Digital core based transmitted ultrasonic wave simulation and velocity accuracy analysis

Transmitted ultrasonic wave simulation （TUWS） in a digital core is one of the important elements of digital rock physics and is used to study wave propagation in porous cores and calculate equivalent velocity. When simulating wave propagates in a 3D digital core, two additional layers are attached to its two surfaces vertical to the wave-direction and one planar wave source and two receiver-arrays are properly installed. After source excitation, the two receivers then record incident and transmitted waves of the digital rock. Wave propagating velocity, which is the velocity of the digital core, is computed by the picked peak-time difference between the two recorded waves. To evaluate the accuracy of TUWS, a digital core is fully saturated with gas, oil, and water to calculate the corresponding velocities. The velocities increase with decreasing wave frequencies in the simulation frequency band, and this is considered to be the result of scattering. When the pore fluids are varied from gas to oil and finally to water, the velocity-variation characteristics between the different frequencies are similar, thereby approximately following the variation law of velocities obtained from linear elastic statics simulation （LESS）, although their absolute values are different. However, LESS has been widely used. The results of this paper show that the transmission ultrasonic simulation has high relative precision.

Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

A simple method of depressing numerical dissipation effects during wave simulation within the Euler model

Numerical wave tanks are widely-acknowledged tools in studying waves and wave-structure interactions. They can generate waves under realistic scales and offers more information on the fluid field. However, most numerical wave tanks suffer from issues known as the numerical dissipation and numerical dispersion. The former causes wave energy to be slowly dissipated and the latter shifts wave frequencies during wave propagation. This paper proposes a simple method of depressing numerical dissipation effects on the basis of solving Euler equations using the finite difference method(FDM). The wave propagation solutions are solved analytically taking into account the influence of the damping terms. The main idea of the method is to append a source term to the momentum equation, whose strength is determined by how strong the numerical damping effect is. The method is verified by successfully depressing numerical effects during the simulation of regular linear waves, Stokes waves and irregular waves. By applying the method, wave energy is able to be close to its initial value after long distance of travel.

K2_SPH Method and its Application for 2-D Water Wave Simulation

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian meshless particle method. However, its low accuracy of kernel approximation when particles are distributed disorderly or located near the boundary is an obstacle standing in the way of its wide application. Adopting the Taylor series expansion method and solving the integral equation matrix, the second order kernel approximation method can be obtained, namely K2_SPH, which is discussed in this paper. This method is similar to the Finite Particle Method. With the improvement of kernel approximation, some numerical techniques should be adopted for different types of boundaries, such as a free surface boundary and solid boundary, which are two key numerical techniques of K2_SPH for water wave simulation. This paper gives some numerical results of two dimensional water wave simulations involving standing wave and sloshing tank problems by using K2_SPH. From the comparison of simulation results, the K2_SPH method is more reliable than standard SPH.

Numerical simulation of typhoon- induced storm surge on the coast of Jiangsu Province,China,based on coupled hydrodynamic and wave models

In order to facilitate engineering design and coastal flooding protection, the potential storm surge induced by a typhoon is studied.Using an unstructured mesh, a coupled model which combines the advanced circulation （ ADCIRC ） hydrodynamic model and simulating waves nearshore （ SWAN ） model is applied to analyze the storm surge and waves on the coast of Jiangsu Province.The verifications of wind velocity, tidal levels and wave height show that this coupling model performs well to reflect the characteristics of the water levels and waves in the studied region.Results show that the effect of radiation stress on storm surge is significant, especially in shallow areas such as the coast of Jiangsu Province and the Yangtze estuary.By running the coupled model, the simulated potential flooding results can be employed in coastal engineering applications in the Jiangsu coastal area, such as storm surge warnings and extreme water level predictions.

Stability Conditions for Wave Simulation in 3-D Anisotropic Media with the Pseudospectral Method

Simulation of elastic wave propagation has important applications in many areas such as inverse problemand geophysical exploration.In this paper,stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method are investigated.They can be expressed explicitly by elasticity constants which are easy to be applied in computations.The 3-Dwave simulation for two typical anisotropic media,transversely isotropic media and orthorhombic media,are carried out.The results demonstrate some satisfactory behaviors of the pseudospectral method.

