodic pontoons is proposed for broadband water wave attenuation.The interaction of surface gravity waves with the MS is investigated using linear wave theory.The potential solutions of water waves by the MS with a finite array are developed by using the eigenfunction expansion matching method(EEMM),and the band structure of the MS is calculated by the transfer matrix method(TMM),in which the evanescent modes of waves are considered.The solution is verified against the existing numerical result for a special case.Based on the present solution,the association between Bragg resonance reflection and Bloch bandgaps is examined,the effects of pontoon geometry are analyzed,and the comparison between floating MS and bottom-mounted periodic structures is conducted.A computational fluid dynamics(CFD)model is further developed to assess the structures in practical fluid environments,and the floating MS presents excellent wave attenuation performance.The study presented here may provide a promising solution for protecting the coast and offshore structures.

Wave Attenuation and Turbulence Driven by Submerged Vegetation Under Current-Wave Flow

A set of laboratory experiments are carried out to investigate the effect of following/opposing currents on wave attenuation.Rigid vegetation canopies with aligned and staggered configurations were tested under the condition of various regular wave heights and current velocities,with the constant water depth being 0.60 m to create the desired submerged scenarios.Results show that the vegetation-induced wave dissipation is enhanced with the increasing incident wave height.A larger velocity magnititude leads to a greater wave height attenuation for both following and opposing current conditions.Moreover,there is a strong positive linear correlation between the damping coefficientβand the relative wave height H_(0)/h,especially for pure wave conditions.For the velocity profile,the distributions of U_(min)and U_(max)show different patterns under combined wave and current.The time-averaged turbulent kinetic energy(TKE)vary little under pure wave and U_(c)=±0.05 m/s conditions.With the increase of flow velocity amplitude,the time-averaged TKE shows a particularly pronounced increase trend at the top of the canopy.The vegetation drag coefficients are obtained by a calibration approach.The empirical relations of drag coefficient with Reynolds and Keulegane-Carpenter numbers are proposed to further understand the wave-current-vegetation interaction mechanism.

Layered metastructure containing freely-designed local resonators for wave attenuation

Combining periodic layered structure with three-dimensional cylindrical local resonators,a hybrid metastructure with improved wave isolation ability was designed and investigated through theoretical and numerical approaches.The metastructure is composed of periodic rubber layers and concrete layers embedded with three-dimensional resonators,which can be freely designed with multi local resonant frequencies to attenuate vibrations at required frequencies and widen the attenuation bandgap.The metastructure can also effectively attenuate seismic responses.Compared with layered rubber-based structures,the metastructure has more excellent wave attenuation effects with greater attenuation and wider bandgap.

Propagation and attenuation of P-waves in patchy saturated porous media

We establish a patchy saturation model and derive the seismic wave equations for patchy saturated porous media on the basis of Biot＇s equations and Johnson＇s bulk modulus. We solve the equations, obtain the attenuation coefficients, and analyze the characteristics of wave attenuation in the seismic frequency range. The results suggest that seismic waves show attenuation and dispersion in partially saturated rocks in the low frequency range. With frequency increasing, attenuation increases. The attenuation of P-waves of the second kind is more pronounced in agreement with Biot＇s theory. We also study the effect of porosity, saturation, and inner sphere radius on the attenuation of the P-waves of the first kind and find that attenuation increases with increasing frequency and porosity, and decreases with increasing frequency and degree of saturation. As for the inner sphere radius, wave attenuation is initially increasing with increasing frequency and inner sphere radius less than half the outer radius. Subsequently, wave attenuation decreases with increasing frequency and inner sphere radius is higher than half the outer sphere radius.

Hydroelastic Investigation on A Pile Breakwater Integrated with A Flexible Tail for Long-Wave Attenuation

A novel concept of wave attenuator is proposed for the defense of long waves,through integrating a flexible tail to the lee-side surface of a pile breakwater.The flexible tail works as a floating blanket made up of hinged blocks,whose scale and stiffness can be easily adjusted.A two-phase-flow numerical model is established based on the open-source computational fluid dynamics(CFD)code OpenFOAM to investigate its wave attenuation performance.Incompressible Navier−Stokes equations are solved in the fluid domain,where an additional computational solid mechanics(CSM)solver is embedded to describe the elastic deformation of the floating tail.The coupling of fluid dynamics and structural mechanics is solved in a full manner to allow assess of wave variation along the deforming body.The accuracy of the numerical model is validated through comparison with experimental data.Effects of the flexible tail on performance of the pile breakwater are investigated systematically.Dynamic behaviours of the tail are examined,and characteristics of its natural frequency are identified.For safety reasons,the wave loads impacting on the main body of the pile breakwater and the stress distribution over the tail are specially examined.It is found that both the length and stiffness of the tail can affect the wave-attenuation performance of the breakwater.A proper choice of the length and stiffness of the tail can greatly improve the long-wave defending capability of the pile breakwater.The maximum stress over the flexible tail can be restrained through optimising the deformation and stiffness of the tail.

