Three-dimensional dynamic sea surface modeling based on ocean wave spectrum

In conventional marine seismic exploration data processing,the sea surface is usually treated as a horizontal free boundary.However,the sea surface is affected by wind and waves and there often exists dynamic small-range fluctuations.These dynamic fluctuations will change the energy propagation path and affect the final imaging results.In theoretical research,different sea surface conditions need to be described,so it is necessary to study the modeling method of dynamic undulating sea surface.Starting from the commonly used sea surface mathematical simulation methods,this paper mainly studies the realization process of simple harmonic wave and Gerstner wave sea surface simulation methods based on ocean wave spectrum,and compares their advantages and disadvantages.Aiming at the shortcomings of the simple harmonic method and Gerstner method in calculational speed and sea surface simulation effect,a method based on wave equation and using dynamic boundary conditions for sea surface simulation is proposed.The calculational speed of this method is much faster than the commonly used simple harmonic method and Gerstner wave method.In addition,this paper also compares the new method with the more commonly used higher-order spectral methods to show the characteristics of the improved wave equation method.

A proposed directional function and wind-wave directional spectrum

A directional function for frequencies equal to and larger than the peak frequency of a wind-wave frequency spectrum is constructed by fitting the angular spreading based on the analytically derived directional spectrum of Wen et al. (1993, Journal of Oceanography, 49(2), 131～147, 149～172). For frequencies smaller than the peak frequency, the directional function is obtained by comparing and analyzing existing formulas. The nondimensional wind-wave frequency spectrum of Wen et al. (1994, Progress in Natural Seience, 4(4). 407～427;4 (5), 586～596) has been used together with the directional function just mentioned to obtain the directional spectrum for easier application.

Modal Wave Number Spectrum for Mesoscale Eddies

The variations of ocean environmental parameters invariably result in variations of local modal wave numbers of a sound pressure field. The asymptotic Hankel transform with a short sliding window is applied to the complex sound pressure field in the water containing a mesoscale eddy to examine the variation of local modal wave numbers in such a range-dependent environment. The numerical simulation results show that modal wave number spectra obtained by this method can reflect the location and strength of a mesoscale eddy, therefore it can be used to monitor the strength and spatial scale of ocean mesoscale eddies.

On the Spectrum Width of Wind Waves

Based on the universal expression of wind wave spectra, four commonly used definitions of the spectrum width are re-examined. The results show that the non-dimensional spectrum width can measure the width of non-dimensional spectra but it does not reflect the developing state of the spectra. The dimensional spectrum width expresses the degree of concentration of wave energy of the spectrum in the process of wind wave growth. Tests show that the spectrum width presented by Wen et al. can objectively measure the degree of concentration of wave energy of the spectrum, reflect the state of wind wave growth, and provides a better result for practical application, The rules for definition of the spectrum width are discussed.

Directional Spectrum of Wind Waves: Part Ⅱ- Comparison and Confirmation

A model on the directional frequency spectrum of wind waves for deep water is introduced. The comparisons of the proposed model with other existing models show that the proposed model is very close to the JONSWAP model and DHH model for describing the developing waves under the normal spectral bandwidth, and has a better description for the transition of the unidirectional spectrum from ω -4 to ω -5 at a position around 3ω p, i.e., three time the peak frequency. Comparisons also show that the proposed model describes closely both field data measured by a four-frequency radar and a laser-optical sensor, and laboratory data measured by a laser slope gauge and an imaging optical method. The comparisons further demonstrate that the inverse spectral bandwidth as a new wave parameter is robust for describing the spectral steepness. Finally, the formula on the local spectral-peak angular frequency is confirmed using the observed two-dimensional spectra.

A Study on the Spectral Form of Nearshore Water Waves

The spectral form of wind waves is investigated based on the ocean wave data observed at three nearshore stations of Taiwan. In this study, the generalized forms of Pierson-Moskowitz spectrum and JONSWAP spectrum are used to describe the local wave spectrum by selecting suitable spectral form parameters. It is shown that, at a specific site, the similarity of wave spectral form exists. Thus it is possible to use a representative spectral form for a given nearshore region to describe the wave spectrum at this nearshore. On the other hand, the effects of relative water depth on spectral form are examined. The feasibility of two spectral models in finite water depth is evaluated by using the same field wave data.

