The physical simulation of wave groups and their variations in a wave flume

The physical simulation method of wave groups in a wave flume is proposed and verified by the exper- iments. The experimental results demonstrate that random waves with desired wave groupiness, which simultaneously includes the wave group height and length, can be generated satisfactorily at the specified position in a wave flume using the proposed method. Furthermore, the transformation properties of the wave groupiness along the fiat-bottomed wave flume are investigated based on the physically simulated waves. Associated proposals with the physical simulation of wave groups are given.

Theoretical and experimental investigation on nonlinear interaction among wave groups

Wave group is important in ocean wave theory and applications. In the past, nonlinear interaction among wave groups has been studied on the basis of the nonlinear Sehrrdinger equation. Using this theoretical approach, we found that the nonlinear interaction among wave groups causes asymmetry in the shape of the wave envelope （steeper in the front of the curve of the envelope）. An important consequence of this asymmetry is that the highest wave in a wave group appears one individual wave length ahead of the center of the wave group. Further results show that the degree of envelope asymmetry increases with increasing spectral width and the wave steepness. This theoretical analysis has been supplemented by a systematic experimental study of wind waves. Laboratory and some open sea wave data were analyzed. The results show that the shape of the wind wave envelope of wind waves has the same asymmetry predicted by the theoretical approach. The observed degree of deformation of the envelope also increases with increasing spectral width and the wave steepness as predicted by theory. These conclusions have important ramifications for practical applications of ocean wave theory.

Physical Simulation of Multidirectional Irregular Wave Groups

Real waves are multidirectional waves. In the present study, the calculation method for the wave maker driving signals for generating multidirectional wave groups in physical wave basin is proposed. Its validity is first confirmed by a numerical model for which the incident boundary condition is determined by use of the proposed method. Then, the physical simulation of multidirectional wave groups is performed in laboratory wave basin. The experimental results show that multidirectional waves with expected wave groupiness, which includes not only its group height but also its group length, can be satisfactorily zenerated at the soecified oosition in the tphvsical wave basin.

Application of Maximum Entropy Distribution to the Statistical Properties of Wave Groups

The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.

Numerical Simulation and Physical Simulation of Sea Wave Groups

Based on field wave data, an empirical formula of wave envelope spectrum is given in this paper. Then the methods of both numerical and physical simulation of sea wave groups with the given spectrum and groupiness parameters are suggested.

Intermittency of Wind Wave Group Breaking

Knowledge on intermittency of wave breaking is so far limited to a few summary statistics, while the probability distribution of time interval between breaking events can provide a full view of intermittency. Based on a series of experiments on wind wave breaking, such probability distributions are investigated. Breaking waves within a wave group were taken as a single breaking event according to recent studies. Interval between successive wave groups with breaker is the focus of this paper. For intervals in our experiments with different fetch and wind conditions, their distributions are all skewed and weighted on small intervals. Results of Kolmogorov-Smirnov tests on time series of these intervals indicate that they all follow gamma distribution, and some are even exponential type. Average breaking-group-interval decreases with friction velocity and significant steepness until the wind is strong enough;most of them are more than 10 times the dominant wave period. Group breaking probability proposed by Babanin recently and the average number of breaking waves in wave groups are also discussed, and they are seemingly more reasonable and sensitive than traditional breaking probability defined in terms of single wave.

Effect of Wave Groups on Wave Run-up

-The effect of wave group on wave run-up on a slope dike is mainly discussed in this paper. Two simulating methods of wave group and their applications in laboratory are introduced. Synthesizing the research results of wave run-up on a slope dike, the effect of wave group on wave run-up on a slope dike in coastal protection engineering is studied as the main point.

Crustal and uppermost mantle structure of SE Tibetan plateau from Rayleigh-wave group-velocity measurements

A shear-wave velocity model of the crust and uppermost mantle beneath the SE Tibetan plateau was derived by inverting Rayleigh-wave group-velocity mea- surements of periods between 10 and 70 s. Rayleigh-wave group-velocity dispersions along more than 3,000 inter- station paths were measured based on analysis of telese- ismic wavelbrm data recorded by temporary seismic stations. These observations were then utilized to construct 2D group-velocity maps in the period range of 10-70 s. Tile new group-velocity maps have an enhanced resolution compared with previous global and regional group-velocity models in this region because of the denser and more uniform data coverage. The lateral resolution across the region is about 0.5° for the periods used in this study. Local dispersion curves were then inverted for a 3D shear-wave velocity model of the region by applying a linear inversion scheme. Our 3D shear-wave model confirms the presence of low-velocity zones （LVZs） in the crust beneath the northern part of this region. Our irnaging shows that the upper-middle crustal LVZ beneath the Tengchong region is isolated from these LVZs beneath the eastern and northern part of this region. The upper-middle crustal LVZ may be regarded as evidence of a rnagma chamber in the crust beneath the Tengchong Volcanoes. Our model also reveals a slow lithospheric structure beneath Tengchong and a fast shield-like mantle beneath the stable Yangtze block.

