共查询到20条相似文献，搜索用时 66 毫秒
1.
M. V. Kosnik V. A. Dulov V. N. Kudryavtsev 《Izvestiya Atmospheric and Oceanic Physics》2010,46(3):369-378
We investigate the role of different physical mechanisms in the generation of the capillary-gravity wind wave spectrum. This
spectrum is calculated by integrating a nonstationary kinetic equation until the solution becomes stready. The mechanisms
of spectrum generation under consideration include three-wave interactions, viscous dissipation, energy influx from wind,
nonlinear dissipation, and the generation of a parasitic capillary ripple. The three-wave interactions are taken into account
as an integral of collisions without additional simplifications. It is shown that the three-wave interactions lead to solution
instability if the kinetic equation takes into account only linear sources. To stabilize the solution, the kinetic equation
should incorporate a nonlinear dissipation term, which in the range of short gravity waves corresponds to energy losses during
wave breaking and microscale wave breaking. In the range of capillary waves, the account of nonlinear dissipation is also
needed to ensure a realistic level of the spectrum for large wind velocities. For the steady-state spectrum, the role of three-wave
interactions remains essential merely in the range of the minimum of phase velocity, where a trough on the curvature spectrum
is formed. At the remaining intervals of the spectrum, the main contribution into the spectral energy balance is provided
by the mechanisms of wave injection, nonlinear dissipation, and the generation of parasitic capillaries. 相似文献
2.
A. N. Dubovik 《Izvestiya Atmospheric and Oceanic Physics》2006,42(3):371-374
Properties of surface singularities and the form of wave crests of limiting gravity waves in steady-state flows of an ideal liquid are considered by analyzing the kinematic boundary condition. It is shown that, for rotational waves, the angle at the crest can have any value from 0° to 180°, while it has the only value 90° in the case of irrotational waves. Two inferences are made from Bernoulli’s integral and the properties of singularities: (i) the Stokes wave is a rotational wave and (ii) no angular points can appear on the profiles of capillary-gravity and capillary waves. 相似文献
3.
Kern E. Kenyon 《Journal of Oceanography》1998,54(4):343-346
The central physics of capillary waves (or ripples) can be understood by an elementary method which makes use of the balance
of static and dynamic pressure differences along the surface streamline between crest and trough, in the steady reference
frame, and conservation of mass through vertical cross-sections beneath crest and trough. Basically Einstein’s (1916) model
of surface gravity waves is adapted for the purpose of explaining the existence of capillary waves of infinitesimal amplitude.
One product of the physical understanding, the phase speed of capillary waves, is derived as a function of the wave length
and surface tension and the result agrees exactly with that obtained by the classical mathematical procedure. In the elementary
method it is not necessary to assume irrotational flow, upon which the classical theory is founded, nor are perturbation expansions
of the nonlinear fluid equations employed. The extension to capillary-gravity waves, by including the acceleration of gravity
in the physical model, is straightforward, and the calculated phase speed of these waves is identical to what is found in
the text books as well. 相似文献
4.
Experimental investigation of the harmonic generation by waves over a submerged plate 总被引：1，自引：0，他引：1
Experiments in a wave flume have been performed to analyse the nonlinear interaction between regular gravity waves and a submerged horizontal plate used as breakwater. A new method, based on the Doppler shift generated by a moving probes, has been used to discriminate the incident fundamental mode and the reflected fundamental mode. The relationships of the reflection and transmission coefficients to the wave number at different submergence depth ratios are presented. The accurate discrimination, by this method, of the phase-locked and free modes allows the quantification of the higher harmonics generated by the breakwater and the analysis of the nonlinear interaction between the waves and the submerged plate. The transfer of energy from the fundamental mode to higher harmonics is very large in the cases of small submergence depth ratios. The vortices produced at the edges take part in the production of higher harmonics by interaction with the free surface but involve, at the same time, a dissipation process that increases the efficiency of the breakwater. 相似文献
5.
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
6.
