A theoretical formulation for wave propagations over uneven bottom

A first-order solution is obtained with a mild-slope parameter within the framework of the linear wave theory using the classical multiple scale method. This solution satisfies (1) the governing equations and free surface condition; (2) the coastal bottom condition in terms of multiple scale with its form analytical. As to two-dimensional wave propagating towards a slope, its solution reduces to the famous Biesel [1952. Study of wave progression in water of gradually varying depth. Gravity Waves, vol. 521. US National Bureau of Standards Circular, pp. 243–253] solution.     

波浪在缓变海底上传播的一个简单数学模型

基于Liu和Shi(2008)的波浪势函数零阶、一阶近似解,采用四阶龙格-库塔法,对缓变海底上一维波浪传播理论模型进行了数值求解,并对波浪在定常坡度的斜坡地形、双曲正切地形为例的传播、变形进行了研究。为了更逼真地描述流体质点的波动特性,将在Euler坐标系下得到的解转换至Lagrange坐标下的解,并绘制Lagrange坐标下坡度为0.2的海滩上的一个波周期内临近破碎前的波形的详细变化过程。此外,计算得到了变水深区域波浪速度势以及自由面的分布,并与Athanassoulis and Belibassakis[34]的结果进行了对比,表明本文模型比保留了六个瞬息项的后者更有效。     

A GIS-based WFD oriented typology of shallow micro-tidal soft bottom using wave exposure and turbidity mapping

Our GIS based project aims at producing a classification scheme to develop a typology of the bottom of the Bay of Gdansk in the southern Baltic. The typology was based on the abiotic factors which are used to define water body types by the European Water Framework Directive (WFD). Significance analysis of particular factors has shown that within the discussed area wave exposure seems to play the most important role. All other factors are to a greater or lesser degree correlated with these two. Taking into consideration the shallows and the varied coastline of the investigated area it was decided to make use of the SWAN numerical wave model to determine the influence of wave impact upon the bottom. The model was used to produce raster maps of orbital velocity near the bottom for each wind scenario. With the help of the GIS analysis the maps were turned into layers: the mean velocity and the maximum velocity at the bottom. To produce the layer of yearly amount of solar radiation a GIS model was built which main parameters were the layer of depth and three layers of turbidity for three seasons. The layers of the maximum orbital velocity and of the solar radiation at the bottom were then used in a classificatory procedure consisted in an iterative sequence of the three following steps: cluster formation, dendrogram analysis and classification using the maximum likelihood method. Ecological importance of the classification has been obtained by means of the aggregation of a part of classes based upon the statistics calculated for them within the GIS system with the help of the zonal function out of the following parameters: salinity, depth, mean and maximum orbital velocity at the bottom, temperature differences between warm and cold seasons, solar radiation, and type of sediments. The method proposed here makes it possible to produce high resolution thematic maps of the bottom even with incomplete data cover of the investigated area.     

有限长正弦地形上的波浪传播问题研究

应用基于势流理论的频域边界元方法,研究了波浪在有限长正弦周期地形上的传播问题.开展了网格收敛性分析,并与物理模型试验结果做了对比,验证了数值方法的准确性.研究了正弦地形长度和幅度对水波反射率的影响,以及波浪在周期性地形上传播时的沿程波幅变化.研究发现,波浪反射系数随波数的变化及波浪幅值沿程的变化均呈包络状;当频率处于布拉格共振区域边缘且反射率为零时,周期地形上会出现极大的波幅;随海床波幅增大,第一布拉格共振带变宽且向低频移动.     

Oblique wave interaction with a floating structure near a wall with stepped bottom

Diffraction of obliquely incident waves by a floating structure near a wall with step-type bottom topography is investigated under the three-dimensional small amplitude wave theory. Full solution of the problem under the potential flow approach is obtained by the matched eigenfunction expansion method. The wave-induced forces on the structure and on the wall, the reflection and transmission characteristics and the wave elevations in the free surface regions are studied for different incident wave angles, water depth ratios and dimension of the structure and the distance of the wall from the center of the structure. The problem is reformulated under shallow water approximations and results are compared with the finite depth results.     