THE WAVE GROUPING EFFECT ON WAVE FORCES ON A VERTICAL BREAKWATER

Linear wave theory and Longuet-Higgins and Steward’s (1964) group-induced second-order longweve (GSLW) theory ware used in this study on the grouping effect on wave forces acting on a verticalbreakwater. The calculated variance of total wave pressure on the vertical breakwater was closer tothe measured value if the wave grouping effect was considered.

Surface Wave Group Velocity Tomography Imaging from Ambient Noise for Fujian Province and Its Adjacent Areas

Two-month continuous waveforms of 108 broadband seismic stations in Fujian Province and its adjacent areas are used to compute noise cross-correlation function(NCF). The signal quality of NCF is improved via the application of time-frequency phase weighted stacking. The Rayleigh and Love waves group velocities between 1 s-20 s are measured on the symmetrical component of the NCF with the multiple filter method. More than 5,000 Rayleigh wave dispersion curves and about 4,000 Love wave dispersion curves are obtained and used to invert for group velocity maps. This data set provides about 50 km resolution that is demonstrated with checkerboard tests. Considering the off great circle effect in inhomogeneous medium, the ray path is traced based on the travel time field computed with a finite difference method. The inverted group velocity maps show good correlation with the geological features in the upper and middle crust. The Fuzhou basin and Zhangzhou basin showed low velocity on the short period group velocity maps. On the long period group velocity maps, the low velocity anomaly in the high heat flow region near Zhangzhou and clear velocity contrast across the Zhenghe-Dapu faults, which suggests that the Zhenghe-Dapu fault might be a deep fault.

STATISTICAL PROPERTIES OF WAVE GROUPS DESCRIBED BY GROUP-INDUCED LONG WAVES

A new method using group-induced second-order long waves (GSLW) to describe wave groups is presented in this paper on the basis of the GSLW theory by Longuet- Higgins and Steward (1964) . In the method , the parabolic relationship between GSLW and the wave envelope is first deduced , and then the distribution function of GSLW amplitude is derived . Thus, the formulae in terms of the moments of GSLW and short wave spectra for the average time duration and the mean length of runs of wave heights exceeding a certain level can be derived . A new groupiness factor equivalent to half the mean wave number in wave groups is defined by taking into account the widths of spectra of GSLW and short waves . Compared with theoretical results of others , ours are closer to measured wave data .

REPRESENTATION OF STATISTICAL PROPERTIES OF WAVE GROUPS FOR SEA PROCESSES WITH DOUBLE-PEAKED SPECTRA

A method using group-induced second-order long waves(GSLW) to represent statistical properties of wave groups with double-peaked spectra is put forward in this paper on the basis of the GSLW theory. The GSLW is regarded as a weighted linear superimposition of the second-order long Wave induced by the low peak frequency section and that induced by the high peak frequency section. There is a parabolic relationship between the GSLW and the wave envelope. Then the probability density function and the distribution function of the GSLW amplitude are derived. Thus the formulas for the average time duration and the mean length of runs can be derived. Good agreement between theoretical results and measured values was achieved. as verified with the measured double-peaked spectra in different regions.

A Wave Group for Entanglement, Linking Uncertainties in Time and Space

A carrier wave in a 5-dimensional wave group is examined for information on electromagnetic waves and on particle probability amplitudes. Simulations by Maxwell’s equations show that the phase and group velocities in electromagnetic waves are equal, both in vacuo and in dielectric media. By contrast, particle probability amplitudes in wave packet motion are more complicated. A dependence of rest mass on relative phase and group velocities is derived by consistency. Occurrences that are simultaneous and connected on wave fronts in the rest frame, appear separated when observed in moving frames. Uncertainties in space and time are linked by the probability amplitude wave group.

A Travelling Wave Group II: Antiparticles in a Force Field

The travelling wave group is a solution to the wave equation. With a Gaussian envelope, this stable wave does not spread as it propagates. The group is derived for electromagnetic waves and converted with Planck’s law to quantized photons. The resulting wave is a probability amplitude, and this is adapted to particles subject to special relativity. By including mass and by inverting the wave group, a description for antiparticles is derived. The consequent explanation is consistent with Dirac’s relativistic equation and with his theory of the electron;while being more specific than his idea of the wave packet, and more stable. The travelling wave group is extended to describe the positron, either free or in an external field.