波浪与起伏水平板防波堤相互作用数值模拟 总被引：1，自引：1，他引：0
利用自主研发的基于紧致插值曲线CIP(constrained interpolation profile)方法的数学模型,开展规则波与起伏水平板防波堤相互作用的数值模拟研究。模型在笛卡尔直角坐标下建立,以CIP方法为流场基本求解器,分步求解Navier-Stokes方程,利用高精度的流体体积类型的THINC/SW (tangent of hyperbola for interface capturing with slope weighting)方法重构自由液面,采用浸入边界IBM(immersed boundary method)方法处理波浪与起伏板防波堤的耦合作用问题,通过动量源项造波方法模拟波浪的产生。重点关注波浪的浅水变形和板两端涡旋脱落的非线性现象,分析不同潜深、波要素下的板周围流场分布、板的运动响应和波浪的反透射系数。结果表明:起伏水平板主要通过能量反射、板上浅水变形和板两端的涡脱落消能,能有效减小板后波高,具有作为防波堤的可行性。 相似文献
7.
《Applied Ocean Research》2004,26(3-4):137-146
A theoretical approach is applied to predict the propagation and transformation of nonlinear water waves. A semi-analytical solution was derived by applying an eigenfunction expansion method. The solution is applied to analyze the effect of wave frequencies and wave steepness on the propagation of nonlinear waves. The main attention is paid to the wave profile, the wave energy spectrum, and the changes of wave profile and energy spectrum due to the interaction of wave components in a wave train. The results show that for waves of low steepness the nonlinear wave effects and effects associated with the interaction of water waves in a wave train are of secondary importance. For waves of moderate steepness and steep waves the effects associated with the interactions between waves in a wave train are becoming significant and a train of initially sinusoidal waves may drastically change its form within a short distance from its original position. The evolution of wave components has substantial effects on the wave spectrum. A train of initially very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short period of time. Laboratory experiments were conducted in a wave flume to verify theoretical approaches. The free-surface elevation recorded by a system of wave gauges was compared with the results provided by the semi-analytical solution. Theoretical results are in a fairly good agreement with experimental data. A reasonable agreement between theoretical results and experimental data is observed often even for relatively steep waves. 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.
Hydroelastic analysis of fully nonlinear water waves with the floating elastic plate is a hard mission. Especially, the behavior of the wave would be more complex when water wave encounter the floating elastic plate. In this paper, the meshless numerical method is devoted to solve such a problem. Fundamental solution method is applied to approximate the velocity potential in the fluid domain. When the water wave encounters the plate, the wave function would not be enough smooth in the edge of plate compared to the other points. Hence, to analyze numerically the behavior of wave, the solution space should include the basis functions that are not enough smooth in the edge of plate. Moreover, to decrease computational cost significantly, the basis functions had better to have local compact support. The multiple knot B-spline basis functions are suitable that contain both properties. The number of repeated knots, the degree of B-spline and the spatial points are challengeable that are discussed in this paper. The results are in good agreement with those obtained from other numerical works. 相似文献
10.
The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered. 相似文献
11.
应用非线性谱分析理论，对三阶Stokes型随机波浪载荷谱进行了分析，将波面方程及海水质点的水平速度用一阶波面的非线性组表示，导出了随机波浪谱的表达式。为了便于求解随机波浪的载荷谱，将阻力项展开为幂级数式，并应用非线性谱分析理论，确定了幂级数的系数，进而将波浪载荷表示为一阶波面及其导数的非线性组合，最后得出波浪载荷谱密度的表达式，并应用数值分析方法，得出单位桩柱波浪力及总波浪力谱密度。 相似文献
12.
A novel theoretical approach is applied to predict the propagation and transformation of transient nonlinear waves on a current. The problem was solved by applying an eigenfunction expansion method and the derived semi-analytical solution was employed to study the transformation of wave profile and the evolution of wave spectrum arising from the nonlinear interactions of wave components in a wave train which may lead to the formation of very large waves. The results show that the propagation of wave trains is significantly affected by a current. A relatively small current may substantially affect wave train components and the wave train shape. This is observed for both opposing and following current. The results demonstrate that the application of the nonlinear model has a substantial effect on the shape of a wave spectrum. A train of originally linear and very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short distance from an initial position. The discrepancies between the wave trains predicted by applying the linear and nonlinear models increase with the increasing wavelength and become significant in shallow water even for waves with low steepness. Laboratory experiments were conducted in a wave flume to verify theoretical results. The free-surface elevations recorded by a system of wave gauges are compared with the results provided by the nonlinear model. Additional verification was achieved by applying a Fourier analysis and comparing wave amplitude spectra obtained from theoretical results with experimental data. A reasonable agreement between theoretical results and experimental data is observed for both amplitudes and phases. The model predicts fairly well multi-peak spectra, including wave spectra with significant nonlinear wave components. 相似文献
13.