Numerical simulation of solitary and random wave propagation through vegetation based on VOF method

A vertical two-dimensional numerical model has been applied to solving the Reynolds Averaged Navier- Stokes （RANS} equations in the simulation of current and wave propagation through vegetated and non- vegetated waters. The k-e model is used for turbulence closure of RANS equations. The effect of vegeta- tion is simulated by adding the drag force of vegetation in the flow momentum equations and turbulence model. To solve the modified N-S equations, the finite difference method is used with the staggered grid system to solver equations. The Youngs＇ fractional volume of fluid （VOF） is applied tracking the free sur- face with second-order accuracy. The model has been tested by simulating dam break wave, pure current with vegetation, solitary wave runup on vegetated and non-vegetated channel, regular and random waves over a vegetated field. The model reasonably well reproduces these experimental observations, the model- ing approach presented herein should be useful in simulating nearshore processes in coastal domains with vegetation effects.

Tomography of the dynamic stress coefficient for stress wave prediction in sedimentary rock layer under the mining additional stress

In this study,the tomography of dynamic stress coefficient(TDSC)was established based on a mechanical model of stress wave propagation in bedding planes and a mathematical model of the stress wave attenuation in rock masses.The reliability of the TDSC was verified by a linear bedding plane model and field monitoring.Generally,the TDSC in the dynamic stress propagation of bedding planes increases with the following conditions:(1)the increase of the normal stiffness of the bedding plane,(2)the increase of the incident angle of the stress wave,(3)the decrease of the incident frequency of the stress wave,or(4)the growth of three ratios(the ratios of rock densities,elastic moduli,and the Poisson’s ratios)of rocks on either side of bedding planes.The additional stress weakens TDSC linearly and slowly during the stress wave propagation in bedding planes,and the weakening effect increases with the growth of the three ratios.Besides,the TDSC decreases exponentially in the rock mass as propagation distance increases.In a field case,the TDSC decreases significantly as vertical and horizontal distances increase and its wave range increases as vertical distance increases in the sedimentary rock layers.

Wave Attenuation Performance and the Influencing Factors of A Lower Arc-Plate Breakwater

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 wave- generating 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.

ON THE INTERACTION OF WATER WAVES AND SEABED BY THE POROUS MEDIUM MODEL

The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory results.

Hydrodynamic Performance of Vertical Porous Structures Under Regular Waves

The hydrodynamic efficiency of the vertical porous structures is investigated under regular waves by use of physical models. The hydrodynamic efficiency of the breakwater is presented in terms of the wave transmission （kt）, reflection （kr） and energy dissipation （ka） coefficients. Different wave and structural parameters affecting the breakwater efficiency are tested. It is found that, the transmission coefficient （kt） decreases with the increase of the relative water depth （h/L）, the wave steepness （Hi^L）, the relative breakwater widths （B/L, B/h）, the relative breakwater height （D/h）, and the breakwater porosity （n）. The reflection coefficient （kr） takes the opposite trend of kt when D/h=l.25 and it decreases with the increasing h/L, HJL and B/L when D/h〈1.0. The dissipation coefficient （kd） increases with the increasing h/L, HilL and B/L when D/h〈_l.O and it decreases when D/h=l.25. In which, it is possible to achieve values ofkt smaller than 0.3, k~ larger than 0.5, and kd larger than 0.6 when D/h=1.25, B/h=0.6, h/L〉0.22, B/L〉O. 13, and H/L 〉0.04. Empirical equations are developed for the estimation of the transmission and reflection coefficients. The results of these equations are compared with other experimental and theoretical results and a reasonable agreement is obtained.

A rapid assessment method for calculating the drag coefficient in wave attenuation by vegetation

Vegetation in wetlands is a large-scale nature-based resource that can provide multiple benefits to human beings and the environment,such as wave attenuation in coastal zones.Traditionally,there are two main calibration approaches to calculate the attenuation of wave driven by vegetation.The first method is a straightforward one based on the exponential attenuation of wave height in the direction of wave transmission,which,however,overlooks the crucial drag coefficient(CD).The other method is in accordance with more complicate equations for predicting the damping factor,which is regarded as a function of CD.In this study,a new relation,combining these above two conventional approaches,is proposed to predict the CD in an operative approach.Results show that values yielded by the new assessment method perform a strong linear relationship with a collection of historical observations,with a promising R2 value of 0.90.Besides,the linear regression derives a new predictive equation for the bulk drag coefficient.Additionally,a calibrated value of 4 for the empirical plant drag coefficient(CP)is revealed.Overall,this new equation,with the superiority of the convenient exponential regression,is expected to be a rapid assessment method for calculating wave attenuation by vegetation and predicting the drag coefficient.