A study of damping factors in perfectly matched layers for the numerical simulation of seismic waves

When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially trtmcated boundaries. In this paper, a damping factor referred to as the Gaussian dmping factor is proposed. The Gaussian damping factor is based on the idea of perfectly matched layers （PMLs）. This work presents a detailed analysis of the theoretical foundations and advantages of the Gaussian damping factor. Additionally, numerical experiments for the simulation of seismic waves are presented based on two numerical models： a homogeneous model and a multi-layer model. The results show that the proposed factor works better. The Gaussian damping factor achieves a higher Signal-to-Noise Ratio （SNR） than previously used factors when using same number of PMLs, and requires less PMLs than other methods to achieve an identical SNR.

Flume simulation of wave-induced release of internal dissolved nitrogen in Taihu Lake,China

A wave flume simulator was used to study internal nitrogen release from the surface sediment collected from Taihu Lake, China. Particulate nitrogen concentrations were positively correlated with the concentrations of suspended solids, primarily from surface erosion related to the shear stress and duration of wave action. In response to 4 cm- and 10 cm-high wave production representing waves generated in Taihu Lake by gentle and gusty winds, respectively, the mean dynamic release rate of ammonium （NH4＋） from the sediment to the overlying water was 1 × 10-3 mg/（m2.s） and the NH4＋ concentration in the overlying water increased by 0.016 mg/L, indicating that waves resulting from strong wind can induce the rapid release of dissolved nitrogen from Taihu Lake sediments. The decrease in interstitial NH4＋ concentrations at all sediment depths was associated with an increase in NH4＋ concentrations in the overlying water by 0.01 mg/L, showing that sediment below the eroded layer was the main source of internal nitrogen release. Changes in the interstitial dissolved oxygen and NH4＋ concentrations showed that wave-induced pore water movement can greatly increase the diffusion rate, and that these 15 cm. Diffusion induced by pore water movement sediment layer in Taihu Lake. effects can influence the sediment to a depth of at least may be very important for the formation of an active

Simulation of the extreme waves generated by typhoon Bolaven (1215) in the East China Sea and Yellow Sea

Record-breaking high waves occurred during the passage of the typhoon Bolaven（1215）（TYB） in the East China Sea（ECS） and Yellow Sea（YS） although its intensity did not reach the level of a super typhoon.Winds and directional wave measurements were made using a range of in-situ instruments mounted on an ocean tower and buoys.In order to understand how such high waves with long duration occurred,analyses have been made through measurement and numerical simulations.TYB winds were generated using the TC96 typhoon wind model with the best track data calibrated with the measurements.And then the wind fields were blended with the reanalyzed synoptic-scale wind fields for a wave model.Wave fields were simulated using WAM4.5 with adjustment of C_d for gust of winds and bottom friction for the study area.Thus the accuracy of simulations is considerably enhanced,and the computed results are also in better agreement with measured data than before.It is found that the extremely high waves evolved as a result of the superposition of distant large swells and high wind seas generated by strong winds from the front/right quadrant of the typhoon track.As the typhoon moved at a speed a little slower than the dominant wave group velocity in a consistent direction for two days,the wave growth was significantly enhanced by strong wind input in an extended fetch and non-linear interaction.

Reliability Analysis of Numerical Simulation of Sea-Crossing Bridge Deformation Under Wave Forces

To study on the numerical simulation calculation reliability of sea-crossing bridge under complex wave forces,the paper applied GPS deformation monitoring and numerical simulation calculation by researching Qingdao Jiaozhou Bay Sea-Crossing Bridge.The db3 wavelet three-layer decomposition was used on the horizontal movement of the sea-crossing bridge and the wind speed of the waves to analyze their correlation.The complex wave forces value of Qingdao Jiaozhou Bay Sea-Crossing Bridge was loaded on FLAC3D software successfully to make numerical simulation calculation of bridge deformation.Since the accuracy of the GPS deformation monitoring reaches millimeter level,it was used to monitor the exact value of the bridge deformation to judge the reliability of numerical simulation.The relative errors of displacement in X,Y and Z directions were between 33%and 41%through comparison.It could be seen that the numerical simulation error was relatively large,which was mainly due to various environmental factors and the deviation of applied wave forces.However,numerical simulation generally reflects the deformation law of the sea-crossing bridge under complex wave forces,providing an effectively technical support for the safe operation assessment of the sea-crossing bridge.

