Efficient computation method for two-dimensional nonlinear waves

I~IOWNUmerics wave tank is a ~ tOOl by which variouS nonlinear wave - ac interactionpwhleln can be treated in time domain. As the face stage, we f~ our efforts on the devious of an effita saution tee~ of fully nofor waves. aam numtried of water - wavesconnected PwhlemS, es~ in a wave tank, is alwayS comas Of PartS: wave generation, P~ and a~. The effi~ Of a nUm~ wave tankdepends not Only on the qwhty Of the wave abotion tecboaue, which allowS the lOng times~ and keePS finite tank leng…     

Numerical simulation for the two-dimensional nonlinear shallow water waves

This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.     

Modelling of the temporal and spatial evolutions of weakly nonlinear random directional waves with the modified nonlinear Schrödinger equations

The temporal and spatial evolutions of nonlinear wave group with an initial Gaussian envelope are theoretically studied under the governing of MNLS equations, demonstrating that the temporal and spatial versions of numerical model are not always consistent in the whole evolution process, particularly in the presence of strong nonlinearity. Moreover, a large set of numerical simulations, performed respectively by these two versions of numerical model, are systematically compared to mechanically generated waves with different initial directional spreading and Benjamin–Feir Index, mainly focusing on the evolution properties of surface elevations such as the coefficients of skewness and kurtosis, the probability density function, and the maximal surface elevation. On the whole, it can be argued that the statistical properties of both numerically simulated wave fields are basically consistent with the laboratory observations.     

Experimental study of wave–wave nonlinear interactions using the wavelet-based bicoherence

The wavelet-based bicoherence, which is a new and powerful tool in the analysis of nonlinear phase coupling, is used to study the nonlinear wave–wave interactions of breaking and non-breaking gravity waves propagating over a sill. Two cases of mechanically generated random waves based on Jonswap spectra are used for this purpose. Values of relative depth, k_ph (k_p is the wave number of the spectral peak and h is the water depth) for this study range between 0.38 and 1.22. The variations of wavelet-based total bicoherence for the test cases indicate that the degree of quadratic phase coupling increases in the shoaling region consistent with a wave profile that is pitched shoreward, relative to a vertical axis as seen in the experiments, but decreases in the de-shoaling region. For the non-breaking case, the degree of quadratic phase coupling continues to increase until waves reach the top of the sill. Breaking waves, however, achieve their highest level of quadratic phase coupling immediately before incipient breaking and the degree of phase coupling decreases sharply following breaking. In addition the wavelet-based bicoherence spectra provide evidence of the harmonics' growth which is reflected in the energy spectra. The bicoherence spectra also show that quadratic phase coupling between modes within the peak frequency as well as between modes of the peak frequency and its higher harmonics are dominant in the shoaling region, even though there are relatively high levels of quadratic phase coupling occurring between other frequencies. Furthermore, using the temporal resolution property of the wavelet-based bicoherence, we find that the quadratic wave interactions occur more readily during segments of time with large change of wave amplitude, rather than those segments having large wave amplitudes, but small gradients in amplitude.     

Comparison of Dirichlet–Neumann operator expansions for nonlinear surface gravity waves

The Dirichlet–Neumann operator for the water-wave problem was introduced and expanded by Craig and Sulem [Craig, W., Sulem, C., 1993. [CS] Numerical simulation of gravity waves. J. Comput. Phys. 108, 73–83] and in a slightly different form and for 3D waves by Bateman, Swan and Taylor [Bateman, W.J.D., Swan, C., Taylor, P.H., 2001. [BST] On the efficient numerical simulation of directionally spread surface water waves. J. Comput. Phys. 174, 277–305]. This approach is supposedly superior to techniques derived earlier by West et al. [West, B.J., Brueckner, K.A., Janda, R.S., Milder, D.M., Milton, R.L., 1987. [WW] A new numerical method for surface hydrodynamics. J. Geophys. Res. 92 (C11), 11803–11824] and Dommermuth and Yue [Dommermuth, D.G., Yue, D.K.P., 1987. [DY] A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288] under seemingly more restrictive assumptions. This paper extracts the Dirichlet–Neumann operator expansions from West et al. and Dommermuth and Yue. Concerning the operator expansions alone it is found that Bateman et al. is identical to West et al. and Dommermuth and Yue while Craig and Sulem is slightly different due to minor differences in the operator definition. For application to the free-surface boundary conditions West et al. devised a consistent truncation at nonlinear order. This alters the equivalence of the different approaches when it comes to the evaluation of the temporal derivative of the free surface elevation, which is decisive for wave evolution. In this regard Craig and Sulem is found to be identical to West et al. while Bateman et al. is identical to Dommermuth and Yue. Pseudo code is provided for alternative computational schemes in Fourier-space and physical space, respectively, along with a discussion of efficiency and potential flexibility.     

