Theoretical and experimental study of breaking wave on sloping bottoms

This paper studies the continuous evolution of breaking wave for the surface water waves propagating on a sloping beach. A Lagrangian asymptotic solution is derived. According to the solution coupled with the wave breaking criteria and the equations of water particles motion, the wave deformation and the continuous wave breaking processes for the progressive water waves propagating on a sloping bottom can be derived. A series of experiments are also conducted to compare with the theoretical solution. The results show that the present solution can reasonably describe the plunging or spilling wave breaking phenomenon.     

Experimental Study on the Bed Shear Stress Under Breaking Waves

The object of present study is to investigate the bed shear stress on a slope under regular breaking waves by a novel instrument named Micro-Electro-Mechanical System (MEMS) flexible hot-film shear stress sensor. The sensors were calibrated before application, and then a wave flume experiment was conducted to study the bed shear stress for the case of regular waves spilling and plunging on a 1:15 smooth PVC slope. The experiment shows that the sensor is feasible for the measurement of the bed shear stress under breaking waves. For regular incident waves, the bed shear stress is mainly periodic in both outside and inside the breaking point. The fluctuations of the bed shear stress increase significantly after waves breaking due to the turbulence and vortexes generated by breaking waves. For plunging breaker, the extreme value of the mean maximum bed shear stress appears after the plunging point, and the more violent the wave breaks, the more dramatic increase of the maximum bed shear stress will occur. For spilling breaker, the increase of the maximum bed shear stress along the slope is gradual compared with the plunging breaker. At last, an empirical equation about the relationship between the maximum bed shear stress and the surf similarity parameter is given, which can be used to estimate the maximum bed shear stress under breaking waves in practice.     

Physical Investigation of Directional Wave Focusing and Breaking Waves in Wave Basin

An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are studied. The distrihution of maximum amplitude and the evolution of time series and spectra during wave packet propagation and the variation of water surface parameters are extensively investigated. The results reveal that the characteristics of focusing waves are significantly influenced hy wave directionality and that that breaking criteria for directional waves are distinctly different from those for unidirectional waves.     

表面波破碎泡径谱的理论研究

采用新的无量纲变量组合推导出波浪破碎形成的气泡总数与气体体积卷入率、湍流能谱密度以及表面张力之间的关系;利用观测结果提出两点假设,并据此将泡径谱N(a)推广为随泡径和深度的分布函数N(a,z)。     

Wave Breaking Phenomena of Irregular Waves Combined with Opposing Current

- Experimental study and theoretical analysis show that the critical value of relative wave height (H/ d)b given by Goda and the critical wave steepness (H/ L)b given by Michell and Miche can be adopted as the spilling breaking indices of regular waves. According to the same principle, a systematic theoretical analysis and experiment of irregular waves have been done by the authors in order to solve the breaking problem of irregular waves. It is indicated that the authors' method for determining wave breaking of regular waves can also be used for irregular waves.     

不同破碎波气液混合区发展特征及其运动特性研究

了解波浪破碎速度场的分布特性对于波浪破碎物理机制的研究极为重要,同时,对比研究不同类型破碎产生的气液混合区的演化特征有利于波浪白冠覆盖率模型的完善。在实验室水槽,生成了深水临界波、单次崩破波和单次卷破波,采用图像测速技术获取了波浪破碎图像、波面下水体和气液混合区速度场。结果表明,崩破波的水平向速度u和垂直向速度v在波峰前和波峰后的分布极为不对称,其水平向最大速度umax并不位于峰顶,而是在主导波峰前0.7$\eta_{\max} $处;卷破波的umax出现在波峰峰顶前端极小的区域内,且该区域与周围区域的速度梯度极大。崩破波和卷破波生成的气液混合区发展特征也存在差异：崩破波的umax值大、影响区域长、混合区厚度较小、各区域影响时间短;而卷破波的各项特征参数与崩破波形成对比。     

Comparisons of Computational and Experimental Results of Solitary Wave Breaking

- In this paper, the solitary wave deformation along a gentle slope and the impact pressure, on the wall are investigated experimentally and the results are compared with numerical results obtained based on the volume of fluid (VOF) method. The topography used in the experiment consists of three segments. The left segment is a 1:4 slope, the middle segment 1 :SO slope and the right segment a horizontal bed. Both the wave heights and breaking points obtained from numerical simulation and experiments are in good agreement. Numerical results give reasonable pressure distributions of breaking waves on the wall.     

Numerical Simulation of Breaking Wave Based on Higher-Order Mild Slope Equation

The "surface roller" to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave transportation including diffraction, refraction and breaking in nearshore areas. The roller breaking random wave higher-order approximate parabolic equation model has been verified by the existing experimental data for a plane slope beach and a circular shoal, and the numerical results of random wave breaking model agree with the experimental data very well. This model can be applied to calculate random wave propagation from deep to shallow water in large areas near the shore over natu ral topography.     

Singularity and Breaking of the Third Order Stokes Waves

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Probabilistic Models for the Probability of Wave Breaking and Whitecap Coverage Based on Kinematic Breaking Criterion

More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact moders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabihstic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks ff the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4.Then the JONSWAP spectrum is used to represent the fetch-limited sea waves in deep water, so as to relate the probahility of wave breaking and the whitecap coverage with wind parameters. To this end, the time-averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.     