Occurrence probability of a freak wave in a nonlinear wave field

The Edgeworth’s form of a cumulative expansion of the probability density function (PDF) of surface elevation expands the maximum wave height distribution to predict the occurrence probability of freak waves. This study investigated the enhancement of the occurrence probability of freak waves due to the fourth order moment of surface elevation, kurtosis, change and found that the nonlinear effects on the occurrence probability of a freak wave linearly depends on kurtosis for a small number of waves N=250. The statistical theory was compared with field data, and freak waves sometimes appear when not expected by the Rayleigh theory, but they were predicted by the proposed theory.     

A three-point method for estimating wave reflection of obliquely incident waves over a sloping bottom

A three-point method for estimating wave reflection is proposed to account for monochromatic oblique incident waves propagating over a sloping beach. The amplitudes of reflected wave and incident wave are separated using wave amplitudes measured at three fixed wave gauges with a distance. The applicability of the theory is verified by comparing the simulated results with the available theoretical, numerical and experimental results for the estimation of wave reflection. The sensitivity is also tested to provide a more accurate prediction of the reflection coefficient.     

弱非线性斯托克斯波在非平整海底上传播的新型抛物型方程

由于缓坡方程计算量大和其本身的缓坡假定而在实际应用中受到了限制,故对斯托克斯波在非平整海底(适用于缓坡和陡坡地形)上传播的Liu和Dingemans的三阶演化方程进行抛物逼近,得到一个新的非线性抛物型方程,它能够包含同类方程未曾考虑的二阶长波效应.通过数值计算结果与Berkhoff等人的经典实验数据的比较,证明所提出的抛物型模型理论具有较高的精度.     

New periodic wave solutions of a time fractional integrable shallow water equation

In this paper, author employed Jacobi elliptic function expansion method to build the new wave solutions of time fractional modified Camassa–Holm equation which is completely integrable dispersive shallow-water equation. In ocean engineering, Camassa–Holm equation is generally used as a tool in computer simulation of the water waves in shallow sees, coastal and harbors. The obtained solutions show that the Jacobi elliptic function expansion method (JEFEM) which based on Jacobi elliptic functions is an efficient, reliable, applicable and accurate tool for analytic approximation of a wide variety of nonlinear conformable time fractional partial differential equations.     

寒潮影响下江苏沿海风浪场数值模拟研究

基于第三代浅水波浪数值预报模型SWAN,建立自西北太平洋嵌套至东中国海、江苏沿海的三重嵌套模型,对2010年12月12日至15日江苏沿海寒潮大风引起的风浪过程进行了数值模拟研究。利用西北太平洋和江苏沿海实测数据对模型进行了验证,结果表明SWAN嵌套模型能较好地模拟江苏沿海寒潮风浪场的时空分布。通过响水站实测数据对江苏沿海底摩擦系数进行了率定,研究表明选取Collins拖曳理论中摩擦因数C_f=0.001时,有效波高模拟误差相对较小。寒潮风浪场的特征分析表明,有效波高分布与风场分布基本一致,寒潮风浪在江苏沿海北部影响较为显著,辐射沙洲附近由于其特殊地形影响相对较小。     

A three-dimensional modeling of multidirectional random wave diffraction by rectangular submarine pits