This study investigates the initialization of nonlinear free-surface simulations in a numerical wave flume.Due to the mismatch between the linear input wavemaker motion and the kinematics of fully nonlinear waves,direct numerical simulations of progressive waves,generated by a sinusoidally moving wavemaker,are prone to suffering from high-frequency wave instability unless the flow is given sufficient time to adjust.A time ramp is superimposed on the wavemaker motion at the start that allows nonlinear free-surface simulations to be initialized with linear input.The duration of the ramp is adjusted to test its efficiency for short waves and long waves.Numerical results show that the time ramp scheme is effiective to stabilize the wave instability at the start of the simulation in a wave flume. 相似文献
14.
合理的刚度和潜深设计可以使升沉水平板获得优异的消浪性能。基于考虑流体黏性的二维不可压缩Navier-Stokes方程,以高阶紧致插值CIP(constrained interpolation profile)方法求解方程对流项,采用VOF(volume of fluid)方法重构自由液面,构建二维数值波浪水槽。采用试验数据验证模型后,研究孤立波与升沉水平板相互作用,分析相对刚度K*、相对潜深d/h、相对波高H/h对于升沉板的消浪性能和运动响应的影响,揭示升沉板对孤立波的消浪机理。研究表明:在孤立波通过时,升沉板会经历一个先上升后下降的运动,随后非线性自由振动,板下方水体近似均匀流动,且水流的垂向流动与板的垂荡方向一致;升沉板主要通过不对称涡旋脱落、浅水变形、波浪反射与辐射波转化等方式消耗孤立波能量;一定条件下,采用最优相对刚度K*=4.0和最优相对潜深d/h=0.52可以取得良好的消浪效果,此时透射系数最小,同时升沉板的运动响应在合理的范围内。 相似文献
15.
An extremely large (“freak”) wave is a typical though rare phenomenon observed in the sea. Special theories (for example, the modulation instability theory) were developed to explain mechanics and appearance of freak waves as a result of nonlinear wave-wave interactions. In this paper, it is demonstrated that the freak wave appearance can be also explained by superposition of linear modes with the realistic spectrum. The integral probability of trough-to-crest waves is calculated by two methods: the first one is based on the results of the numerical simulation of a wave field evolution performed with one-dimensional and two-dimensional nonlinear models. The second method is based on calculation of the same probability over the ensembles of wave fields constructed as a superposition of linear waves with random phases and the spectrum similar to that used in the nonlinear simulations. It is shown that the integral probabilities for nonlinear and linear cases are of the same order of values 相似文献
16.
Using data from laboratory, field, and numerical experiments, we investigated regularities in changes in the relative limit height of breaking waves (the breaking index) from peculiarities of nonlinear wave transformations and type of wave breaking. It is shown that the value of the breaking index depends on the relative part of the wave energy in the frequency range of the second nonlinear harmonic. If this part is more than 35%, then the breaking index can be taken as a constant equal to 0.6. These waves are spilling breaking waves, asymmetric on the horizontal axis, and are almost symmetric on the vertical axis. If this part of the energy is less than 35%, then the breaking index increases with increasing energy in the frequency range of the second harmonic. These waves are plunging breaking waves, asymmetric on the vertical axis, and are almost symmetric on the horizontal axis. It is revealed that the breaking index depends on the asymmetry of waves on the vertical axis, determined by the phase shift between the first and second nonlinear harmonic (biphase). It is shown that the relation between the amplitudes of the second and first nonlinear harmonics for an Ursell number less than 1 corresponds to Stokes’ second-order wave theory. The empirical dependences of the breaking index on the parameters of nonlinear transformation of waves are proposed. 相似文献
17.