A Parameterization Scheme for Wind Wave Modules that Includes the Sea Ice Thickness in the Marginal Ice Zone

The global wave model WAVEWATCH III®works well in open water.To simulate the propagation and attenuation of waves through ice-covered water,existing simulations have considered the influence of sea ice by adding the sea ice concentration in the wind wave module;however,they simply suppose that the wind cannot penetrate the ice layer and ignore the possibility of wind forcing waves below the ice cover.To improve the simulation performance of wind wave modules in the marginal ice zone(MIZ),this study proposes a parameterization scheme by directly including the sea ice thickness.Instead of scaling the wind input with the fraction of open water,this new scheme allows partial wind input in ice-covered areas based on the ice thickness.Compared with observations in the Barents Sea in 2016,the new scheme appears to improve the modeled waves in the high-frequency band.Sensitivity experiments with and without wind wave modules show that wind waves can play an important role in areas with low sea ice concentration in the MIZ.

Wave Extraction and Attenuation Performance of An Edinburgh Duck Wave Energy Converter

Edinburgh Duck wave energy converter(ED WEC)has excellent energy extraction performance and shows a great potential to integrate with other marine structures.This paper aims to investigate its wave energy extraction performance as a WEC and wave attenuation performance as a protection method for shoreline or marine structures.The wave and ED WEC interactions in regular waves are modeled using the Star-CCM+software and verified by comparisons with published experimental results.The motion response,energy conversion efficiency,and transmission coefficient of the ED WEC with different attack angles,rotation center,and incident wave heights are investigated.Results indicate that the ED WEC with an attack angle of 42°and a rotation center of 0.55 m below the mean water line can achieve both good wave energy extraction and wave attenuation performances.The wave energy extraction and wave attenuation performance of the ED WEC decrease significantly with the increase of wave nonlinearity characterized by the wave steepness.This paper can guide the practical application of the ED WEC at the early stage of design.

Modeling wave attenuation by vegetation with accompanying currents in SWAN

Coastal wetlands such as salt marshes and mangroves provide important protection against stormy waves.Accurate assessments of wetlands’capacity in wave attenuation are required to safely utilize their protection services.Recent studies have shown that tidal currents have a significant impact on wetlands’wave attenuation capacity,but such impact has been rarely considered in numerical models,which may lead to overestimation of wave attenuation in wetlands.This study modified the SWAN(Simulating Waves Nearshore)model to account for the effect of accompanying currents on vegetation-induced wave dissipation.Furthermore,this model was extended to include automatically derived vegetation drag coefficients,spatially varying vegetation height,and Doppler Effect in combined current-wave flows.Model evaluation against an analytical model and flume data shows that the modified model can accurately simulate wave height change in combined current-wave flows.Subsequently,we applied the new model to a mangrove wetland on Hailing Island in China with a special focus on the effect of currents on wave dissipation.It is found that the currents can either increase or decrease wave attenuation depending on the ratio of current velocity to the amplitude of the horizontal wave orbital velocity,which is in good agreement with field observations.Lastly,we used Hailing Island site as an example to simulate wave attenuation by vegetation under hypothetical storm surge conditions.Model results indicate that when currents are 0.08–0.15 m/s and the incident wave height is 0.75–0.90 m,wetlands’wave attenuation capacity can be reduced by nearly 10%compared with pure wave conditions,which provides implications for critical design conditions for coastal safety.The obtained results and the developed model are valuable for the design and implementation of wetland-based coastal defense.The code of the developed model has been made open source,in the hope to assist further research and coastal management.

Dispersion of Axisymmetric Longitudinal Waves in A Bi-Material Compound Solid Cylinder Made of Viscoelastic Materials

The paper studies the dispersion of axisymmetric longitudinal waves in the bi-material compound circular cylinder made of linear viscoelastic materials.The investigations are carried out within the scope of the piecewise homogeneous body model by utilizing the exact equations of linear viscoelasto-dynamics.The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution.Concrete numerical results are obtained for the case where the relations of the constituents of the cylinder are described through fractional exponential operators.The influence of the viscosity of the materials of the compound cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials.Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed.As a result of the numerical investigations,in particular,it is established that in the case where the rheological parameters of the components of the compound cylinder are the same,the viscosity of the layers’materials causes the axisymmetric wave propagation velocity to decrease.