A three-dimensional modeling of multidirectional random-wave diffraction by a group of rectangular submarine pits is presented in this paper. The fluid domain is divided into N interior regions representing the pit area and an overall exterior region separated by the imaginary pit boundaries. In the interior region, the analytical expressions of the Fourier series expansion for velocity potentials in the pit regions have been derived with the unknown coefficients determined from a series of Green's function based boundary integral equations. The boundary integral approach has also been applied to obtain the velocity potential and free-surface elevation in the exterior region. The Pierson–Moskowitz (P–M) frequency spectrum was selected for the random wave simulation using the superposition of solutions of a finite number of decomposed wave components. Numerical results for the cases of regular waves and random waves are presented to examine the influences of the pit geometry and incident wave condition on the overall wave field. The general diffraction pattern of alternate bands of increase and decrease of relative wave height in front of the pit system can be observed. It is found that, in the shadow region, the relative wave height is reduced. As the number of pit increases, the effectiveness of reducing the relative wave height behind the multiple-pit system increases. However, the relative wave height within the pit area and in front of the leading pit shows increasing trend. It is noticed that under the random-wave condition, the level of increase and decrease of the relative wave height due to the existence of submarine pits is less pronounced than that observed from results in regular-wave condition.     

A numerical study of three-dimensional wave interaction with a square cylinder

In this study, a three-dimensional numerical model is used to study the wave interaction with a vertical rectangular pile. The model employs the large eddy simulation (LES) method to model the effect of small-scale turbulence. The velocity and vorticity fields around the pile are presented and discussed. The drag and inertial coefficients are calculated based on the numerical computation. The calculated coefficients are found to be in a reasonable range compared with the experimental data. Additional analyses are performed to assess the relative importance of drag and initial effects, which could be quantified by the force-related Keulegan and Carpenter (KC) number: KC_f=UT/(4πL). Here U is the maximum fluid particle velocity, T the wave period and L the length of structure aligned with the wave propagation direction. For small KC_f, the effective drag coefficient is proportional to 1/KC_f, provided the wavelength is much longer than the structural length. When wavelength is comparable to the structure dimension, the effective drag coefficient would be reduced significantly due the cancellation of forces, which has been demonstrated by numerical results.     

A two-point method for estimating wave reflection over a sloping beach

This work presents a frequency-domain method for estimating incident and reflected waves when normally incident waves’ propagating over a sloping beach in a wave flume is considered. Linear wave shoaling is applied to determine changes of the wave amplitude and phase due to variations of the bathymetry. The wave reflection coefficient is estimated using wave heights measured at two fixed wave gauges with a distance. The present model demonstrates a high capacity of estimating reflection and shoaling coefficients from synthetic wave-amplitude data. Sensitivity tests for the present model due to measurement errors of wave amplitudes and distance of two probes can more accurately predict the reflection coefficients. The measurement error of wave amplitude affects more significantly than measurement error of distance of two probes on calculating reflection coefficient of waves over a sloping bed.     

A new approximate analytic solution for water wave scattering by a submerged horizontal porous disk

This study gives a new approximate analytic solution for water wave scattering by a submerged horizontal porous disk in the context of the linear potential theory. The solution is based on the domain decomposition method. The velocity potentials are determined by two different approaches. One approach is to adopt decompositions for velocity potentials, and the other is to expand the vertical derivative of the velocity potential on the porous disk along the radial direction. Hence the velocity potentials are determined by the matched eigenfunction expansions. Differing from previous solutions with respect to the porous disk, the present solution needs no complex dispersion relations. Thus the new solution is easier for numerical implementation. According to numerical examples, the convergence of the present solution is satisfactory. In addition, the present predictions of the wave surface elevation and the vertical wave force on the disk agree very well with previous results by different approaches. The present solution can also be extended to other structures involving disks, such as a fish cage, a porous disk with finite thickness, and a submerged elastic disk.     

A new approximation for ocean waves propagating over a beach with variable depth

In this paper, the phenomenon of ocean waves propagating over a beach with variable water depth is re-examined. Based on the assumption of shallow water, a linearised shallow water equation is solved with an arbitrary beach profile. These irregular beach profiles form a set of partial differential equation with variable coefficient as the governing equation, which is the main obstacle in obtaining analytical solutions. In this paper, two families of beach profile are used as examples. A parametric study is conducted to investigate the influence of the beach profiles on the water surface elevation (η) and velocities (u).     