A modified Euler–Lagrange transformation for particle orbits in nonlinear progressive waves

This paper presents a modified Euler–Lagrange transformation method to obtain the third-order trajectory solution in a Lagrangian form for the water particles in nonlinear water waves. We impose the assumption that the Lagrangian wave frequency is a function of wave steepness and an arbitrary vertical position for each water particle. Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, the third-order asymptotic expressions for the Lagrangian particle trajectories, the mass transport velocity and the period of particle motion can be derived directly in Lagrangian form. The wave frequency and mean level of the particle motion in Lagrangian form differ from those of the Eulerian. Finally, the third-order asymptotic solution obtained is uniformly valid in contrast with early works containing resonant terms presented by Wiegel [1964. Oceanographical Engineering. Prentice-Hall, New Jersey, pp. 37–40] (Eqs. (B.1) and (B.1), (B.2) in Appendix B) or Chen et al.[2006. Theoretical analysis of surface waves shoaling and breaking on a sloping bottom. Part 2 nonlinear waves. Wave motion, 43, 356–369] based on a straightforward expansion for two-dimensional progressive waves.     

Satellite altimeter observations of nonlinear Rossby eddy–Kuroshio interaction at the Luzon Strait

Satellite altimeter sea level data from 1993 to 2008 are used to analyze the interaction of nonlinear Rossby eddies with the Kuroshio at the Luzon Strait (LS). The sea level anomaly data show that the west Pacific (WP) is a source of nonlinear Rossby eddies, and the South China Sea (SCS) is a sink. The LS serves as a gateway between the two. The scale analysis indicates that eddies with a radius larger than 150 km are strong enough to significantly alter the Kuroshio and are able to modify the local circulation pattern. Statistical analysis indicates that the probability for eddies to penetrate through the Kuroshio may reach at least 60%. A case study of an anticyclonic mesoscale eddy passing through the LS in June–July 2004 indicates that the Kuroshio behaves as an unsteady flow with its stream path frequently modified, in a way of cutting off, meandering and branching during its interaction with the eddy. We therefore suggest that nonlinear Rossby eddies may play a significant role in modification of the local circulation system near the LS and in exchanges of the mass, momentum and energy between the WP and the SCS.     

Full-range nonlinear analysis of fatigue behaviors of reinforced concrete structures by finite element method

Ｆｕｌｌ－ｒａｎｇｅｎｏｎｌｉｎｅａｒａｎａｌｙｓｉｓｏｆｆａｔｉｇｕｅｂｅｈａｖｉｏｒｓｏｆｒｅｉｎｆｏｒｃｅｄｃｏｎｃｒｅｔｅｓｔｒｕｃｔｕｒｅｓｂｙｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄ￥ＳｏｎｇＹｕｐｕ；ＺｈａｏＳｈｕｎｂｏ；ＷａｎｇＲｕｉｍ...     

Probability distribution of surface slope for nonlinear random sea waves and calculation of whitecap

Ｂａｓｅｄｏｎｔｈｅｎｏｎｌｉｎｅａｒｍｏｄｅｌｏｆｔｗｏ－ｄｉｍｅｎｓｉｏｎａｌｒａｎｄｏｍｓｅａｗａｖｅｓ，ａｓｔａｔｉａｔｉｃａｌｄｉｓｔｒｉｂｕｔｔｔ崳铮睿铮妫鳎幔觯澹螅酰颍妫幔悖澹螅欤铮穑澹澹幔悖簦簦铮簦瑁澹簦瑁椋颍洌铮颍洌澹颍椋螅洌澹颍椋觯澹洌猓酰螅椋睿纾簦瑁澹澹穑幔睿螅椋铮睿铮妫簦瑁澹悖瑁幔颍幔悖簦澹睿螅簦簦椋悖妫酰睿悖簦簦铮睿幔睿洌洌椋颍澹悖簦悖幔欤悖酰欤幔簦椋铮睿螅铮妫澹幔悖瑁铮颍洌澹颍恚铮恚澹睿簦拢幔螅澹洌铮睿簦瑁澹洌椋螅簦颍椋猓酰簦椋铮睿铮妫鳎幔觯澹螅酰颍妫幔悖澹螅欤铮穑澹洌澹颍椋觯澹洌椋睿簦瑁椋螅穑幔穑澹颍幔鳎瑁椋簦澹悖幔穑悖铮觯澹颍幔纾澹恚铮洌澹欤椋螅穑颍铮穑铮螅澹洌猓酰螅椋睿纾簦瑁澹欤椋恚椋簦螅酰颍妫幔悖澹螅欤铮穑澹幔螅幔悖悖椋簦澹颍椋铮睿铮妫鳎幔觯澹猓颍澹幔耄椋睿纾裕瑁澹鳎瑁椋簦澹悖幔穑悖铮觯澹恚纾澹澹穑颍澹螅螅澹洌猓觯簦瑁澹恚铮洌澹欤洌澹穑澹睿螅铮睿簦瑁颍澹澹穑幔颍幔恚澹簦澹颍螅鳎瑁椋悖瑁悖幔睿猓澹洌澹簦澹颍恚椋睿澹洌椋睿穑颍椋睿悖椋穑欤澹猓簦瑁澹欤椋睿澹幔颍鳎幔觯澹螅穑澹悖簦颍酰恚幔睿洌簦瑁颍澹澹耄椋睿洌螅铮妫鳎幔觯澹鳎幔觯澹椋睿簦澹颍幔悖簦椋铮睿     

