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1.
A run-up of irregular long sea waves on a beach with a constant slope is studied within the framework of the nonlinear shallow-water theory. This problem was solved earlier for deterministic waves, both periodic and pulse ones, using the approach based on the Legendre transform. Within this approach, it is possible to get an exact solution for the displacement of a moving shoreline in the case of irregular-wave run-up as well. It is used to determine statistical moments of run-up characteristics. It is shown that nonlinearity in a run-up wave does not affect the velocity moments of the shoreline motion but influences the moments of mobile shoreline displacement. In particular, the randomness of a wave field yields an increase in the average water level on the shore and decrease in standard deviation. The asymmetry calculated through the third moment is positive and increases with the amplitude growth. The kurtosis calculated through the fourth moment turns out to be positive at small amplitudes and negative at large ones. All this points to the advantage of the wave run-up on the shore as compared to a backwash at least for small-amplitude waves, even if an incident wave is a Gaussian stationary process with a zero mean. The probability of wave breaking during run-up and the applicability limits for the derived equations are discussed.  相似文献   

2.
We study the run-up of long solitary waves of different polarities on a beach in the case of composite bottom topography: a plane sloping beach transforms into a region of constant depth. We confirm that nonlinear wave deformation of positive polarity (wave crest) resulting in an increase in the wave steepness leads to a significant increase in the run-up height. It is shown that nonlinear effects are most strongly pronounced for the run-up of a wave with negative polarity (wave trough). In the latter case, the run-up height of such waves increases with their steepness and can exceed the amplitude of the incident wave.  相似文献   

3.
The random long wave runup on a beach of constant slope is studied in the framework of the rigorous solutions of the nonlinear shallow water theory. These solutions are used for calculation of the statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. It is shown that probability characteristics of the runup heights and extreme values of the shoreline velocity coincide in the linear and nonlinear theory. If the incident wave is represented by a narrow-band Gaussian process, the runup height is described by a Rayleigh distribution. The significant runup height can also be found within the linear theory of long wave shoaling and runup. Wave nonlinearity nearshore does not affect the Gaussian probability distribution of the velocity of the moving shoreline. However the vertical displacement of the moving shoreline becomes non-Gaussian due to the wave nonlinearity. Its statistical moments are calculated analytically. It is shown that the mean water level increases (setup), the skewness is always positive and kurtosis is positive for weak amplitude waves and negative for strongly nonlinear waves. The probability of the wave breaking is also calculated and conditions of validity of the analytical theory are discussed. The spectral and statistical characteristics of the moving shoreline are studied in detail. It is shown that the probability of coastal floods grows with an increase in the nonlinearity. Randomness of the wave field nearshore leads to an increase in the wave spectrum width.  相似文献   

4.
The effect of nonlinearities, such as wave-breaking and vertical asymmetry associated with sea waves, on the distribution of wave amplitudes is explored. Semiclosed theoretical expressions are derived to describe the distributions of breaking-limited crest and trough amplitudes for Stokes-type nonlinear sea waves. These are compared with the conventional Rayleigh distribution appropriate to linear wave amplitudes. The construction of nonlinear wave envelopes with the fast Fourier transform technique is described. The technique can be utilized to enlarge the data base in empirical analyses of field records which typically contain limited information on amplitude characteristics. The theoretical distributions and the proposed data enlargement technique are demonstrated with the analysis of a nonlinear wave record.  相似文献   

5.
应用基于势流理论的时域高阶边界元方法,建立一个完全非线性的三维数值波浪水槽,通过实时模拟推板造波运动的方式产生波浪。通过混合欧拉-拉格朗日方法和四阶Runge-Kutta方法更新自由水面和造波板的瞬时位置。利用所建模型分别模拟了有限水深波和浅水波,与试验结果、相关文献结果和浅水理论结果吻合较好,且波浪能够稳定传播。系统地讨论造波板的运动圆频率、振幅和水深等对波浪传播和波浪特性的影响,并对波浪的非线性特性进行分析,研究发现造波板运动频率、运动振幅以及水深均将对波浪形态和波浪非线性产生显著影响。结果为真实水槽造波机的运动控制以及波浪生成试验提供了依据,便于实验室设置更合理的参数来准确模拟不同条件下的波浪。  相似文献   

6.
In the Boussinesq approximation, we study weakly nonlinear topographic waves trapped by a flat slope of arbitrary orientation. We compute the mean currents induced by the waves due to the nonlinearity in the quadratic approximation with respect to the wave amplitude in the presence of dissipation of the wave energy into the turbulent motion. In the diffusion approximation, we determine the vertical distribution of the concentration of wave-suspended sediments. It is shown that the consumption of sediments across the isobaths is directed downward along the slope. At the same time, the consumption of sediments along the isobaths has the same direction as the projection of the horizontal wave vector.  相似文献   