It is well known that wave induced bottom oscillations become more and more negligible when the water depth exceeds half the wavelength of the surface gravity wave. However, it was experimentally demonstrated for regular waves that the bottom pressure oscillations at both first and second wave harmonic frequencies could be significant even for incoming waves propagating in deep water condition in the presence of a submerged plate [16]. For a water depth h of about the wavelength of the wave, measurements under the plate (depth immersion of top of plate h/6, length h/2) have shown bottom pressure variations at the wave frequency, up to thirty times larger than the pressure expected in the absence of the plate. In this paper, not only regular but also irregular wave are studied together with wave following current conditions. This behavior is numerically verified by use of a classical linear theory of waves. The wave bottom effect is explained through the role of evanescent modes and horizontally oscillating water column under the plate which still exist whatever the water depth. Such a model, which allows the calculation of the velocity fields, has shown that not only the bottom pressure but also the near bed fluid velocity are enhanced. Two maxima are observed on both sides of the location of the plate, at a distance of the plate increasing with the water depth. The possible impact of such near bed dynamics is then discussed for field conditions thanks to a scaling based on a Froude similarity. It is demonstrated that these structures may have a significant impact at the sea bed even in very deep water conditions, possibly enhanced in the presence of current. 相似文献
18.
基于二阶斯托克斯波理论推导了辐射应力的垂向分布表达式,通过算例讨论了辐射应力在深水和有限水深条件下的垂向分布规律,并与基于微幅波理论的辐射应力进行了比较.结果表明,在波浪非线性不强时,基于二阶斯托克斯波理论的辐射应力与基于微幅波理论的辐射应力表达式计算结果接近;而当水深较浅波浪非线性较强时,基于二阶斯托克斯波理论的辐射应力在近表面处明显大于基于微幅波理论的辐射应力.采用二阶斯托克斯波理论推导的波浪辐射应力更为合理地反映了波浪非线性效应. 相似文献
19.
本文运用基于自适应网格的流体动力学开源软件Gerris,来建立基于Boussinesq近似下的二维不可压缩Euler方程组的数值模型,以模拟不同层化条件下稳定状态的完全非线性大振幅内孤立波。文中比较了完全非线性的用Gerris实现的Euler模型与弱非线性的KdV理论模型在刻画大振幅内孤立波结构及特征参数上的差异,说明在模拟大振幅内孤立波时,高阶非线性不应忽略。Euler模型模拟结果表明,完全非线性大振幅内孤立波的等密度面半宽度随深度变化,这使得基于KdV方程解析解、利用卫星SAR(Synthetic Aperture Radar)图像提取内孤立波极值间距来反演内波振幅的可行性存疑,需要重新评估。此外,本文用两组实测数据验证了用Gerris实现的Euler模型模拟大振幅内波的有效性。 相似文献
20.
海啸波传播的线性和非线性特征及近海陆架效应影响的数值研究 总被引：3，自引：2，他引：1
浅水方程被广泛应用于海啸预警报业务及研究,而针对线性浅水方程与非线性浅水方程在不同海区水深地形条件下的适用范围、计算效率问题是海啸研究人员急需了解的。本文应用基于浅水方程的海啸数值预报模型就海啸波在南海、东海传播的线性、非线性特征以及陆架对其传播之影响进行了数值分析研究。海啸波在深水的传播表征为强线性特征,此时线性系统对海啸波幅的模拟计算具有较高的精度和效率,而弱的非线性特征及弱的色散特征对海啸波幅的预报影响甚微,可以忽略不计。海啸波传播至浅水大陆架后受海底坡度变化、海底粗糙度等因素影响,波动的非线性效应迅速传播、积累,与线性浅水方程计算的海啸波相比表现出较大差异,主要表现为:在南海区,水深小于100m时,海啸波首波以后的系列波动非线性特征比较明显,两者波幅差别较大,但首波波幅的区别不大,因此对于该区域在不考虑海啸爬高的情况下,应用线性系统计算得到的海啸波幅也可满足海啸预警报的要求;在东海区由于陆架影响,海啸波非线性特征明显增强,水深小于100m区域,首波及其后系列波波幅均差异较大,故在该区域必须考虑海啸波非线性作用。本文就底摩擦项对海啸波首波波幅的影响进行了数值对比分析,结果表明:底摩擦作用对海啸波首波波幅影响仅作用于小于100m水深。最后,该文通过敏感性试验,初步分析了陆架宽度及陆架边缘深度对海啸波波幅的影响,得出海啸波经陆架传播共振、变形后,海啸波幅的放大或减小与陆架的宽度及陆架边缘水深有关。 相似文献