Probability distribution of surface slope for nonlinear random sea waves and calculation of whitecap coverage

Based on the nonlinear model of two-dimensional random sea waves, a statistical distribution of wave surface slope exact to the third order is derived by using the expansion of the characteristic function and direct calculations of each order moment. Based on the distribution of wave surface slope derived in this paper, a whitecap coverage is proposed by using the limit surface slope as a criterion of wave breaking. The whitecap coverage expressed by the model depends on three parameters which can be determined in principle by the linear wave spectrum and three kinds of wave-wave interaction.     

Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model

1 IntroductionThe El Ni’o atmospheric physics oscillation is anabnormal phenomenon involved in the tropical Pacificocean- atmosphere interactions. Studies on the El Ni(ophenomenon are very attractive (Lin et al., 2000; Linet al., 2001, 2002; Wang, 2001; Feng et al., 2001;Feng et al., 2002; Liu et al., 2002; Wei and Chen,2003; Xie et al., 2002; Zhu et al., 2002; Pu et al.,2003; Gu et al., 2004; Yu and Liu, 2004). Lin and Mo(2004), Mo and Lin (2004) and Mo et al. (2004) alsostudied a s…     

An experimental study of the relations between bispectra and nonlinear apparent features of wind waves

To investigate the nonlinear properties of wind waves, experiments are carried out in a wind-wave flume with slope bottom at different wind speeds and fetches. Both the internal structure and apparent features of the nonlin-earity of wind waves are studied by using bispectral and statistical analysis of surface elevations. The relations between bispectra and nonlinear apparent characteristics of wind waves are established and confirmed.     

Variational iteration solving method for El Niño phenomenon atmospheric physics of nonlinear model

A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.     

Numerical simulation of nonlinear dispersive waves propagating over a submerged bar by IB–VOF model

It is a good test for a numerical model to simulate progressive waves propagating over a submerged bar with a relatively high ratio of slopes. In this paper, the combined IB–VOF model is used to predict nonlinear dispersive waves propagating over a submerged bar with both slopes of 1:2. The predicted free surface elevations are compared with the experimental data and numerical results presented by other researchers. The comparison shows that the IB–VOF model is able to provide satisfactory wave profiles in the shallow water with strong nonlinear effects and in the wave transmitted region with strong wave dispersion in particular. Moreover, the wave evolution behind the submerged bar is described in detail, including the spatial wave profile modulation, spectral analysis of the time-series waves, flow velocity and pressure fields, and kinetic energy distribution. The effect of fluid viscosity on the numerical simulations is also studied, and it is found that the effect on the wave evolution considered in this paper is not significant. Finally, the hydrodynamic force acting on the bar is calculated using the IB–VOF model.     

85—904—08—01和85—904—08—02通过评审

８５—９０４—０８—０１和８５—９０４—０８—０２通过评审１９９５年１２月１２—１３日，受国家科委委托地矿部科技司组织专家鉴定组，在北京对“八五”国家科技攻关项目的“８５—９０４—０８一川和８５—９０４—０８—０２”专题进行了评审。卜述两专题经过５年...     

85—904—06—01和85—904—06—02课题通过评审

８５—９０４—０６—０１和８５—９０４—０６—０２课题通过评审受国家科委委托，由地矿部科技司组织同行专家，于１９９５年９月２５日在北京，对国家重点科技攻关项目８５—９０４—０６所属的专题报告８５—９０４—０６—０１和８５—９０４—０６—０２进行了评审...     

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.     

南沙——中国魂

美哉,南沙上午八点,琼渔XX号徐徐地离开码头,离开潭门港,驶向烟波浩淼的南海。著名考古学家王恒杰教授双手凭着船舷,望着渐渐远去的绿色岸线,望着北国湛蓝的天空,陷入了深思。去南沙考古是他多年的心愿,如今,这个心愿就要实现了,这高兴是可想而知的。经过七天七夜的航行,渔船到达永登暗沙。这里是     

里约热内卢——奇迹之城

每年,每月,甚至每天,世界各地大大小小的选美、选秀和类似活动从没有中断过。这不,今年又有好事者发起了重选世界七大奇迹的活动,咱