7.
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   

8.
Waves generated by vertical seafloor movements are simulated by use of a fully nonlinear two-dimensional numerical wave tank. In the souree region, the seafloor lifts to a designated height by a generation function. The numerical tests show that the linear theory is only valid for estimating the wave behaviors induced by the seafloor movements with a small amplitude, and the fully nonlinear numerical model should be adopted in the simulation of the wave generation by the large amplitude seafloor movements. Without the background surface waves, many numerical tests on the stable maximum elevations η0^max are carried out by beth the linear theory and the fully nonlinear model. The results of two models are compared and analyzed. For the fully nonlinear model, the influences of the amplitudes and the horizontal lengths on η^max are stronger than that of the characteristic duration times. Furthermore, results reveal that there are significant differences be- tween the linear theory and the fully nonlinear model. When the influences of the background surface waves are considered, the corresponding numerical analyses reveal that with the fully nonlinear model the η0^max near-linearly varies with the wave amplitudes of the surface waves, and the η0^max has significant dependences on the wave lengths and the wave phases of the surface waves. In addition, the differences between the linear theory and the fully nonlinear model are still obvious, and these differences are significantly affected by the wave parameters of the background surface waves, such as the wave amplitude, the wave length and the wave phase.  相似文献   

9.
The statistical properties of long-crested nonlinear wave time series measured in an offshore basin have been analyzed in different aspects such as the distributions of surface elevation, wave crest, wave trough, and wave period. Comparison with linear, second-order and third-order theoretical models indicates that although bound wave effects also contribute to the deviation from a Gaussian process, it is the modulational instability that primarily determines the discrepancy in the evolution process in the presence of strong nonlinearity. Interestingly enough, wave crest is more sensitive to the quasi-resonant four-wave interaction effect than wave trough and the scaled maximal wave crest presents a linear regression model with the coefficient of kurtosis. Meanwhile, the estimation of the observed statistical properties is reconstructed on the basis of an ensemble of 100 wave series simulated by the NLS-type equations and compared favourably with the experimental results in most cases. Moreover, with the increased third-order nonlinear effect the difference between NLS and Dysthe simulations is enlarged and mainly reflected on the distribution of wave crest.  相似文献   

10.
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.  相似文献   

11.
Jiang  Sheng-chao  Liu  Chang-feng  Sun  Lei 《中国海洋工程》2020,34(2):279-288
Numerical simulations on focused wave propagation are carried out by using three types of numerical models,including the linear potential flow, the nonlinear potential flow and the viscous fluid flow models. The wave-wave interaction of the focused wave group with different frequency bands and input wave amplitudes is examined, by which the influence of free surface nonlinearity and fluid viscosity on the related phenomenon of focused wave is investigated. The significant influence of free surface nonlinearity on the characteristics of focused wave can be observed, including the increased focused wave crest, delayed focused time and downstream shift of focused position with the increase of input amplitude. It can plot the evident difference between the results of the nonlinear potential flow and linear potential flow models. However, only a little discrepancy between the nonlinear potential flow and viscous fluid flow models can be observed, implying the insignificant effect of fluid viscosity on focused wave behavior. Therefore, the nonlinear potential flow model is recommended for simulating the non-breaking focused wave problem in this study.  相似文献   

12.
The intensification of gentle plane waves at the initial stage of their generation by a steady wind flow in a laboratory setup is investigated. It is found that the wave form is changed by eddies that are formed in the viscous layer of a steady air flow on the leeward slope: the water surface rises under the action of eddies to form a complexly shaped slope. Calculated and measured data for gentle nonlinear waves on clean water are in good compliance with each other. It is shown that, in the presence of an oil film, the region of eddy separation encompasses the wave trough as well, because oil flows down and the film is thickened in passing from the slope to the trough. The water-surface rise by eddies in the trough restricts an increase in the amplitude and steepness of the wave.  相似文献   