Observations and Estimations of Directional Spectrum of Sea Waves

The directional spectrum is one of the basic characteristics of sea waves. The observations of directional spectrum of sea waves were successfully conducted at platform Bohai 8 during 1991 and 1992 using a wave gage array for the first time in China. Based on the field data, the directional spectrum which depends on the wave growth is given in this paper. Before observations, the effects of the type of gage array, the distance between the gages and the platform itself on the measured results and the precision of some methods for estimating the directional spectrum were investigated and compared with the methods of numerical simulations and model tests of multi-direcitonal irregular waves. This ensures the quality of the observations and estimations of the directional spectrum.

3-D simulations of freak waves based on high-order spectral method

Three-dimensional ( 3-D) directional wave focusing is one of the mechanisms that contribute to the generation of freak waves. To simulate and analyze this phenomenon,a 3-D wave focusing model is proposed based on the enhanced high-order spectral method,which solves the fully nonlinear potential flow equations with a free surface within periodic unbounded 3-D domains. The numerical model is validated against a fifth-order Stokes solution for regular waves. Laboratory-scale freak waves are observed with wave components having equal amplitudes. Investigations of the appearance and propagation of freak-wave events in a 3-D open wavefield defined by a directional wave spectrum are then realized.

Directional Spectrum of Wind Waves: Part Ⅰ- Model and Derivation

A new model on the directional spectrum of wind waves for deep water is proposed based on the statistics of wind waves. This model contains three parameters: the wave age, the inverse spectral bandwidth and the local spectral-peak angular frequency. The inverse spectral bandwidth is a robust parameter for describing the spectral steepness of wind waves. Using the inverse spectral bandwidth parameter, the proposed model can well describe various observations obtained from the open ocean and laboratory tank.

Spectral Characteristics of Wind-Waves in Laboratory

Spectral characteristics of wind-generated waves in labortaory are presented on the basis of a systematic measurement in a large-scale wind-wave channel and compared with those in the field. A marked characteristics of the measured spetra is the existence of secondary spectrum-peak. The dependence of spectral peak-frequency, peak-value and zeroth-order moment on wind speed and fetch are presented and found roughly similar to those in the field represented by the JONSWAP spectrum, regardless of the differences in coefficient. The spectral slope beta at high-frequencies are found somewhat greater than those of field wind-waves in both cases of deep and shallow waters. Except for the low-frequency part, the spectral forms measured in different wind conditions are similar and fit for the JONSWAP spectrum with gamma = 6 and beta = 5.5. Some relevant problems are discussed.

Wave height statistical characteristic analysis

When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore, the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station. An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis (MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island, Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.

Estimation of Wind Wave Frequency Spectra by Use of the Arcsine Law

In the present study, the surface elevation of wind waves observed in laboratory and in the Bohai Sea are adopted for the estimation of the wind wave frequency spectrtm by use of the method of the arcsine law （MAL）. The traditional method uses the surface elevation to calculate the correlation and then estimate the frequency spectrum while the MAL, presented by Yu and l.an （1979）, uses the time sequence of zero-crossing points of surface elevation rather than directly the surface elevation to calculate the correlation. 66 sets of wind wave data obtained in laboratory and 420 sets of data observed in the Bohai Sea are adopted for the examination of the method introduced by Yu and Lan. Results show that the MAL can give reliable estimation of wind wave spectra. Correlation and form of spectra estimated by the MAL are similar to those estimated by the traditional method. The peak frequency and the spectral density in peak frequency by the MAL are close to those obtained by the traditional method.

Response Characteristics of Load on Vessels in Waves

Considering the requirement of direct design and fatigue test for ships and floating structures by use of FEM technique, a computational procedure of spectral analysis for wave load on the hull surface is developed in this paper. The response of hydrodynamic pressure on the body surface to a designated sea state for ships and floating structures is calculated by use of the revised strip method with the hull bound perturbation flow concept. The spectral function of wave load for the defined point on the body surface can be determined from the Wiener-Khinhine theorem and the characteristic load value can be also obtained from spectral moment analysis. A container ship is taken as a computational example acid the sample of wave load with a certain probability and corresponding encountered frequency is provided.

Bimodality and growth of the spectra of typhoon-generated waves in northern South China Sea

Buoy-based observations of wave spectra during the passage of three typhoons in the northern South China Sea are examined.Though most spectra of mature typhoon-generated waves are unimodal,double-peaked spectra account for a significant proportion during the growing and decaying stages.This is due either to the superposition of swells on local wind waves or to the mechanism of nonlinear interaction between different wave components.The growth rate of energy density is an effective way to predict spectrum variation.The dominant wave direction depends on the location of the typhoon center to the site,but the direction spread shows no regularity in distant regions.In this study,a new six-parameter spectral formula is proposed to represent doublepeaked spectra and is shown to provide a better fit than previous models.The theoretical relationship between shape parameter and spectral width is still applicable to each peak.The characteristics of the variations of spectral parameters are analyzed.It is demonstrated that the spectral parameters are not only related to the typhoon intensity and typhoon track,but also have strong intercorrelations.Moreover,the growth relation between significant wave height and significant wave period is obtained to fit the typhoon-generated waves.

