Development of Forced Nonlinear Waves in a Bounded Basin

The process of development of nonlinear oscillations of the free surface of a fluid caused by the action of a periodic mass force in a bounded basin is numerically studied within the framework of the theory of long waves. The action of dissipative forces is taken into account. The effect of nonlinearity and geometric characteristics of the basin on the parameters of the generated wave field is analyzed. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 3–12, September–October, 2005.     

Nonlinear Surface Waves in a Basin with Floating Broken Ice

The method of multiple scales is used to deduce equations for three nonlinear approximations of a wave disturbance in a basin of constant depth covered with broken ice. In deducing these equations, we take into account the space and time variability of the wave profile in the expression for the velocity potential on the basin surface. These equations are used to construct uniformly suitable asymptotic expansions up to quantities of the third order of smallness for the liquid-velocity potential and elevations of the basin surface formed by a periodic running wave of finite amplitude. We analyze the dependence of the amplitude-phase characteristics of elevations of the basin surface on the thickness of ice, nonlinearity of its vertical acceleration, and the amplitude and wavelength of the fundamental harmonic.     

Interaction of Surface Waves in a Basin with Floating Broken Ice

The multiscale method is used to obtain asymptotic expansions up to the quantities of the third order for the elevations of the surface of the basin and the velocity potential of motion of liquid particles in the wave disturbances formed in the process of nonlinear interaction of periodic running waves of the first and second harmonics in a homogeneous ideal incompressible liquid of constant finite depth covered with broken ice. The dependences of the amplitude-phase structure of disturbances on the ice thickness, depth of the basin, and the parameters of interacting harmonics are investigated. We estimate the error of evaluation of the characteristics of the formed vertical displacement of the surface of the basin and nonlinear mass transfer introduced by neglecting the curvature of the wave profile in the expression for the velocity potential in deducing the kinematic and dynamic surface boundary conditions for nonlinear approximations.     

水槽中浅水非线性长波传播的 Boussinesq 数值模拟

浅水非线性长波传播变形中会产生波-波相互作用,为较好地模拟这种现象,在非交错网格下建立了近似在阶完全非线性的高阶 Boussinesq 数值模型.数值模型中采用了混合 4 阶 Adams- Bashforth -Moulton 格式和内部造波技术.数值计算了非线性长波在波浪水槽中的传播变形,计算结果与相关实验数据吻合较好,验证了该数值模型实用性.     

Numerical Study of Influence of Currents on Nonlinear Focusing Waves

In this paper,a numerical model for nonlinear wave propagation in currents is formulated by a set of enhanced fully nonlinear Boussinesq equations with ambient currents.This model is verified by comparison with the published results.Then the influence of currents on nonlinear focusing waves is studied by use of the numerical model.It is found that the effect of currents on the surface elevations at the focal location is negligible.Following currents can augment the maximum crest of focusing wave while decre...     

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.     

Acoustic Ducting, Reflection, Refraction, and Dispersion by Curved Nonlinear Internal Waves in Shallow Water

Nonlinear internal waves in shallow water have been shown to be effective ducts of acoustic energy, through theory, numerical modeling, and experiment. To date, most work on such ducting has concentrated on rectilinear internal wave ducts or those with very slight curvature. In this paper, we examine the acoustic effects of significant curvature of these internal waves. (By significant curvature, we mean lateral deviation of the internal wave duct by more than half the spacing between internal waves over an acoustic path, giving a transition from ducting to antiducting.) We develop basic analytical models of these effects, employ fully 3-D numerical models of sound propagation and scattering, and examine simultaneous acoustical and oceanographic data from the 2006 Shallow Water Experiment (SW06). It will be seen that the effects of curvature should be evident in the mode amplitudes and arrival angles, and that observations are consistent with curvature, though with some possible ambiguity with other scattering mechanisms.      

The Nonlinear Wave Force on a Circular Cylinder in Shallow Water

Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier.     