13.
A semi-analytical nonlinear wavemaker model is derived to predict the generation and propagation of transient nonlinear waves in a wave flume. The solution is very efficient and is achieved by applying eigenfunction expansions and FFT. The model is applied to study the effect of the wavemaker and its motion on the generation and propagation of nonlinear waves. The results indicate that the linear wavemaker theory may be applied to predict only the generation of waves of low steepness for which the nonlinear terms in the kinematic wavemaker boundary condition and free-surface boundary conditions are of secondary importance. For waves of moderate steepness and steep waves these nonlinear terms have substantial effects on wave profile and wave spectrum just after the wavemaker. A wave spectrum corresponding to a sinusoidally moving wavemaker possesses a multi-peak form with substantial nonlinear components, which disturbs or may even exclude physical modeling in wave flumes. The analysis shows that the widely recognized weakly nonlinear wavemaker theory may only be applied to describe the generation and propagation of waves of low steepness. This is subject to further restrictions in shallow and deep waters because the kinematic wavemaker boundary condition as well as the nonlinear interaction of wave components and the evolution of wave energy spectrum is not properly described by weakly nonlinear wavemaker theory. Laboratory experiments were conducted in a wave flume to verify the nonlinear wavemaker model. The comparisons show a reasonable agreement between predicted and measured free-surface elevation and the corresponding amplitudes of Fourier series. A reasonable agreement between theoretical results and experimental data is observed even for fairly steep waves.  相似文献   

14.
This study investigates the behaviour of internal solitary waves crossing a continental slope in the presence of a seasonal thermocline. Comparisons are made between a fully non-linear computational fluid dynamics (CFD) model, and weakly non-linear theory. Previous observations suggested that the amplitudes of solitary waves are capped as they pass across the continental slope, which may be due to laminar dynamics, or due to the effect of turbulence. Across the continental slope, CFD and second order variable depth KdV (vEKdV) predictions agree well with observations of a limited change in solitary wave amplitude. First order variable depth KdV theory overpredicts the final amplitude significantly. In terms of the wave shape, the CFD modeled wave changes from a KdV shape in deep water towards an EkdV solution in shallow water, as observations suggest. The phase speed of the CFD and vEKdV waves are similar to that observed in waters of 400–500 m deep, but are slightly lower than observed in 140 m depth. CFD predictions using a standard k, turbulence model showed that turbulence had little effect on the amplitude. These preliminary results indicate that in this situation wave capping is due to laminar, large amplitude solitary wave dynamics and is independent of turbulent mixing.  相似文献   

15.
In this paper, we study the harmonic generation and energy dissipation as water waves propagating through coastal vegetation. Applying the homogenization theory, linear wave models have been developed for a heterogeneous coastal forest in previous works (e.g. [17], [10], [11]). In this study, the weakly nonlinear effects are investigated. The coastal forest is modeled by an array of rigid and vertically surface-piercing cylinders. Assuming monochromatic waves with weak nonlinearity incident upon the forest, higher harmonic waves are expected to be generated and radiated into open water. Using the multi-scale perturbation theory, micro-scale flows in the vicinity of cylinders and macro-scale wave dynamics are separated. Expressing the unknown variables (e.g. velocity, free surface elevation) as a superposition of different harmonic components, the governing equations for each mode are derived while different harmonics are interacting with each other because of nonlinearity in the cell problem. Different from the linear models, the leading-order cell problem for micro-scale flow motion, driven by the macro-scale pressure gradient, is now a nonlinear boundary-value-problem, while the wavelength-scale problem for wave dynamics remains linear. A modified pressure correction method is employed to solve the nonlinear cell problem. An iterative scheme is introduced to connect the micro-scale and macro-scale problems. To demonstrate the theoretical results, we consider incident waves scattered by a homogeneous forest belt in a constant shallow depth. Higher harmonic waves are generated within the cylinder array and radiated out to the open water region. The comparisons of numerical results obtained by linear and nonlinear models are presented and the behavior of different harmonic components is discussed. The effects of different physical parameters on wave solutions are discussed as well.  相似文献   

16.
As known, the rolling motion characteristics, amplitudes and accelerations, greatly influence the ability of a ship to operate and survive in bad weather. On the other hand, traditional computer codes for seakeeping calculations fail the forecasting of large amplitude rolling. There is a great need of using semi-empirical damping models and coefficients. This stresses the importance of campaigns of measurements as described in the paper, to get a deeper insight into the physical-mathematical modelling of the different contributions to rolling equation.Experimental tests on nonlinear rolling in a regular beam sea of a Ro-Ro ship model have been conducted by varying both the wave steepness and the wave frequency. The use of a parameter estimation technique, based on the least squares fitting of the stationary numerical solution of the nonlinear rolling motion differential equation, allowed to obtain informations on the damping model and on the linear and nonlinear damping coefficients. These exhibit a quite strong dependence on frequency that reduces the efficiency of constant coefficients rolling equation to simulate large amplitude nonlinear rolling. The results indicate that a good quality prediction model of nonlinear rolling cannot be based on constant coefficients time domain simulations. These can infact lead to incorrect estimates of rolling amplitudes even when the parameters have been obtained through high level parameter estimation procedures based on experimental data. The analysis indicates also a marked dependence of the effective wave slope coefficient on wave amplitude. The introduction of both these dependences on the rolling equation allows to reproduce the experimental results with great accuracy even at large amplitudes.  相似文献   

