Bble Size Distribution for Waves Propagating over A Submerged Breakwater

Experiments are carried out to study the characteristics of active bubbles entrained by breaking waves as these propagate over an abruptly topographical change or a submerged breakwater. Underwater sounds generated by the entrained air bubbles are detected by a hydrophone connected to a charge amplifier and a data acquisition system. The size distribution of the bubbles is then determined inversely from the received sound frequencies. The sound signals are converted from time domain to time-frequency domain by applying Gabor transform. The number of bubbles with different sizes are counted from the signal peaks in the time-frequency domain. The characteristics of the bubbles are in terms of bubble size spectra, which account for the variation in bubble probability density related to the bubble radius r. The experimental data demonstrate that the bubble probability density function shows a-2.39 power-law scaling with radius for r＞0.8 mm, and a-1.11 power law for r＜0.8 mm.     

RANS Modeling of Solitary Wave Propagation over A Submerged Rectangular Breakwater

In this paper a series of numerical simulations are performed to investigate the vortex shedding mechanism for a solitary wave propagating over a submerged breakwater by use of Reynolds averaged Navier-Stokes (RANS) model combined with a k-ε model. Flows of different Reynolds numbers up to Re=1.4×105 corresponding to varying incident wave heights are considered in which the characteristic fluid velocity is represented by the maximum horizontal velocity above the submerged breakwater. For the verification of...     

RANS Modeling of Solitary Wave Propagation over A Submerged Rectangular Breakwater

In this paper a series of numerical simulations are performed to investigate the vortex shedding mechanism for a solitary wave propagating over a submerged breakwater by use of Reynolds averaged Navier-Stokes (RANS) model combined with a k-ε model. Flows of different Reynolds numbers up to Re=1.4×105 corresponding to varying incident wave heights are considered in which the characteristic fluid velocity is represented by the maximum horizontal velocity above the submerged breakwater. For the verification of the accuracy of the numerical model, the incident waves and the velocity field in the vicinity of the breakwater are compared with experimental data. The result shows that the model is capable of describing vortex shedding for a solitary wave propagating over a rectangular submerged breakwater. Key features of vortex generation, evolution and dissipation are investigated. It is found that the vortex shedding and their evolution due to separated boundary layer over the breakwater are strongly related to the Reynolds number. A considerable number of vortices and complicated vortex pattern are observed as the Reynolds number increases.     

Flow Separation and Vortex Dynamics in Waves Propagating over A Submerged Quartercircular Breakwater

The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a Reynolds-Averaged Navier–Stokes (RANS) flow solver with a Volume of Fluid (VOF) surface capturing scheme (RANS-VOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation, therefore, scour on the leeside of the breakwater.     

Experimental and Numerical Study on the Hydrodynamic Characteristics of Solitary Waves Passing Over A Submerged Breakwater

In this study, solitary waves passing over a submerged breakwater are investigated both experimentally and numerically. A total of 9 experimental conditions are carried out, including different incident wave heights and water depths. Numerical simulations are performed using a high-order finite-difference model solving Navier–Stokes (N–S) equations. The predicted water wave elevation, velocity and pressure show good agreement with experimental data, verifying the accuracy and capacity of the numerical model. Furthermore, parametric studies are conducted by numerical modelling to examine the effects of the geometrical features of submerged dike on hydrodynamic characteristics around the breakwater.     

潜堤对波浪传播变形的物理模型试验研究

以不可渗透光滑潜堤为研究对象,基于波浪水槽试验,分析了规则波和不规则波通过淹没梯形潜堤时的波浪外部形态变化以及内部能量变化规律。探讨了不同波浪要素(周期、波高、淹没水深)对潜堤附近波高影响的变化规律。同时,探究了潜堤斜坡坡度、堤顶淹没水深对波浪频谱在频域分布的影响。研究结果表明:当波浪通过潜堤时,波浪主频能量衰减,波浪能量由低频向高频移动;潜堤斜坡坡度越大、堤顶水深越小,波浪主频能量衰减越剧烈;波浪通过潜堤后高频波能量占潜堤次生波能量的1%~30%。     

Numerical Simulation of Waves Interaction with A Submerged Horizontal Twin-Plate Breakwater

The numerical investigation of regular waves interacting with a submerged horizontal twin-plate breakwater is presented in this paper. A numerical model with an absorbing wave-maker is established based on the VOF method. The validity of the model is verified by experimental results. Comparisons between the numerical and experimental results show that both the water surface profiles and the wave-induced pressures can be modeled accurately. Wave deformation over the breakwater,water particle velocities aroun...     