A Travelling Wave Group III—Consistent with QED

The travelling wave group is a stable wave packet. Many surprising results are derived from it. The group is easily quantized for photons and applied, as a solution to the relativistic Klein-Gordon equation, to free particles. Further solutions to the resulting algebraic equation provide a stable wave function for free antiparticles. Consistency with the superstructure of quantum electrodynamics is obtained by an assignment to the electron antiparticle of negative mass and negative charge. Then in 5-dimensional space-time-mass, CPT invariance transforms to M’PT conservation in either charged or neutral particles, while many other consequences are also evident.

Groupiness of Sea Waves and Their Characteristic Parameters

Three methods for studying wave groups and their main parameters for describing wave groupiness are reviewed in this paper. Then they are analyzed and compared combined with field data from both aspects of group height and group length. A method and two parameters that can describe wave groupiness are suggested. The groupiness parameters of sea waves at three field stations are given. The effects of groupiness on both distributions of the wave height and the phase of component waves are investigated. The effects of datum length on the calculated value of grouping parameters are also discussed.

DYNAMIC RESPONSE ANALYSIS OF DDMS PLATFORM SUBJECTED TO ACTIONS OF WAVE GROUPS AND CURRENT FOURCES

Coupled dynamic analysis of the Deep Draft Multi-Spar （DDMS） platform and the mooring system under the action of waves and current is carried out in the time domain. Using a geometrically nonlinear finite element method, the mooring-line dynamics is simulated based on the total Lagrangian formulation. Wave groups are obtained by the JONSWAP spectrum and an empirical wave envelope spectrum involving two envelope-based factors Group Height Factor （GFH） and Group Length Factor （GLF）. The results show that the wave groups have a significant effect on the motion responses of the platform and the mooring line tensions.

Experiments and calculations of wave breaking and evolution of wave groups with high steepness

The evolution of the nonlinear wave groups in deep water is investigated through laboratory measurements and numerical analysis.Laboratory experiments are conducted in deep-water wave tank,focusing on the characteristics of breaking waves arising from the evolved wave train.Some quantitative results are obtained for the significant breaking wave train,including the surface elevation time series,the local geometry,and the energy dissipation.A nonlinear model for the evolution of the wave groups in deep water is developed by adding eddy viscosity dissipation terms in the High Level Irrotational Green-Naghdi(HLIGN)equations.The results of the simulation are compared with the laboratory measurements,and good agreement is observed for the evolved wave train.

THE EFFECT OF WAVE GROUPINESS ON A MOORED SHIP STUDIED BY NUMERICAL SIMULATIONS

Waves with the same wave parameters, such as significant wave height and period, but with different wave groupiness factors are simulated, to study the motion behavior of a moored ship under the action of waves with different Groupiness Factors of Height （GFH） and Group Length Factors （GLF）. The numerical results show that both the sway and heave motions increase with an increase in GFH. In contrast, the influence of GLF on the motions of a moored ship is weak.

Group velocity distribution of Rayleigh waves and crustal and upper mantle velocity structure of the Chinese mainland and its vicinity

Based on the long period digital surface wave data recorded by 11 CDSN stations and 11 IRIS stations, the dispersion curves of the group velocities of fundamental mode Rayleigh waves along 647 paths, with the periods from 10 s to 92 s, were measured by multi-filter. Their distribution at 25 central periods within the region of 18~54N, 70~140E was inverted by Dimtar-Yanovskaya method. Within the period from 10 s to 15.9 s, the group velocity distribution is laterally inhomogeneous and is closely related to geotectonic units, with two low velocity zones located in the Tarim basin and the East China Sea and its north regions, respectively. From 21 s to 33 s, the framework of tectonic blocks is revealed. From 36.6 s to 40 s, the lithospheric subdivision of the Chinese mainland is obviously uncovered, with distinct boundaries among the South-North seismic belt, the Tibetan plateau, the North China, the South China and the Northeast China. Four cross-sections of group velocity distribution with period along 30N, 38N, 90E and 120E, are discussed, respectively, which display the basic features of the crust and upper mantle of the Chinese mainland and its neighboring regions. There are distinguished velocity differences among the different tectonic blocks. There are low-velocity-zones (LVZ) in the middle crust of the eastern Tibetan plateau, high velocity featured as stable platform in the Tarim basin and the Yangtze platform, shallow and thick low-velocity-zone in the upper mantle of the North China. The upper mantle LVZ in the East China Sea and the Japan Sea is related to the frictional heat from the subduction of the Philippine slab and the strong extension since the Himalayan orogenic period.