17.
分层流体中内孤立波在潜浮式竖直薄板上透射和反射   总被引：2，自引：0，他引：2  
采用边缘层理论研究了两层流体系统中内孤立波在潜浮式竖直薄板上的透射和反射问题,提出了非线性演化方程的“初值”条件,分析了内孤立波与薄板非线性相互作用的效应。研究表明:流体层的密度比以及薄板伸入上下层的深度对于反射和透射波结构具有显著的影响,薄板伸入下层越深、密度差越小,则薄板阻碍孤立波透射的效率越高;透射波通常演化为单峰孤立波和迅速衰减的尾波,反射波演化为缓慢衰减的尾波列;对于具有小密度差的跃层结构,内孤立波在潜浮式竖直薄板上的透射及其演化近乎是无障碍的。  相似文献   

18.
The equations of dynamics of eddy—wave disturbances of two-dimensional stratified flows in an ideal incompressible fluid that are written in a Hamiltonian form are used to study the resonant interaction of waves of discrete and continuous spectra. A gravity—shear wave generated at a jump of the density and vorticity of the undisturbed flow and a wave generated at a weak vorticity jump, which is similar to a wave of a continuous spectrum, participate in the interaction. The equations are written in terms of normal variables to obtain the system of evolution equations for the amplitudes of the interacting waves. The stability condition for eddy—wave disturbances is derived within the framework of the linear theory. It is shown that a cubic nonlinearity may lead to the stabilization of unstable disturbances if the coefficient of the nonlinear term is positive.  相似文献   

19.
An analytical study of the influence of three-wave resonant interactions on the evolution of unstable wave disturbances is presented in the Kelvin-Helmholtz model. These results may be of interest in analyzing the dynamics of disturbances at the ocean-atmosphere interface and in two-layer flows which arise in the ocean and are characterized by large gradients of flow velocity at the boundary of layers. In the case under consideration, the instability arises when eigenfrequencies coincide in the framework of a single mode and the instability is algebraic. The amplitudes of the two other interacting stable waves are assumed to be small compared to the amplitude of the third, unstable, mode. The system of amplitude equations for this case is investigated using the WKB method. As a result, we obtain the formulas coupling the solutions for the time before and after a transition through a singular point, where the amplitude of the linearly unstable wave has a local minimum. These formulas give the rule of transformation of the parameter that characterizes a phase shift between fast and slow modes and determines the behavior of the system. It is shown that, in a transition through a singular point, this parameter changes randomly. As long as the parameter is positive, the amplitude of the linearly unstable wave remains limited and oscillates stochastically. In a transition of the parameter through zero, we exit the stabilization region and have an infinite growth of amplitude. The transition into the instability region is random. However, if the time interval where the amplitude remains limited is large enough, the scenario of the behavior of the system we have obtained can be treated as the partial stabilization of instability. The results make it possible for us to investigate the stochasticity caused by the nonlinear interaction of gravity-capillary waves in a two-layer model of a shear flow. These results are also of interest in analyzing secondary flows in laboratory facilities modeling the ocean and atmospheric processes.  相似文献   

20.
Experimental investigations on internal solitary wave (ISW) propagation and their reflection from a smooth uniform slope were conducted in a two-layered fluid system with a free surface. A 12-meter-long wave flume was in use which incorporated with: (1) a movable vertical gate for generating ISW; (2) six ultrasonic probes for measuring the fluctuation of an ISW; and (3) a steep uniform slope (from one of θ=30°, 50°, 60°, 90°, 120° and 130°) much greater than those ever published in the literature. This paper presents the wave profile properties of the ISW recorded in the flume and their nonlinear features in comparison with the existing Korteweg de Vries (KdV) and modified Korteweg-de Vries (MKdV) theories. Experimental results show that the KdV theory is suitable for most small-amplituded ISWs and MKdV theory is appropriate for the reflected ISWs from various uniform slopes. In addition, both the amplitude-based reflection coefficient and reflected energy approach a constant value asymptotically when plotted against the slope and the characteristic length ratio, respectively. The reflected wave amplitudes calculated from experimental data agree well with those reported elsewhere. The optimum reflection coefficient is found within the limit of 0.85 for wave amplitude, among the test runs from steep normal slope of 30° to inverse angle of 130°, and around 0.75 for the reflected wave energy, produced by an ISW on a vertical wall.  相似文献   

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