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.     

Wave Height Transformation and Set-up Between a A Submerged Permeable Breakwater and A Seawall

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.     

A Numerical Study on Water Waves Generated by A Submerged Moving Body in A Two-Layer Fluid System

This is a numerical study on the time development of surface waves generated by a submerged body moving steadily in a two-layer fluid system, in which a layer of water is underlain by a layer of viscous mud. The fully nonlinear Navier-Stokes equations are solved on FLUENT with the Volume-of-Fluid (VOF) multiphase scheme in order to simulate the free surface waves as well as the water-mud interface waves as functions of time. The numerical model is validated by mimicking a reported experiment in a one-layer ...     

A Numerical Study on Water Waves Generated by a A Submerged Moving Body in a A Two-Llayer Fluid System

This is a numerical study on the time development of surface waves generated by a submerged body moving steadily in a two-layer fluid system, in which a layer of water is underlain by a layer of viscous mud. The fully nonlinear Navier–Stokes equations are solved on FLUENT with the Volume-of-Fluid (VOF) multiphase scheme in order to simulate the free surface waves as well as the water–mud interface waves as functions of time. The numerical model is validated by mimicking a reported experiment in a one-layer system before it is applied to a two-layer system. It is found that the presence of bottom mud in a water layer can lead to large viscous damping of the surface waves. To investigate the problem systematically, the effects of the Froude number and the mud layer thickness, density and viscosity relative to those of water are evaluated and discussed in detail.     

Nonlinear Lagrangian Breaker Characteristics for Waves Propagating Normally Toward A Mild Slope

Because of shoaling, refraction, friction, and other effects, a surface-wave propagating on a gently sloping bottom of slope will eventually break. In this paper, by nonlinearizing the problem and using a perturbation method, an analytical solution for the velocity potential is derived to the second order for the bottom slope a and the wave steepness e in a Eulerian system. Then, the wave profile and the breaking wave characteristics are found by transforming the flow field into a Lagrangian system. By use of the kinematic stability parameter （K. S. P. ）, new theoretical breaker characteristics are derived. Thus, the linear theories of other scholars are extended to breaking waves. A Comparison of the present analytical solution with experimental studies of other scholars shows reasonable agreement except that the breaking depth is underestimated.     

Higher Harmonics Induced by Waves Propagating over A Submerged Obstacle in the Presence of Uniform Current

To investigate higher harmonics induced by a submerged obstacle in the presence of uniform current, a 2D fully nonlinear numerical wave flume（NWF） is developed by use of a time-domain higher-order boundary element method（HOBEM） based on potential flow theory. A four-point method is developed to decompose higher bound and free harmonic waves propagating upstream and downstream around the obstacle. The model predictions are in good agreement with the experimental data for free harmonics induced by a submerged horizontal cylinder in the absence of currents. This serves as a benchmark to reveal the current effects on higher harmonic waves. The peak value of non-dimensional second free harmonic amplitude is shifted upstream for the opposing current relative to that for zero current with the variation of current-free incident wave amplitude, and it is vice versa for the following current. The second-order analysis shows a resonant behavior which is related to the ratio of the cylinder diameter to the second bound mode wavelength over the cylinder. The second-order resonant position slightly downshifted for the opposing current and upshifted for the following current.     

Estimating Directional Distribution for Co-Existent Field of Incident and Reflected Waves

In the nearshore,the wave field contains reflected and incident waves in which there iscorrelation between their phases due to the effect of reflection by some obstacles.Based on the extendedeigenvector method(EEV)derived by Guan et al.,a modified method(MEEV)is proposed as a generaland practical approach to estimating directional spectra for the co-existent field of incident and reflectedwaves and a formula is given for direct calculation of the reflection coefficient.The results of numericalsimulations show that MEEV is superior to EEV in resolution power,and the computed reflectioncoefficient agrees well with the real value within a certain range of incident angle.     

A General Linear Wave Theory for Water Waves Propagating over Uneven Porous Bottoms

Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green‘s scond identity. This theory can be reduced to a number of the most typical mild-slope equations curreutly in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.