The grouping characteristics of sea waves in the Shijiu Port

A review concerning the methods of studying and describing wave groups is presented in this paper. After analysing 78 field records collected in the Shijiu Port, China, the measured parameters of wave groups and some factors describing wave groupness and their variations are given. Moreover, these results are compared with those of theory.

NONLINEAR WATER WAVE PROPAGATING OVER UNEVEN BOTTOMS

Various types of wave group solutions of the weakly nonlinear waves may exist over uneven bottoms. In this paper, the variation of the zeroes of the dispersive and nonlinear terms,and the wave group solution in the third-order evolution equations are described for the case of mild and locally fastvarying water depths.

Wave Characteristics at the South Part of the Radial Sand Ridges of the Southern Yellow Sea

Based on one-year wave field data measured at the south part of the radial sand ridges of the Southern Yellow Sea, the wave statistical characteristics, wave spectrum and wave group properties are analyzed. The results show that the significant wave height （H1/3） varies from 0.15 to 2.22 m with the average of 0.59 m and the mean wave period （Tmean） varies from 2.06 to 6.82 s with the average of 3.71 s. The percentage of single peak in the wave spectra is 88.6 during the measurement period, in which 36.3% of the waves are pure wind waves and the rest are young swells. The percentage with the significant wave height larger than 1 m is 12.4. The dominant wave directions in the study area are WNW, W, ESE, E and NW. The relationships among the characteristic wave heights, the characteristic wave periods, and the wave spectral parameters are identified. It is found that the tentative spectral model is suitable for the quantitative description of the wave spectrum in the study area, while the run lengths of the wave group estimated from the measured data are generally larger than those in other sea areas.

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.

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.

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.

Observations of Freak Waves in Random Wave Field in 2D Experimental Wave Flume

Long time series of wave field are experimentally simulated by JONSWAP spectra with random phases in a 2D wave flume. Statistic properties of wave surface, such as significant wave height, skewness and kurtosis, are analyzed, and the freak wave occurrence probability and its relations with Benjamin-Feir index （BFI） are also investigated. The results show that the skewness and the kurtosis are significantly dependent on the wave steepness, and the kurtosis increases along the flume when BFI is large. The freak waves are observed in random wave groups. They occur more frequently than expected, especially for the wave groups with large BFI.

Harmonic Energy Transfer for Extreme Waves in Current

Ning et al. （2015） developed a 2D fully nonlinear potential model to investigate the interaction between focused waves and uniform currents. The effects of uniform current on focusing wave crest, focal time and focal position were given. As its extension, harmonic energy transfer for focused waves in uniform current is studied using the proposed model by Ning et al. （2015） and Fast Fourier Transformation （FFT） technique in this study. It shows that the strong opposing currents, inducing partial wave blocking and reducing the extreme wave crest, make the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide an explanation to address the shifts of focal points in consideration of the combination effects of wave nonlinearity and current.

Review on second-harmonic generation of ultrasonic guided waves in solid media(Ⅰ): Theoretical analyses

Considering the high sensitivity of the nonlinear ultrasonic measurement technique and great advantages of the guided wave testing method, the use of nonlinear ultrasonic guided waves provides a promising means for evaluating and characterizing the hidden and/or inaccessible damage/degradation in solid media. Increasing attention on the development of the testing method based on nonlinear ultrasonic guided waves is largely attributed to the theoretical advances of nonlinear guided waves propagation in solid media. One of the typical acoustic nonlinear responses is the generation of second harmonics that can be used to effectively evaluate damage/degradation in materials/structures. In this paper, the theoretical progress of second-harmonic generation（SHG） of ultrasonic guided wave propagation in solid media is reviewed. The advances and developments of theoretical investigations on the effect of SHG of ultrasonic guided wave propagation in different structures are addressed. Some obscure understandings and the ideas in dispute are also discussed.

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.

Experimental Investigation on the Extreme Waves Induced by Single Wave Packets in Finite Water Depth

Single Gaussian wave groups with different initial wave steepness εand width N are produced in laboratory in finite depth to study the nonlinear evolution, the extreme events and breaking. The results show that wave groups with larger εwill evolve to be several envelope solitons(short wave groups). By analyzing geometric parameters, a break in the evolution of the wave elevation and asymmetric parameters after extreme wave may be an indicator for the inception of refocus and the maximal wave moving to the middle, namely, wave down-shift occurs. The analysis of the surface elevations with HHT(Hilbert-Huang Transform), which presents the concrete local variation of energy in time and frequency can be exhibited clearly, reveals that the higher frequency components play a major role in forming the extreme event and the contribution to the nonlinearity. Instantaneous energy and frequency in the vicinity of the extreme wave are also examined locally. For spilling breakers, the energy residing in the whole wave front dissipates much more due to breaking, while the energy in the rear of wave crest loses little, and the intra-wave frequency modulation increases as focus. It illustrates that the maximal first order instantaneous frequency fand the largest crest tend to emerge at the same time after extreme wave when significant energy dissipation happens, and vice versa. In addition, it shows that there is no obvious relation of the CDN(combined degree of nonlinearity) to the wave breaking for the single Gaussian wave group in finite water depth.

