共查询到19条相似文献，搜索用时 234 毫秒
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适合复杂地形的高阶Boussinesq水波方程 总被引：17，自引：4，他引：17
针对海底坡度较大(量阶为O(1))或海底曲率较大的复杂地形,建立了一个新型高阶Boussinesq水波方程.该方程可用于研究海底存在若干相互平行沙坝引起的Bragg反射问题.方程的水平速度沿水深的分布为四次多项式,色散性和变浅作用性能的精度比经典Boussinesq方程高了一阶.方程在浅水水域可以是完全非线性的. 相似文献
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建立基于四阶完全非线性Boussinesq水波方程的二维波浪传播数值模型。采用Kennedy等提出的涡粘方法模拟波浪破碎。在矩形网格上对控制方程进行离散,采用高精度的数值格式对离散方程进行数值求解。对规则波在具有三维特征地形上的传播过程进行了数值模拟,通过数值模拟结果与实验结果的对比,对所建立的波浪传播模型进行了验证。同时,为了考察非线性对波浪传播的影响,给出和上述模型具有同阶色散性、变浅作用性能但仅具有二阶完全非线性特征的波浪模型的数值结果。通过对比两个模型的数值结果以及实验数据,讨论非线性在波浪传播过程中的作用。研究结果表明,所建立的Boussinesq水波方程在深水范围内不但具有较精确的色散性和变浅作用性能,而且具有四阶完全非线性特征,适合模拟波浪在近岸水域的非线性运动。 相似文献
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建立具有色散性的水平二维非线性波浪方程,方程的非线性近似到了三阶。方程以波面升高和自由表面速度势表达的微分-积分型数学方程,给出方程的数值求解方法和算例,对方程积分项的处理给出了计算方法。计算结果与Boussinesq方程模型和缓坡方程模型的对应计算结果进行了对比。 相似文献
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二维非线性浅水波的数值模拟 总被引：3，自引：0，他引：3
研究工作的目的在于建立一个能够模拟二维潮流、洪水波(长波)和浅水波浪(短波)的综合数学模型.基本模型建立在非线性的Boussinesq方程基础之上.本文主要讨论浅水波浪即短波的数值模拟.模型可以考虑必要的外力项,如柯氏力、风应力、大气压力和底摩阻力等.针对Boussinesq方程提出了一个全隐的二维差分格式,讨论了人工开边界的处理方法.模型被用来计算了突然扩张渠槽中的环流和单突堤后的水波绕射,取得了满意的结果. 相似文献
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Liu等给出的最高导数为2的双层Boussinesq水波方程具有较好的色散性和非线性,基于该方程建立了有限差分法的三维波浪数值模型。在矩形网格上对方程进行了空间离散,采用高阶导数近似方程中的时、空项,时间积分采用混合4阶Adams-Bashforth-Moulton的预报—校正格式。模拟了深水条件下的规则波传播过程,计算波面与解析结果吻合较好,反映出数值模型能很好地刻画波面过程及波面处的速度变化;在kh=2π条件下可较为准确获得沿水深分布的水平和垂向速度,这与理论分析结果一致。最后,利用数值模型计算了规则波在三维特征地形上的传播变形,数值结果和试验数据吻合较好;高阶非线性项会对波浪数值结果产生一定的影响,当波浪非线性增强,水深减少将产生更多的高次谐波。建立的双层Boussinesq模型对强非线性波浪的演化具有较好的模拟精度。 相似文献
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应用内外解匹配的方法和驻相法推导了柱坐标系下地震引起的水面波动方程的解,即推导了地震海啸波生成与传播的理论方程,并对越洋地震海啸理论方程进行了求解。基于Boussinesq方程出发,建立了二维越洋海啸波传播数学模型,并对越洋海啸进行了数值计算,计算方法采用有限差分方法,差分格式采用交替方向隐格式(Alternating Direction Implicit即ADI方法)。利用越洋海啸计算模式对发生在大洋中的地震海啸进行了模拟,将数值模拟结果与地震海啸波理论方程的计算结果进行了比较,两种计算结果吻合较好。 相似文献
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波群演化有非常特殊的物理现象。模拟这一过程要求模型具有较好的色散性性能同时具有良好的波幅离散性能、非线性性能。采用分层Boussinesq类方程对深水波群得到非线性演化开展数值模拟研究。利用Stansberg(1993)的物理实验验证了分层Boussinesq方程波浪模型在该研究中具有很好的适用性和较高的精度。模型较好地预报了组成波的倍频、和频及差频波浪。越接近造波板,结果吻合的越好。随着长时间的演化,主频部分的组成波的波高数值结果要大于实测结果,高频部分的组成波出现明显差异。 相似文献
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《海洋湖沼通报》2021,(4)
在Liu和Fang推导的双层Boussinesq方程基础上,将其简化为一层水波方程,并建立了基于混合4阶Adams-Bashforth-Moulton时间格式的立面二维数值模型;数值模拟了波浪在潜堤上的演化过程,并将数值计算结果与相关实验结果进行了对比,验证了该数值模型的正确性。进而在不同的入射波条件下,将沿着水深分布的水平速度和垂向速度的数值模拟结果与线性、二阶、三阶解析解解析结果进行综合对比。对比结果表明,在不同的无因次水深kh条件下,数值解与解析解的整体吻合程度较好。在不同的波陡H/L条件下,数值解展现了较好的非线性特征。在不同的波高水深比H/h条件下,数值解与解析解之间的整体差异较小。可以看到,该数值模型较好地模拟了波浪垂向速度场分布,体现了其优良的综合性能。 相似文献
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Recent progress in formulating Boussinesq-type equations includes improved features of linear dispersion and higher-order nonlinearity. Nonlinear characteristics of these equations have been previously analysed on the assumption of weak nonlinearity, being therefore limited to moderate wave height. The present work addresses this aspect for an important class of wave problems, namely, regular waves of permanent form on a constant depth. Using a numerical procedure which is valid up to the maximum wave height, permanent-form waves admitted by three sets of advanced Boussinesq-type equations are analysed. Further, the characteristics of each set of the Boussinesq-type equations are discussed in the light of those from the potential theory satisfying the exact free-surface conditions. Phase velocity, amplitude dispersion, harmonic amplitudes (namely, second and third) and skewness of surface profile are shown over a two-parameter space of frequency and wave height. 相似文献
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For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with padé approximation. 相似文献
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Higher order Boussinesq equations 总被引：2，自引：0，他引：2
Z. L. Zou 《Ocean Engineering》1999,26(8):239
A new form of Boussinesq-type equations accurate to the third order are derived in this paper to improve the linear dispersion and nonlinearity characteristics in deeper water. Fourth spatial derivatives in the third order terms of the equations are transformed into second derivatives and present no difficulty in numerical computations. With the increase in accuracy of the equations, the nonlinear and dispersion characteristics of the equations are of one order of magnitude higher accuracy than those of the classical Boussinesq equations. The equations can serve as a fully nonlinear model for shallow water waves. The shoaling property of the equations is also of high accuracy through shallow water to deep water by introducing an extra source term into the second order continuity equation. An approach to increase the accuracy of the nonlinear characteristics of the new equations is introduced. The expression for the vertical distribution of the horizontal velocities is a fourth order polynomial. 相似文献
