离岸式潜堤对海堤越浪量影响的实验研究

外海波浪作用下海堤越浪是一个复杂的水动力学过程,越浪量则是评估海堤安全的重要因素之一。离岸式潜堤作为一种典型的护岸工程结构物,已被应用于淤泥质海岸复合式海堤工程,其主要作用是促淤保滩和降低越浪量。本文针对不同的潜堤与海堤距离以及不同的潜堤高程,进行了规则波作用下越浪量系列物理模型实验,给出了各工况下的实测越浪量。实验结果表明:潜堤是否导致波浪破碎是控制海堤越浪量的主要因素之一;当潜堤使得波浪破碎时,潜堤位置对海堤越浪量有较大影响。潜堤与海堤距离接近1/2波长时越浪量偏大。     

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.     

Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling

In this paper a truly incompressible version of the smoothed particle hydrodynamics (SPH) method is presented to investigate the surface wave overtopping. SPH is a pure Lagrangian approach which can handle large deformations of the free surface with high accuracy. The governing equations are solved based on the SPH particle interaction models and the incompressible algorithm of pressure projection is implemented by enforcing the constant particle density. The two‐equation k–ε model is an effective way of dealing with the turbulence and vortices during wave breaking and overtopping and it is coupled with the incompressible SPH numerical scheme. The SPH model is employed to reproduce the experiment and computations of wave overtopping of a sloping sea wall. The computations are validated against the experimental and numerical data found in the literatures and good agreement is observed. Besides, the convergence behaviour of the numerical scheme and the effects of particle spacing refinement and turbulence modelling on the simulation results are also investigated in further detail. The sensitivity of the computed wave breaking and overtopping on these issues is discussed and clarified. Copyright © 2005 John Wiley & Sons, Ltd.     

Experimental and numerical analysis of solitary waves generated by bed and boundary movements

This paper is an experimental and numerical study about propagation and reflection of waves originated by natural hazards such as sea bottom movements, hill slope sliding and avalanches. One‐dimensional flume experiments were conducted to study the characteristics of such waves. The results of the experimental study can be used by other researchers to verify their numerical models. A finite volume numerical model, which solves the shallow water equations, was also verified using our own experimental results. In order to deal with reflection on sloping surfaces and overtopping walls, a new condition for the treatment of the coastline is suggested. The numerical simulation of wave generation is also studied considering the bed movement. A boundary condition is proposed for this case. Those situations when the shallow water equations are valid to simulate this type of phenomena have been studied, as well as their limitations. Copyright © 2004 John Wiley & Sons, Ltd.     

Directional Wave Propagation in a Highly Nonlinear Square Packing of Spheres

We studied the dynamic response of a two-dimensional square packing of uncompressed stainless steel spheres excited by impulsive loadings. We developed a new experimental measurement technique, employing miniature tri-axial accelerometers, to determine the stress wave properties in the array resulting from both an in-plane and out-of-plane impact. Results from our numerical simulations, based on a discrete particle model, were in good agreement with the experimental results. We observed that the impulsive excitations were resolved into solitary waves traveling only through initially excited chains. The observed solitary waves were determined to have similar (Hertzian) properties to the extensively studied solitary waves supported by an uncompressed, uniform, one-dimensional chain of spheres. The highly directional response of this system could be used as a basis to design granular crystals with predetermined wave propagation paths capable of mitigating stress wave energy.     

Exact solutions,conservation laws,bifurcation of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver equation

In the present work, we observe the dynamical behavior of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver (STO) equation. Exact solutions are derived using \({1}/{G^{^{\prime }}}\) expansion and modified Kudryashov methods. The wave transformation is used to transform STO equation into an ordinary differential equation. Combining Runge–Kutta fourth-order and Fourier spectral technique, we use a mixed scheme for the numerical study of STO equation. Since spectral methods expand the solution in trigonometric series resulting into higher-order technique and Runge–Kutta produces improved accuracy, we extract these qualities for a mixed scheme. Results so produced are presented graphically which provide a useful information about the dynamical behavior. Bifurcation behavior of nonlinear and supernonlinear traveling waves of STO equation is studied with the help of bifurcation theory of planar dynamical systems. It is observed that STO equation supports nonlinear solitary wave, periodic wave, shock wave, stable oscillatory wave and most important supernonlinear periodic wave.     