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.

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.

Multi-mode Spiral Wave in a Coupled Oscillatory Medium

Multi-mode spiral wave and its breakup in 1-d and 2-d coupled oscillatory media is studied here by theoretic analysis and numerical simulations. The analysis in 1-d system shows that the dispersion relation curve could be nonmonotonic depending on the coupling strength. It may also lead to the coexistence of different wave numbers within one system. Direct numerical observations in 1-d and 2-d systems conform to the prediction of dispersion relation analysis. Our findings indicate that the wave grouping can also be observed in oscillatory media without tip meandering and waves with negative group velocity can occur without inhomogeneity.

The irregular wave force on pier group

-In this paper, the irregular wave force on a cylindrical pier group is calculated by the method of spectrum analysis, and the coefficients of the group effect of piers in the pier group are given here. The calculated results, using P-M and Bretshneider's. (B's) spectra, are obtained for the cases of 2 piers, 3 piers and 4 piers. To compare these results with those obtained for regular waves, we can come to some significant conclusions. Under the action of the irregular wave, when the distance between the piers in the pier group increases, the coefficient of the group effect decreases and tends rapidly to the case of a single pier. In general, when the ratio of the distance between the piers to the diameter of the pier is greater than 4, the group effect can be neglected.

Simulating Long Waves in a Coifs Harbour 3D Physical Model Using Short Wave Spectra

This paper presents examples of field data of extreme seiche waves measured at Coffs Harbour by MHL and describes the generation and measuring methodology to detect and reduce seiche agitation in the Coifs Harbour boat ramp using a 3D physical model. The paper also discusses the techniques in investigating a short wave problem of stability in the same model where a long wave is simulated. Waves offshore of Coffs Harbour at 80 m depth have been recorded by MHL for a period of over 30 years. Long waves have been simultaneously measured in the harbour over a period of a decade. These data enabled the model to be verified on two dates （4/6/12, 5/9/14） when high long waves were recorded at the boat ramp harbour under storm and non-storm conditions. Long waves are generated in harbours due to group bounded long wave and surf beat or edge waves. The paper presents methodologies of generating long waves both numerically and by using physical models, and discusses the advantages and disadvantages of these generation techniques. Numerical modelling carried out using long period regular waves in a previous investigation predicted reductions up to 50% due to change of planform of the boat ramp harbour where an area next to the boat ramp was excavated and roughness elements introduced to dampen long periods. The 3D physical model simulated a 25% decrease in the long wave energy in the boat ramp when a suitable change in the planform was made. A 3D undistorted model of scale 1：58 was used in the investigation.

Basic Features of the Crustal Structure in the Lower Yangtze and Its Neighboring Area in the Chinese Mainland： Review of Deep Seismic Sounding Research

The Deep Seismic Sounding( DSS) projects carried out from the 1970 s in the lower Yangtze region and its neighboring area were reviewed in this paper,then the basic wave group features of those wide angle reflection / refraction record sections,and of the crustal structure are summarized. It shows that there were in total five clear wave groups on the record sections,which include the first arrival Pg,the reflection P1 from the bottom interface of the upper crust,the reflection P3 from the bottom interface of the middle crust,the strong reflection Pm from the Moho boundary,and the refraction Pn from uppermost mantle. In general,these phases are easily consistently traced and compared,despite some first arrivals being delayed or arriving earlier than normal due to the shallow sedimentary cover or bedrocks. In particular,in the Dabie Mountain region the seismic events of a few gathered shots always have weak reflection energy,are twisted,or exhibit disorganized waveforms, which could be attributed to the disruption variations of reflection depth,the broken Moho,and the discontinuity of the reflection boundary within crust. The regional crustal structures are composed of the upper,middle and lower crust,of which the middle and lower layers can be divided into two weak reflection ones. The crustal thickness of the North China and Yangtze platform are 30km- 36 km,and the Moho exhibits a flat geometry despite some local uplifts. The average pressure velocity in lower crust beneath this two tectonic area is 6. 7 ± 0. 3km / s. Nevertheless,beneath the Dabieshan area the crustal thickness is 32km- 41 km,the Moho bends down sharply andtakes an abrupt 4km- 7km dislocation in the vertical direction. The average pressure velocity in the lower crust beneath the Dabieshan area is 6. 8 ± 0. 2km / s.

Theoretical research on intensity envelope function of strong ground motion

After the time history of seismic motion is represented by superposition of a series of narrow frequency band wave groups, we obtain a general relation between wave group arrival time and derivative of phase spectra in the paper. On the basis of the relation, frequency number distribution function of wave group arrival time is completely equivalent to that of phase difference spectra. Under the assumption that phase angles of seismic motionobey uniform distribution ranged from 0 to ─ 2π, a quantitative relation between intensity envelope function of seismic motion and energy distribution function with wave group arrival time has been derived in this paper. The relation illuminates inner links among Fourier amplitude spectra and derivative of phase spectra and intensity envelope function. Some examples given by the paper support the conclusions mentioned above.