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A higher-order non-hydrostatic σ model is developed to simulate non-linear refraction–diffraction of water waves. To capture non-linear (or steep) waves, a 4th-order spatial discretization is utilized to approximate the large horizontal pressure gradient. A higher-order top-layer pressure treatment is further implemented to resolve wave propagation. The model's characteristics including linear wave dispersion and non-linearity are carefully examined. The accuracy of the present model using only two vertical layers is validated by laboratory data and the available results predicted by the non-linear Schrödinger equation, Boussinesq-type equations, the non-linear mild slope equation, and the Laplace equation. Features of harmonic generation as well as the influences of dispersion and non-linearity on wave energy transfer processes are discussed. 相似文献
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It is difficult to compute far-field waves in a relative large area by using one wave generation model when a large calculation domain is needed because of large dimensions of the waterway and long distance of the required computing points. Variation of waterway bathymetry and nonlinearity in the far field cannot be included in a ship fixed process either. A coupled method combining a wave generation model and wave propagation model is then used in this paper to simulate the wash waves generated by the passing ship. A NURBS-based higher order panel method is adopted as the stationary wave generation model; a wave spectrum method and Boussinesq-type equation wave model are used as the wave propagation model for the constant water depth condition and variable water depth condition, respectively. The waves calculated by the NURBS-based higher order panel method in the near field are used as the input for the wave spectrum method and the Boussinesq-type equation wave model to obtain the far-field waves. With this approach it is possible to simulate the ship wash waves including the effects of water depth and waterway bathymetry. Parts of the calculated results are validated experimentally, and the agreement is demonstrated. The effects of ship wash waves on the moored ship are discussed by using a diffraction theory method. The results indicate that the prediction of the ship induced waves by coupling models is feasible. 相似文献
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Based on a set of Boussinesq-type equations with improved linear frequency dispersion characteristics in deeper water, the present paper incorporates the simplified effect of spilling wave breaking into the equations. The analysis is restricted to a single horizontal dimension but the method can be extended to include the second horizontal dimension. Inside the surf zone the vertical variation of the horizontal velocity profile is assumed to be composed of an (initially unknown) organised velocity component below the roller and a surface roller travelling with the wave celerity. This leads to a new set of equations which is capable of simulating the transformation of waves before, during and after wave breaking. The model is calibrated and verified by comparison with several wave flume measurements. The results show that the model produces sound physical results. 相似文献
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《Coastal Engineering》2006,53(2-3):181-190
Two-dimensional depth-averaged Boussinesq-type equations were presented with the consideration of slowly varying bathymetry and effects of bottom viscous boundary layer. These Boussinesq-type equations were written in terms of the horizontal velocity components evaluated at an arbitrary elevation in the water depth and the free surface displacement. The leading order effects of the bottom boundary layer were represented by a convolution integral in the depth-integrated continuity equation. To test the validity of the theory, a set of laboratory experiments was performed to measure the viscous damping and shoaling of a solitary wave propagating in a wave tank. The time histories of the free surface profiles were measured at several locations along the centerline of the flume. To compare these laboratory data with theoretical results, the two-dimensional Boussinesq-type equations were integrated across the wave tank, resulting in a set of one-dimensional equations, while the side-wall boundary layers were properly considered. The agreement between the experimental data and numerical results was very good. The bottom shear stress formula was also given and its impact on the sediment transport rate was discussed. 相似文献
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《Ocean Engineering》1999,26(4):287-323
A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model. 相似文献