Numerical Simulation of Multi-Directional Random Wave Transformation in a Yacht Port

This paper extends a prediction model for multi-directional random wave transformation based on an energy balance equation by Mase with the consideration of wave shoaling, refraction, diffraction, reflection and breaking. This numerical model is improved by 1) introducing Wen's frequency spectrum and Mitsuyasu's directional function, which are more suitable to the coastal area of China; 2) considering energy dissipation caused by bottom friction, which ensures more accurate results for large-scale and shallow water areas; 3) taking into account a non-linear dispersion relation. Predictions using the extended wave model are carried out to study the feasibility of constructing the Ai Hua yacht port in Qingdao, China, with a comparison between two port layouts in design. Wave fields inside the port for different incident wave directions, water levels and return periods are simulated, and then two kinds of parameters are calculated to evaluate the wave conditions for the two layouts. Analyses show that Layout I is better than Layout II. Calculation results also show that the harbor will be calm for different wave directions under the design water level. On the contrary, the wave conditions do not wholly meet the requirements of a yacht port for ship berthing under the extreme water level. For safety consideration, the elevation of the breakwater might need to be properly increased to prevent wave overtopping under such water level. The extended numerical simulation model may provide an effective approach to computing wave heights in a harbor.

Simulation and analysis of point-source surface wave fields

The complexity of near surface intensifies the diversity of seismic wave fields, which makes study on near surface wavefields important in many aspects. The strong absorption of low velocity layer can affect the resolution of seismic data, and free boundary can cause surface wave. Considering the above problems, we focus on the Rayleigh wavefields simulation using finite-difference wave equation of higher-order staggered grids and PML boundary conditions. Free boundary, buried source and overlying low velocity layer are taken into consideration and point explosion source is adopted. Through some numerical simulation with different parameters, we quantitatively analyze relationship between wave intensity and source depth, as well as the energy variation with propagation and obtain some practical knowledge and conclusions.

Parametric Instabilities of Parallel Propagating Circularly Polarized Alfven Waves:One-Dimensional Hybrid Simulations

By performing one-dimensional （l-D） hybrid simulations, we analyze in detail the parametric instabilities of the Alfv^n waves with a spectrum in a low beta plasma. The parametric instabilities experience two stages. In the first stage, the density modes are excited and immediately couple with the pump Alfv6n waves. In the second stage, each pump Alfv^n wave decays into a density mode and a daughter Alfv6n mode similar to the monochromatic cases. Ftlrthermore, the proton velocity beam will also be formed after the saturation of the parametric instabilities. When the plasma beta is high, the parametric decay in the second stage will be strongly suppressed.

Simulation of Deep Water Wave Climate for the Indian Seas

The ocean wave climate has a variety of applications in Naval defence.However,a long-term and reliable wave climate for the Indian Seas(The Arabian Sea and The Bay of Bengal)over a desired grid resolution could not be established so far due to several constraints.In this study,an attempt was made for the simulation of wave climate for the Indian Seas using the third-generation wave model(3g-WAM)developed by WAMDI group.The 3g-WAM as such was implemented at NPOL for research applications.The specific importance of this investigation was that,the model utilized a“mean climatic year of winds”estimated using historical wind measurements following statistical and probabilistic approaches as the winds which were considered for this purpose were widely scattered in space and time.Model computations were carried out only for the deep waters with current refraction.The gridded outputs of various wave parameters were stored at each grid point and the spectral outputs were stored at selected locations.Monthly,seasonal and annual distributions of significant wave parameters were obtained by post-processing some of the model outputs.A qualitative validation of simulated wave height and period parameters were also carried out by comparing with the observed data.The study revealed that the results of the wave climate simulation were quite promising and they can be utilized for various operational and ocean engineering applications.Therefore,this study will be a useful reference/demonstration for conducting such experiments in the areas where wind as well as wave measurements are insufficient.