基于势流理论的内孤立波与立管作用数值研究

内孤立波是一种发生在水面以下的在世界各个海域广泛存在的大幅波浪, 其剧烈的波面起伏所携带的巨大能量对以海洋立管为代表的海洋结构物产生严重威胁, 分析其传播演化过程的流场特征及立管在内孤立波作用下的动力响应规律对于海洋立管的设计具有重要意义. 本文基于分层流体的非线性势流理论, 采用高效率的多域边界单元法, 建立了内孤立波流场分析计算的数值模型, 可以实时获得内孤立波的流场特征. 根据获得的流场信息, 采用莫里森方程计算内孤立波对海洋立管作用的载荷分布. 将内孤立波流场非线性势流计算模型与动力学有限元模型结合来求解内孤立波作用下海洋立管的动力响应特征, 讨论了内孤立波参数、顶张力大小以及内部流体密度对立管动力响应的影响. 发现随着内孤立波波幅的增大, 海洋立管的流向位移和应力明显增大. 由于上层流体速度明显大于下层, 且在所研究问题中拖曳力远大于惯性力, 因此管道顺流向的最大位移发生在上层区域. 顶张力通过改变几何刚度阵的值进而对立管的响应产生明显影响. 对于弱约束立管, 内部流体的密度对管道的流向位移影响较小.      

Ray method for surface waves on a ferromagnetic fluid

The ray method, or geometrical optics method, is used to study surface waves on a ferromagnetic fluid of variable depth. Both time-dependent and time-reduced cases are considered on the basis of the shallow-water approximation. An application of the time-reduced ray method leads to the discovery of edge waves on a ferromagnetic fluid over a uniformly sloping bottom.     

Solitary waves for a nonlinear dispersive long wave equation

All the possible traveling wave solutions of Whitham-Broer-Kaup （WBK） equation are investigated in the present paper. By employing phase plane analysis, transition boundaries are derived to divide the parameter space into several regions associated with different types of phase portraits corresponding to different forms of wave solutions. All the exact expressions of bounded wave solutions are obtained as well as their existence conditions. The mechanism of bifurcation between different waves with varying Hamiltonian value has been revealed. It is pointed out that as the periods of two coexisted periodic waves tend to infinity, they may evolve to two solitary waves. Furthermore, when their trajectories pass through the common saddle point, the two solitary waves may merge into a periodic wave, and its amplitude is nearly equal to the sum of the amplitudes of the two solitary wave solutions.     

Solitary wave trains in a cold plasma

The existence of traveling solitary waves, the products of modulation instability in a cold quasi-neutral plasma, is considered. Solitary waves of this type (solitary wave trains) are formed as a result of bifurcation from a nonzero wave number of the linear wave spectrum. It is shown that the complete system of equations describing the wave process in a cold plasma has solutions of the solitary wave train type, at least when the undisturbed magnetic field is perpendicular to the wave front. Sufficient conditions of existence of solitary wave trains in weakly dispersive media are also formulated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 154–161, September–October, 1996.     

Three-dimensional overturned traveling water waves

Traveling gravity-capillary water waves on the interface of a three-dimensional fluid of infinite depth are computed. The vortex sheet formulation with the small scale approximation is used as the mathematical model for the fluid motion. The fluid interface is parameterized isothermally. The traveling wave ansatz for parameterized surfaces is described. Waves are computed using Fourier collocation and quasi-Newton iteration; large amplitude overturned traveling waves are computed via a dimension-breaking based numerical continuation method.     

海堤越浪的数值模拟

基于RANS方程和两方程湍流模型,采用有限体积法,将人射波波场作为人工的分布源项加人动量方程,提出了适用于VOF方法的源造波一消波技术。通过对行波及驻波的计算,分别考察了数值波浪水槽前端及末端消波段的有效性。在本文建立的数值波浪水槽内对规则波在海堤上爬高和越浪过程进行了数值模拟,并将计算结果与现有实验结果进行了比较。验证计算结果表明,数值模拟结果较好地复演了海堤越浪过程。为了研究模型尺度对越浪量的影响,文中设计了一组满足重力相似但具有不同几何比尺的数值实验模型。系列数值实验结果表明,若按重力相似换算越浪量,计算结果与实验预报值间的偏差随模型比尺的增大和堤前波浪破碎强度的增强而增大,建议在进行越浪物理模型实验时需进一步考虑模型比尺对原型预报值的影响。     

Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation

In this paper, we consider a dissipative-dispersive nonlinear equation appliable to many physical phenomena. Using the geometric singular perturbation method based on the theory of dynamical systems, we investigate the existence of its traveling wave solutions with the dissipative terms having sufficiently small coefficients. The results show that the traveling waves exist on a two-dimensional slow manifold in a three-dimensional system of ordinary differential equations （ODEs）. Then, we use the Melnikov method to establish the existence of a homoclinic orbit in this manifold corresponding to a solitary wave solution of the equation. Furthermore, we present some numerical computations to show the approximations of such wave orbits.     

