Boussinesq方程与抛物型缓坡方程2种波浪模型的比较分析

波浪破碎的模拟对于波浪模拟的准确性十分重要。为了解波浪破碎模型的问题,本文对抛物型缓坡方程和Boussinesq方程这2种波浪模型所采用的破碎方法进行比较和分析。运用基于Boussinesq方程的Funwave模型和基于抛物型缓坡方程的REF/DIF模型,分别对特拉华大学的未破碎圆形浅滩试验和作者于实验水槽进行的Undertow试验这2个物理模型进行波高模拟、比较与分析。模拟结果表明:Funwave和REF/DIF这2种波浪模型都能准确的模拟出波高随水深的变化情况,但对于波浪破碎后的情况,REF/DIF模型模拟的更为精确一些。     

The New Form of Time-Dependent Mild Slope Equation for Random Waves

The mild-slope equation derived by Berkhoff (1972), has widely been used in the numerical calculation of refraction and diffraction of regular waves. However, it is well known that the random sea waves has a significant effect in the refraction and diffraction problems. In this paper, a new form of time-dependent mild slope equation for irregular waves was derived with Fade approximation and Kubo's time series concept. The equation was simplified using WKB method, and simple and practical irregular mild slope equation was obtained. Results of numerical calculations are compared with those of laboratory experiments.     

Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect： Regular Waves

A new form of hyperbolic mild slope equations is derived with the inclusion of the amphtude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved nu- merically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model＇ s performance on prediction of wave heights around breaking point for the wave motions in surf zone.     

Calculation of Wave Radiation Stress in Combination with Parabolic Mild Slope Equation

A new method for the calculation of wave radiation stress is proposed by linking the expres-sions for wave radiation stress with the variables in the parabolic mild slope equation.The governing equa-tions are solved numerically by the finite difference method.Numerical results show that the new methodis accurate enough,can be efficiently solved with little programming effort,and can be applied to the calcu-lation of wave radiation stress for large coastal areas.     

Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect: Random Waves

New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves. The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves, which is done by introducing a representative wave amplitude for the carrier waves. The computation time is greatly saved by the introduction of the representative wave amplitude. The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone. The model is validated for random waves propagate over a shoal and in surf zone against measurements.     

波浪谱形对不规则波数值模拟的影响

通过数值模拟分析了波浪谱形对不规则波浪数值模拟结果的影响.采用不同参数的JONSWAP谱模拟入射波要素,基于抛物型缓坡方程模拟不规则波浪的传播,分析了波浪谱形状对波浪数值模拟结果的影响.结果表明,采用抛物型缓坡方程模拟不规则波浪时,入射波浪谱形对模拟结果影响不明显;但由于模型中非线性项的影响,采用不规则波模拟的波高分布和采用规则波模拟的结果略有差别.     

Numerical Simulation of Spatial Lag Between Wave Breaking Point and Location of Maximum Wave-Induced Current

A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point.The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direction.The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress.An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy.The wave driver model is a phase-averaged wave model based on the wave action balance equation.Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach are used to evaluate the model's performance.The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.     

Numerical Prediction of Regular Wave Breaking on Very Gentle Slopes

Regular wave deformation and breaking on very gende 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 time-stepping integration are detertnined 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 occu     

Applications of A Numerical Model to Wave Propagation on Mild Slopes

Based on the mild slope equation that has heen deeomposed inlo three equations related to wave phase function, wave amplitude and wave approach angle, a refraction-diffraction model is developed. The finite difference method has been selected as the solution method. The model results are compared with experimental results and the model is applied to coastal waters of the Fethiye Bay, whieh is located at the Mediterranean Sea of Turkey.     

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.     

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.     

Nonlinear Dispersion Effect on Wave Transformation

—A new nonlinear dispersion relation is given in this paper.which can overcome the limitationof the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple(1986).and which has a better approximation to Hedges'empirical relation than the modified relations by Hedges(1987).Kirby and Dalrymple(1987)for shallow waters.The new dispersion relation is simple in form.thusit can be used easily in practice.Meanwhile,a general explicit approximation to the new dispersion rela-tion and other nonlinear dispersion relations is given.By use of the explicit approximation to the newdispersion relation along with the mild slope equation taking into account weakly nonlinear effect.amathematical model is obtained,and it is applied to laboratory data.The results show that the model de-veloped with the new dispersion relation predicts wave transformation over complicated topography quitewell.     

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.     

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.     

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.     

近岸波浪破碎区不规则波浪的数值模拟

基于近岸不规则波浪传播的抛物型缓坡方程和两类波浪破碎能量损耗因子,对近岸波浪破碎区不规则波浪的波高分布进行了数值模拟,并结合实验结果对数值模拟结果进行了验证分析,结果表明采用两类波浪破碎能量损耗因子所模拟的破碎区波高与实测值均吻合良好,波浪破碎能量损耗因子及波浪破碎指标对破碎区波浪波高分布影响较明显。     

Efficient Elliptic Solver for the Mild Slope Equation Using BI-CGSTAB Method

The elliptic mild slope equation is used to simulate linear wave propagation over variable seabed topography with mild slopes.The governing equation is discretized by the finite difference method.Ba-sed on the BI-CGSTAB technique.an attractive variant of BI-Conjugate Gradients(BI-CG)method,theobtained linear algebraic system of equations is solved.Numerical experiments show that the BI-CGSTABmethod is efficient for solving the elliptic mild slope equation.The results obtained by the BI-CGSTAB-Ba-sed method are much the same as those obtained by other authors with different solution methods,but theconvergence rate is much faster than that of other methods.     

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.     

近岸较大区域波浪数值模型的比较

将适用于近岸较大区域波浪传播变形的三种模型,即基于抛物型缓坡方程的不规则波模型、引入浅水波浪谱 TMA 谱的 SWAN(simulating waves nearshore)模型以及采用默认 JONSWAP 谱的 SWAN模型应用于特拉华大学(University of Delaware)圆形浅滩实验进行比较.结果显示,抛物型缓坡方程和SWAN 的模拟结果与实验所测数据符合都比较好; SWAN 在非线性作用较强的浅滩中心及靠后部效果更佳,而抛物型缓坡方程由于没有考虑非线性作用,模拟得到的最大波高较实测值偏高,且波高变化较为剧烈.     

Parabolic Approximation of the Weakly Nonlinear Mild Slope Equation with Bottom Friction

This paper presents a refined parabolic approximation model of the mild slope equation to simu-late the combination of water wave refraction and diffraction in the large coastal region.The bottom frictionand weakly nonlinear term are included in the model.The difference equation is established with the Crank-Nicolson scheme.The numerical test shows that some numerical prediction results will be inaccurate in com-plicated topography without considering weak nonlinearity;the bottom friction will make wave height damp-ing and it can not be neglected for calculation of wave field in large areas.