Experimental Study of Wave Breaking on Gentle Slope

—An experimental study of regular wave and irregular wave breaking is performed on a gentleslope of 1:200.In the experiment,asymmetry of wave profile is analyzed to determine its effect on wavebreaker indices and to explain the difference between Goda and Nelson about the breaker indices of regu-lar waves on very mild slopes.The study shows that the breaker index of irregular waves is under less influ-ence of bottom slope i,relative water depth d/L_0 and the asymmetry of wave profile than that of regularwaves.The breaker index of regular waves from Goda may be used in the case of irregular waves, whilethe coefficient A should be 0.15.The ratio of irregular wavelength to the length calculated by linear wavetheory is 0.74.Analysis is also made on the waveheight damping coefficient of regular waves after break-ing and on the breaking probability of large irregular waves.     

Approach to Calculating Methods of Wave Breaking Depth and Height

- Engineers in coastal engineering have been paying much attention to the research subject on wave breaking. In this paper, previous research results on the calculating methods of wave breaking depth and height are enumerated, the laws of wave transformation before and after wave breaking are investigated, an adequate supposition is made, and the effect of beach slope, bed friction and breaking turbulence on wave breaking is considered. By applying the theory of wave energy dissipation rate and combining with proper formulas of solitary waves, a new calculating formula of wave breaking depth and height on the movable bed is derived and examined with the data from experimental pools of different sizes, and it is proved to be of practicability.     

平缓岸坡上波浪破碎的实验研究

在１／２００的缓坡上进行了规则波与不规则波破碎的实验研究。在本实验条件下,分析了波形的不对称必至波浪破碎指标的影响,并以此对合田良实和Ｎｅｌｓｏｎ关于极平缓坡上规则波破碎指标的分歧作了解释。本文的研究还表明,底坡坡度ｉ、相对水深ｄ／Ｌ。及波形的不对称必至不规则波的破碎指标的影响较小。合田对规则波的破碎指标在不规则波条件下仍然可用,但系数Ａ应取为０．１５。不规则波波长与同周期按线悸理论计算之波长的比     

Effects of Wave Breaking on Freak Wave Generation in Ramdom Wave Train

The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index, AI=Hmax/Hs, being used to characterize the freak waves, and the changes of the coefficient due to wave breaking. The results show that the occurence in deep water is larger than that in shallow water.     

Effects of Wave Breaking on Freak Wave Generation in Random Wave Train

The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index,AI=Hmax/Hs,being used to characterize the freak waves,and the changes of the coefficient due to wave breaking. The results show that the occurrence probability of freak wave events in non-breaking waves is much larger than that in breaking waves and such occurrence in deep water is larger than that in ...     

Theoretical and Experimental Study on the Acoustic Wave Energy After the Nonlinear Interaction of Acoustic Waves in Aqueous Media

Based on the Burgers equation and Manley?Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and the pump wave, the analytical solutions of acoustic waves’ amplitude in the field are deduced. The relationship between normalized energy of high-frequency and the change of acoustic energy before and after the nonlinear interaction of the acoustic waves is analyzed. The experimental results about the changes of the acoustic energy are presented. The study shows that new frequencies are generated and the energies of the low-frequency are modulated in a long term by the pump waves, which leads the energies of the low-frequency acoustic waves to change in the pulse trend in the process of the nonlinear interaction of the acoustic waves. The increase and decrease of the energies of the low-frequency are observed under certain typical conditions, which lays a foundation for practical engineering applications.     

Determining the Onset and Strength of Unforced Wave Breaking in A Numerical Wave Tank

A numerical wave tank is used to investigate the onset and strength of unforced wave breaking, and the waves have three types of initial spectra: constant amplitude spectrum, constant steepness spectrum and Pierson-Moscowitz spectrum. Numerical tests are performed to validate the model results. Then, the onset of wave breaking is discussed with geometric, kinematic, and dynamic breaking criteria. The strength of wave breaking, which is always characterized by the fractional energy loss and breaking strength coefficient, is studied for different spectra. The results show how the energy growth rate is better than the initial wave steepness on estimating the fractional energy losses as well as breaking strength coefficient.     

Wave Reflection Caused by Wave Overtopping and Sloping Top of Spructure

In this paper, the theoretical analysis and experimental studies are employed to investigate the reflection characteris-tics of partial standing waves caused by wave overtopping and sloping top of structures. Based on the principle of conser-vation of wave energy flux, the third-order Stokes wave theory is used to formulate the reflection coefficient at wave overtopping; the calculation results are regressed into an applied expression. A series of experiments of wave reflection for a vertical-wall structure with chamfered and overhanging upper sections are carried out to investigate the influence of top slope on wave reflection. The regularity of variation of wave reflection in this case is analysed based on the experimental results.     

Parameterization of Wave Breaking Probability and Whitecap Coverage

1 .Introduction Wave breaking and associated whitecapping have long beeninteresting due totheir close relationto many fields of ocean study,including air-sea interaction,remote sensing,ocean engineering,aswell as wave dynamics .The breaking probabilityBan…     

Wave Transformation and Breaking in Diagonal Opposing Current

- When waves propagate into diagonal opposing current from non-current area, not only the wave parameters but also the direction of wave propagation will change, that is, wave refraction will occur. The authors have calculated the changes of wave parameters, including wave refraction, by Linear Wave Theory, and have also done systematic study on wave transformation and breaking in opposing current by means of experimental analysis and theoretical calculation. In order to know the effect of wave refraction, computation is done in this paper about wave transformation and breaking on gentle slopes in diagonal opposing current.