南黄海非线性内波的数值模拟研究(2)——内潮的非线性演变

在本工作的先行部分的基础上,本文中考虑第一模态半日内潮波分别从A站位(34°4′N,125°6′E)和B站位(36°34′N,123°51′E)向西、西南和西北方向的反射和非线性演变过程,使用的数学物理模型为适用于连续层化海洋并且考虑背景正压落潮流与涨潮流不同作用的一般化的KdV模型(简称之为GKdV模型)。模拟结果表明,南黄海的内孤立波集中分布于南黄海的南部,而在其北部极少出现内孤立波的主要原因是在南黄海的南部存在较强的背景斜压环流和很强的背景正压潮流,而且在涨潮时段(相对于朝鲜半岛的西海岸而言)背景斜压环流和背景正压潮流的方向基本相同,而在南黄海的北部这2种背景流都很弱。另外,由于出现高达0.75 m/s的正压潮流,自A站位向西北方向传播的半日内潮波处于不稳定状态。     

Theoretical Model and Random Simulation for Nonlinear Interaction of Irregular Waves with Vertical Wall

According to the theoretical solutions for the nonlinear three-dimensional gravity surface waves and their interactions with vertical wall previously proposed by the lead author, in this paper an exact second-order random model of the unified wave motion process for nonlinear irregular waves and their interactions with vertical wall in uniform current is formulated, the corresponding theoretical nonlinear spectrum is derived, and the digital simulation model suitable to the use of the FFT (Fast Fourier Tansform) algorithm is also given. Simulations of wave surface, wave pressure, total wave pressure and its moment are performed. The probability properties and statistical characteristics of these realizations are tested, which include the verifications of normality for linear process and of non-normality for nonlinear process; the consistances of the theoretical spectra with simulated ones; the probability properties of apparent characterstics, such as amplitudes, periods, and extremes (maximum and minimum, positive and negative extremes). The statistical analysis and comparisons demonstrate that the proposed theoretical and computing models are realistic and effective, the estimated spectra are in good agreement with the theoretical ones, and the probability properties of the simulated waves are similar to those of the sea waves. At the same time, the simulating computation can be completed rapidly and easily.     

Instability of Two Interacting Quasi-Monochromatic Waves in Shallow Water

The nonlinear interactions of waves with a double-peaked power spectrum have been studied in shallow water.The starting point is the prototypical equation for nonlinear unidirectional waves in shallow water,i.e.the Korteweg de Vries equation.By means of a multiple-scale technique two defocusing coupled Nonlinear Schrdinger equations are derived.It is found analytically that plane wave solutions of such a system are unstable for small perturbations,showing that the existence of a new energy exchange mechanism which can influence the behavior of ocean waves in shallow water.     

Forced Waves in a Bounded Basin with Two Pycnoclines

The behavior of waves induced in a continuously stratified fluid with two pycnoclines by periodic variations of pressure on the free surface is studied within the framework of the linear theory by taking into account the action of the Coriolis force. The fluid fills a bounded basin of constant depth. We establish the dependences of the amplitudes and velocities of waves on the period of disturbing pressure. The process of transition of generated waves from the barotropic character of propagation to baroclinic with changes in the period of disturbing pressure is studied in detail.     

Forced Waves in a Bounded Basin with One Thermocline

Within the framework of the linear theory taking into account the action of the Coriolis force, we study waves induced in a continuously stratified fluid with one thermocline by periodic variations of pressure on the free surface. The fluid fills a bounded basin of constant depth. We establish the dependences of the wave amplitudes and wave velocities on the period of disturbing pressure. The sequence of transformations of generated waves from the barotropic character of motion to baroclinic depending on changes in the period of disturbing pressure is studied in detail.     