SEM Numerical Simulation of Vertical and Inclined Fault Zone Trapped Waves and Comparison of Their Wave Fields

Fault zone trapped waves （FZTWs） mainly travel along the fractured fault zone （FZ） which is of low velocity and high attenuation. FZTWs often carry significant information about a fault＇s internal structure, so it is important to understand their wave field characteristics for FZ structure inversion. Most previous simulations are based on vertical faults, while in this paper we implement the FZTW simulations on vertical or inclined faults and compare their wave fields in both time and frequency domains. The results show that the existence of fault zone and inclined angle of fault can significantly influence the features of waves near faults. In amplitude, a fault zone can generate a larger amplitude of waves. The velocity contrast between two wails of fault may lead to amplification of amplitudes in the low velocity fault wall. In frequency, a fault zone tends to influence the waves in the low frequency range. In a pattern of particle polarization of FZTWs, it tends to be single direction for vertical faults but fork to multiple directions for inclined faults, which might provide a new way to study the fault zone with FZTWs. These conclusions may be valuable for FZ structure inversion, and will enhance the knowledge on near-fault strong ground motions.

Numerical simulation of non-gaussian process of wind waves

In this paper further mathematical analysis on 'correlation transfer technique' by Polge el al. is carried out, the tenable conditions and the extent of suitability for the said method are proved as well. In consideration of the influence of skewness of the sea surface elevation on spectral shape, a 'quasi-correlation transfer techique' is developed by the modification of the simulated target spectrum. Meanwhile, the numerical simulation of the non-Gaussian process of wind waves is carried out in view of the two conditions of the surface elevation probability distribution and the spectrum. By using its simulated results, the influence of skewness of the sea surface elevation on two parameters in the distribution of wave heights (which had been fitted by using the Weibull distribution) is analysed. The 'quasi- correlation tranfer technique' is verified and compared with the selection wave data observed in the Jiaozhou Bay in the period of 1980 to 1981. Results make clear (hat, as far as the statistical distribution of the wave heights and the distribution of the maximum (minimum) values of the sea surface elevation are concerned, the said method is obviously superior to the conventional mothed of the linear wave superposition, and that the simulated results are closer to the observation data.

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.

Particle-in-Cell Simulation of the Reflection of a Korteweg-de Vries Solitary Wave and an Envelope Solitary Wave at a Solid Boundary

Reflections of a Korteweg-de Vries （KdV） solitary wave and an envelope solitary wave are studied by using the particle-in-cell simulation method. Defining the phase shift of the reflected solitary wave, we notice that there is a phase shift of the reflected KdV solitary wave, while there is no phase shift for an envelope solitary wave. It is also noted that the reflection of a KdV solitary wave at a solid boundary is equivalent to the head-on collision between two identical amplitude solitary waves.

Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme

To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic （VTI） media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.

Laboratory Research on Effective Test Area of Short-Crested Waves Generated by Two-Sided Segmented Wavemakers

The size and shape of the effective test area are crucial to consider when short-crested waves are created by segmented wavemakers. The range of the effective test area of short-crested waves simulated by two-sided segmented wavemakers is analyzed in this paper. The experimental investigation on the wave field distribution of short-crested waves generated by two-sided segmented wavemakers is conducted by using an array of wave gauges. Wave spectra and directional spreading function are analyzed and the results show that when the main direction is at a certain angle with the normal line of wave generators, the wave field of 3D short-crested waves generated by two-sided segmented wavemakers has good spatial uniformity within the model test area. The effective test area can provide good wave environments for seakeeping model tests of various ocean engineering structures in the deep ocean engineering basin.