基于新型高频声学多普勒流速剖面仪的河口近底部边界层观测初探

河口物质输运、能量交换与底边界层内的水动力过程密切相关,底边界层参数(如切应力、拖曳系数)的确定至关重要。挪威Nortek公司生产的新型声学多普勒流速剖面仪AD2CP相比传统ADCP具有高频、低噪的优点,可用于高频(16Hz)流速剖面观测,而被广泛应用于底边界层观测的ADV只能测量单点高频流速。本文采用AD2CP在长江口南槽最大浑浊带区域进行座底式观测,并与同步近底部三脚架上ADV的观测结果进行对比。结果表明,使用AD2CP测得的近底部平均流速与ADV的测量结果吻合良好;使用惯性耗散法计算了底切应力,基于ADV的单点高频流速数据计算结果为2.16×10~(-2)～5.69×10~(-1)N/m~2,基于AD2CP的结果为2.09×10~(-2)～4.26×10~(-1)N/m~2,二者范围大致相当。在此基础上,基于AD2CP数据计算出摩阻流速为4.55×10~(-3)～2.06×10~(-2)m/s、底拖曳系数范围为1.84×10~(-4)～2.49×10~(-3),与ADV的计算结果基本一致。此外,由于AD2CP可以获得高频的流速剖面数据,优于单点ADV,具备观测近底部边界层参数和边界层内湍流剖面的潜力。     

Distribution characteristics of delta reservoirs reshaped by bottom currents: A case study from the second member of the Yinggehai Formation in the DF1-1 gas field,Yinggehai Basin,South China Sea

The Dongfang1-1 gas field (DF1-1) in the Yinggehai Basin is currently the largest offshore self-developed gas field in China and is rich in oil and gas resources. The second member of the Pliocene Yinggehai Formation (YGHF) is the main gas-producing formation and is composed of various sedimentary types; however, a clear understanding of the sedimentary types and development patterns is lacking. Here, typical lithofacies, logging facies and seismic facies types and characteristics of the YGHF are identified based on high-precision 3D seismic data combined with drilling, logging, analysis and testing data. Based on 3D seismic interpretation and attribute analysis, the origin of high-amplitude reflections is clarified, and the main types and evolution characteristics of sedimentary facies are identified. Taking gas formation upper II (IIU) as an example, the plane distribution of the delta front and bottom current channel is determined; finally, a comprehensive sedimentary model of the YGHF second member is established. This second member is a shallowly buried “bright spot” gas reservoir with weak compaction. The velocity of sandstone is slightly lower than that of mudstone, and the reflection has medium amplitude when there is no gas. The velocity of sandstone decreases considerably after gas accumulation, resulting in an increase in the wave impedance difference and high-amplitude (bright spot) reflection between sandstone and mudstone; the range of high amplitudes is consistent with that of gas-bearing traps. The distribution of gas reservoirs is obviously controlled by dome-shaped diapir structural traps, and diapir faults are channels through which natural gas from underlying Miocene source rocks can enter traps. The study area is a delta front deposit developed on a shallow sea shelf. The lithologies of the reservoir are mainly composed of very fine sand and coarse silt, and a variety of sedimentary structural types reflect a shallow sea delta environment; upward thickening funnel type, strong toothed bell type and toothed funnel type logging facies are developed. In total, 4 stages of delta front sand bodies (corresponding to progradational reflection seismic facies) derived from the Red River and Blue River in Vietnam have developed in the second member of the YGHF; these sand bodies are dated to 1.5 Ma and correspond to four gas formations. During sedimentation, many bottom current channels (corresponding to channel fill seismic facies) formed, which interacted with the superposed progradational reflections. When the provenance supply was strong in the northwest, the area was dominated by a large set of delta front deposits. In the period of relative sea level rise, surface bottom currents parallel to the coastline were dominant, and undercutting erosion was obvious, forming multistage superimposed erosion troughs. Three large bottom current channels that developed in the late sedimentary period of gas formation IIU are the most typical.