大尺度圆柱墩群周围的波流场的数值模拟

本文对波流共同作用下大尺度圆柱墩群周围的波流场进行了数值研究。利用波浪弥散关系的迭代计算求得波向与流向的夹角以及波浪的相对频率。流场通过求解浅水环流方程得到,波浪场通过求解含流的缓坡方程得到,通过二者的迭代计算得到大尺度圆柱墩群周围的波流场的耦合解。用有限元法建立了数值模型,并将本文的计算数据与试验数据以及其他学者计算数据进行了比较,结果较为合理。     

Effects of Topography and Current on Horizontal Irrotational Waves in Shallow Water

Based on the Boussinesq assumption,derived are couple equations of free surface elevationand horizontal velocities for horizontal irrotational flow,and analytical expressions of the correspondingpressure and vertical velocity.After the free surface elevation and horizontal velocity at a certain depth areobtained by numerical method,the pressure and vertical velocity distributions can be obtained by simplecalculation.The dispersion at different depths is the same at the O(ε)approximation.The waveamplitude will decrease with increasing time due to viscosity,but it will increase due to the matching ofviscosity and the bed slope.thus,flow is unstable.Numerical or analytical results show that the waveamplitude.velocity and length will increase as the current increases along the wave direction.but theamplitude will increase.and the wave velocity and length will decrease as the water depth decreases.     

Nonlinear Wave Force on Pier Group in Shallow Water

Based on the 1st order cnoidal wave theory, the wave diffraction around the pier group inshallow water is studied in this paper. The formulas for calculating the nonlinear wave forces are also presented here. In order to verify the theoretical results, model tests are conducted in the wave flume in The State Key Laboratory of Coastal and Offshore Engineering located in Dalian University of Technology. The range of the wave parameters in the experiments is characteristic wave period T g/d~(1/2) = 8.08- 22.86, characteristic wave height H/ d= 0.1 ~ 0.45. The results obtained from the experiments agree with the theoretical results quite well. It is shown that, in shallow water the nonlinear wave forces acting on a pier group are greater than those calculated by linear wave theory, the value of increment in wave force increases with the increases of the nonlinearity of the wave. In the wave range studied in this paper, the nonlinear wave force can reach over 4 times the force calculatecd by linear wave theory. Thus, it is suggested that, when Tg / d~(1/2)> 8, the wave force on the piers in the pier group in shallow water should be calculated by using the cnoidal wave theory.     

Study on the Interaction of Water Waves with Semi-Circular Breakwater

—The present study investigates the interaction of steep waves with semi-circular breakwaterwith the complex plane＇s Cauchy boundary integral theorem.The boundary integral method is used totransform the calculation in fluid domain into its boundary alone.In the calculation the computation do-main is moved with the propagation of waves.A numerical solution is obtained for incident Stokes wavespassing the submerged obstacles.This method has been extended to the calculation of wave run-up on aslope for estimating wave overtopping.     

Investigation of Internal Waves in a Basin with Parabolic Profile of the Bottom

Within the framework of the linear theory of long waves, we study baroclinic free waves in a bounded basin of variable depth without vertical walls. We consider the case of two-layer stratification. The profile of the bottom of the basin and the form of the interface vary according to the parabolic law. Under these conditions, for the first three modes, we obtain analytic expressions for the frequencies of free oscillations, wave velocities, and the profiles of the free surface and interface. We analyze the dependences of frequencies, wave amplitudes, and wave velocities on the parameters of stratification and geometric characteristics of the basin.     

行星尺度阻塞波和天气尺度波相互作用的数值模拟

用数值方法研究了行星尺度阻塞波和天气尺度波之间的相互作用,得到在涡源强迫下,当不存在地形时,大尺度流场可发展成偶极型阻塞,瞬时流场分裂成南北对称的2支,总流场可以看到明显的多涡结构;加上双波地形后,大尺度流场发展成Ω型阻塞,瞬时流场同样分裂成2支,但北支要明显强于南支.而且通过一系列对比试验发现,适当的弱的基本西风气流是阻塞发生的有利条件.此外,讨论了初始阻塞和造波器（扰动源）位置的配置,以及造波器关闭时间的不同对阻塞强度和生命周期的可能影响.     

Analytical Study on Transmission and Reflection of Non-Linear Shallow Water Waves

The analytical study is made by using the method of matched asymptotic expansions on the transmission and reflection of solitary waves and cnoidal waves on two-dimensional floating bodies. The solutions give explicitly the variation pattern of the transmitted waves and the characteristics of the reflected waves, including the wave profile, amplitude, phase shift and evolution. The effects of the gap between the body and the sea bottom on the transmission and reflection of those waves are also discussed.