高度非线性孤立波与弹性大板的耦合作用研究

一维颗粒链的一端受到一个有初速度颗粒的撞击,导致颗粒连中产生稳定传播的应力波——高度非线性孤立波,该应力波的波长、波速以及幅值都能保持很好的稳定性,且遇到边界才会反射. 孤立波是一种良好的信息载体,广泛应用于无损检测技术中. 基于孤立波的特性,研究高度非线性孤立波与弹性大板耦合作用,基于赫兹定律和板的内在非弹性理论,推导出晶体链与大板的耦合微分方程组. 用龙格库塔法求解该微分方程组,得到颗粒链中各颗粒的位移、速度曲线. 通过分析回弹波出现的时间、回弹波所携带的能量以及模量、厚度、重力等对孤立波的影响,发现反射孤立波对大板的弹性模量和厚度尤为敏感,此外,颗粒链的摆放对整个耦合过程也有影响. 研究的结果为孤立波对结构体的无损探伤提供了理论依据,该技术可实现对结构体的快速检查和可控性研究.     

On the nonlinear dynamics of the traveling-wave solutions of the Serre system

We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes a high-order finite-element method with smooth, periodic splines in space and explicit Runge–Kutta methods in time. Other forms of solutions such as cnoidal waves and dispersive shock waves are also considered. The differences between solutions of the Serre equations and the Euler equations are also studied.     

Solitary wave interactions and reshaping in coupled systems

The interaction of the components of composite solitary waves governed by nonlinear coupled equations is studied numerically. It is shown how predictions of the known exact traveling wave solutions may help in understanding and explaining the process of reshaping seen as head-on and take-over collisions of individual solitary waves. The most interesting results concern the switch in the sign or the periodic modulation of the amplitude of the solitary wave and the direction of its propagation due to collisions.     

A lattice Boltzmann method for viscous free surface waves in two dimensions

We propose a new method based on the combination of the lattice Boltzmann equation (LBE) and the kinematic boundary condition (KBC) method to simulate viscous free surface wave in two dimensions. In our method, the flow field is modeled by LBE, whereas the free surface is explicitly tracked by the local height function, which is calculated by the KBC method. The free surface boundary condition (FSBC) for LBE is revised from previous researches. Interpolation‐supplemented lattice Boltzmann (ISLB) method is introduced, which enables our approach to be applied on arbitrary, nonuniform mesh grids. Five cases are simulated respectively to validate the LBE–KBC method: the stationary flow and the solitary waves simulated by the revised‐FSBC are more accurate than the one obtained by the former‐FSBC; numerical results of standing waves show that our method is compatible to the existing two‐dimensional finite‐volume scheme; cases of small amplitude Stokes wave and waves traveling over a submerged bar show good agreement on wave celerity, wavelength, wave amplitude and wave period between numerical results and corresponding analytical solutions and/or experiment data.Copyright © 2012 John Wiley & Sons, Ltd.     

Symmetry and Uniqueness of the Solitary-Wave Solution for the Ostrovsky Equation

We consider herein the Ostrovsky equation which arises in modeling the propagation of the surface and internal solitary waves in shallow water, or the capillary waves in a plasma with the effects of rotation. Using the modified sliding method, we prove that the solitary wave moving to the left to the Ostrovsky equation is symmetric about the origin and unique up to translations. We also establish the regularity and decay properties of solitary waves and obtain some results of the nonexistence of solitary wave solutions depending on the wave speed, weak rotation, and dispersive parameter.     

Higher-order theory of internal solitary waves with a free surface in two-layer fluid system of finite depth

A higher-order approximation theory of internal solitary waves with a free surface is presented. Using the method of strained co-ordinates, the third-order approximation evolution equation of interface has been found. An analytic expression of the wave velocity is given. The evolution equation has been solved numerically. It is found that the effects of free surface on the shape and wave velocity of solitary wave are O(ε²), and the third-order numerical solutions are closer to experimental data than the first-and second-order solutions.     

Numerical analysis of breaking waves using the moving particle semi-implicit method

The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave. © 1998 John Wiley & Sons, Ltd.