Experimental Study on Wave Attenuation Performance of A New Type of Floating Breakwater with Twin Pontoons and Multi Porous Vertical Plates

A floating breakwater(FB)has extensive potential applications in the fields of coastal,offshore,and ocean engineering owing to its advantages such as eco-friendliness,low cost,easy and rapid construction,and quick dismantling and reinstallation.An FB composed of twin pontoons and multi-porous vertical plates is proposed to improve the wave attenuation performance.The wave attenuation performance is investigated for different FB structures and vertical plate types under different incident wave heights and periods using 2D wave physical model tests in a wave flume.The results demonstrate that the proposed FB has a better performance than that of the conventional single pontoon-type FB.It reduces the wave transmission due to its enhanced wave reflection and energy loss.The wave transmission coefficient of the proposed FB decreases with an increase in the number of layers and relative draft depth of the vertical plates.However,a further decrease in the wave transmission coefficient is not observed when the number of porous vertical plates is increased from 4 to 5 layers.An equation has been derived to predict the wave transmission of the proposed FB based on the experimental results.

Wave Attenuation and Friction Coefficient on the Coral-Reef Flat

Several sets of S4 direction-wave-current-tide meters have been deployed on the coral-reef flat of Yongshu Reef in the sea area of Nansha Islands.Based on the observational sea wave data, the attenuation characteristics of the waves propagating on the coral reef flat, the bottom friction coefficients and the transfer of wave energy are discussed in the paper. The results show that, in the relative depths of 0.0613～0.0867, the wave height attenuation per unit distance of wave propagation is 22.09%～46.56%, with an average of 31.35%; the wave energy attenuation coefficient, 33.74%～53.22%, with an average of 43.61%. The average of the bottom friction coefficients on the coral-reef flat is 0.1346, which is about 10 times that on the sand or silt bottom. In the course of propagation on the reef flat, the waves sustain more loss in high frequency than in low frequency and the spectral energy transfers to the low frequency. These results may be used for reference in island and reef engineering.

Characteristics of Vibrational Wave Propagation and Attenuation in Submarine Fluid-Filled Pipelines

As an important part of lifeline engineering in the development and utilization of marine resources, the submarine fluid-filled pipeline is a complex coupling system which is subjected to both internal and external flow fields. By utilizing Kennard＇s shell equations and combining with Helmholtz equations of flow field, the coupling equations of submarine fluid-filled pipeline for n=0 axisymmetrical wave motion are set up. Analytical expressions of wave speed are obtained for both s=1 and s=2 waves, which correspond to a fluid-dominated wave and an axial shell wave, respectively. The numerical results for wave speed and wave attenuation are obtained and discussed subsequently. It shows that the frequency depends on phase velocity, and the attenuation of this mode depends strongly on material parameters of the pipe and the internal and the external fluid fields. The characteristics of PVC pipe are studied for a comparison. The effects of shell thickness/radius ratio and density of the contained fluid on the model are also discussed. The study provides a theoretical basis and helps to accurately predict the situation of submarine pipelines, which also has practical application prospect in the field of pipeline leakage detection.

Wave Extraction and Attenuation Performance of A Hybrid System of An Edinburgh Duck WEC and A Floating Breakwater

Installing the Edinburgh Duck Wave Energy Converter(ED WEC)on a floating breakwater provides a potential solution to reduce costs and improve the reliability of the ED WEC.To investigate the interactions between the ED WEC and the breakwater,a two-dimensional numerical model of a hybrid WEC-breakwater system is established based on Star-CCM+Computational Fluid Dynamics(CFD)software.The wave energy extraction performance,wave attenuation performance,and wave forces on the breakwater of the hybrid system are compared with those of the corresponding single device.The effects of the initial attack angle,the distance between the WEC and the breakwater,and the incident wave height on the pitch motion,energy conversion efficiency,transmission coefficient,and wave forces on the breakwater of the hybrid system are analyzed.The results indicate that combing the ED WEC with a breakwater can improve the energy extraction performance of the ED WEC and reduce the wave forces on the breakwater in shorter-period waves.The conversion efficiency of the hybrid system with the initial attack angle of 42°is the largest in shorter-period waves,but is reduced with the increase of initial attack angle in longer-period waves.The wave attenuation performance of the hybrid system is determined by the draft of the breakwater.The distance between the WEC and the breakwater has little effect on the hybrid system.Wave energy extraction of the ED WEC of the hybrid system decreases significantly with the increase of the incident wave height.