Instant Effects of Radiofrequency Electromagnetic Wave on Hemoglobin in Single Living Intact Red Blood Cell

The absorption spectrum of the hemoglobin （Hb） in single riving intact red blood cell（RBC）, exposed in 900 MHz radiofrequency electromagnetic wave （RF-EMW）, was non-invasive,in situ, real-time measured by employing a highly sensitive fast multi-channel microspectrophotometer system. Both the absorption intensity and site of intracellular Hb were altered after RBCs were exposed in 900 MHz RF-EMW with power density at 5 mW/cm^2. It was indicated that not only the concentration of Hb in living RBCs was decreased, but the molecular structure of Hb was changed by the RF-EMW action.

Simulation of Random Waves and Associated Laminar Bottom Shear Stresses

This work presents a new approach for simulating the random waves in viscous fluids and the associated bottom shear stresses. By generating the incident random waves in a numerical wave flume and solving the unsteady two-dimensional Navier-Stokes equations and the fully nonlinear free surface boundaiy conditions for the fluid flows in the flume, the viscous flows and laminar bottom shear stresses induced by random waves axe determined. The deterministic spectral amplitude method implemented by use of the fast Fourier transform algorithm was adopted to generate the incident random waves. The accuracy of the numerical scheme is confirmed by comparing the predicted wave spectrum with the target spectrum and by comparing the nanlerical transfer function between the shear stress and the surface elevation with the theoretical transfer function. The maximum bottom shear stress caused by random waves, computed by this wave model, is compared with that obtained by Myrhaug＇ s model （1995）. The transfer function method is also employed to determine the maximum shear stress, and is proved accurate.

A Wave Modulation Model of Ripples over Long Surface Waves

A study is presented on the modulation of ripples induced by a long surface wave (LW) and a new theoretical modula-tion model is proposed. In this model, the wind surface stress modulation is related to the modulation of ripple spectrum. The model results show that in the case of LW propagating in the wind direction with the wave age parameter of LW increasing, the area with enhanced shear stress shifts from the region near the LW crest on the upwind slope to the LW trough. With a smaller wave age parameter of LW, the ripple modulation has the maximum on the upwind slope in the vicinity of LW crest, while with a larger parameter the enhancement of ripple spectrum does not occur in that region. At low winds the amplitude of ripple modulation transfer function (MTF) is larger in the gravity wave range, while at moderate or high winds it changes little in the range from short gravity waves to capillary waves.

GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS

A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation （nonlinear convection- diffusion problem） and KdV equation（single solitary and 2-solitary wave problems）, where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.

Absorption Spectrum Studies on the RDX Crystals with Different Granularity in Terahertz Frequency Range

The absorption spectrum of the cyclotrime-thylenetrinitramine （RDX） with four different particle sizes are measured in the frequency range from 0.1THz to 2.5THz by using the terahertz time-domain spectroscopy （THz-TDS）, and the characteristic absorption peaks are acquired. All the samples are measured in a loose condition, which is very close to the real using environment of the RDX. The results show that the four kinds of samples have similar absorption peaks around the frequency of 0.82THz, 1.05 THz, 1.30THz, 1.46THz, 1.65THz, and 1.95THz. The sample with a large particle size obtains more peaks than the small one, while the peaks obtained from the sample with a small size are more protrudent. The reasons for these differences can be the refraction, scattering, and attenuation of the terahertz wave when it passes through the crystal samples. The theoretical terahertz spectrum of RDX was simulated by using density functional calculations, in which, the Becke ＆amp; Perdew-Wang＇s functional is used in a double numerical plus polarization method （BP/DNP）. Good agreements between the experimental and computed results show that the three peaks located in the frequency of 1.30THz, 1.48THz, and 1.96THz are caused respectively by the twisting of three-nitrogen heterocyclic, the symmetrical oscillations of the double nitro groups, and the oscillations of a single nitro group.

Hilbert spectrum and intrinsic oscillation mode of dynamic response of a bilinear SDOF system: influence of harmonic excitation amplitude

Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.