Numerical analysis of the transformation of tsunami waves in the south crimea shelf area

The paper analyses the transformation of tsunami-type solitary waves, propagating from the abyssal part of the Black Sea towards its shelf zone. The study is performed by solving numerically unidimensional non-linear equations for non-dispersive long waves, using the finite-difference slope and shelf, with the full wave reflection prescribed at a 10 m depth contour. The non-linearity of the process is shown to throughly impact the reflection of waves by the shore and the shape of the reflected wave. Tsunami wave heights have been seen to increase by several times in the Black sea shelf area. Translated by Vladimir A. Puchkin.     

Statistical estimates of characteristics of long-wave run-up on a beach

A run-up of irregular long sea waves on a beach with a constant slope is studied within the framework of the nonlinear shallow-water theory. This problem was solved earlier for deterministic waves, both periodic and pulse ones, using the approach based on the Legendre transform. Within this approach, it is possible to get an exact solution for the displacement of a moving shoreline in the case of irregular-wave run-up as well. It is used to determine statistical moments of run-up characteristics. It is shown that nonlinearity in a run-up wave does not affect the velocity moments of the shoreline motion but influences the moments of mobile shoreline displacement. In particular, the randomness of a wave field yields an increase in the average water level on the shore and decrease in standard deviation. The asymmetry calculated through the third moment is positive and increases with the amplitude growth. The kurtosis calculated through the fourth moment turns out to be positive at small amplitudes and negative at large ones. All this points to the advantage of the wave run-up on the shore as compared to a backwash at least for small-amplitude waves, even if an incident wave is a Gaussian stationary process with a zero mean. The probability of wave breaking during run-up and the applicability limits for the derived equations are discussed.     

Analysis of dune erosion processes in large-scale flume experiments

Large-scale physical model tests were conducted with different wave periods to examine the physical processes driving dune erosion. The model tests have been carried out in a flume (2DV) with a sandy dune exposed to extreme surge and wave conditions [Van Gent, M.R.A., Van Thiel de Vries, J.S.M., Coeveld, E.M., De Vroeg, J.H. and Van de Graaff, J., 2008. Large-scale dune erosion tests to study the effect of wave periods. Coastal Engineering. doi:10.1016/j.coastaleng.2008.04.003.]. Detailed measurements in time and space of water pressure, flow velocities and sediment concentrations were performed in the near shore area. The data revealed that both short- and long waves are important to inner surf hydrodynamics. Depth averaged flows are directed offshore and increase towards the shore line. The corresponding mean sediment concentrations rise sharply towards the dune face (up to 50 g/l near the bed). The strong increase in the mean sediment concentration towards the dune face correlates well with the maximum wave surface slope which in turn is coupled to both the pressure gradient and the near-bed wave-breaking induced turbulence. Analysis shows that the pressure gradient is only partially coupled to the flow acceleration suggesting that the latter cannot always be used as a proxy for the first. Weak correlation is obtained with the near-bed flows related to the bed shear stress. Tests with a larger wave period resulted in a larger dune erosion volume. During these tests more wave energy (combined incident and infragravity waves) reached the dune face, but more importantly, this wave energy is dissipated by fewer waves resulting in more intense wave breakers and steeper wave fronts. It is therefore expected that the wave-breaking induced near-bed turbulence increases resulting in significantly higher (O(100%)) mean sediment concentrations. In addition the mean flow velocities are comparable, yielding a substantially larger offshore directed sediment transport capacity. This increase in offshore directed transport is only partially compensated by a concurrent increase in the wave related onshore transport capacity associated with intrawave processes, resulting in a net increase in the dune erosion rate.     

Numerical study of pollutant movement in waves and wave-induced long-shore currents in surf zone

Water waves, wave-induced long-shore currents and movement of pollutants in waves and currents have been numerically studied based on the hyperbolic mild-slope equation, the shallow water equation , as well as the pollutant movement equation, and the numerical results have also been validated by experimental data. It is shown that the long-shore current velocity and wave set-up increase with the increasing incident wave amplitude and slope steepness of the shore plane ; the wave set-up increases with the in- creasing incident wave period;and the pollutant morement proceeds more quiekly with the increasing incident wave amplitude and slope steepness of the shore palane. In surf zones, the long-shore currents induced by the inclined incident waves have effectively affected the pollutant movement.     

Sand wave deposition in the Taiwan Shoal of China

The Taiwan Shoal is the convex terrain in the southern Taiwan Strait, the largest strait in China. In 2006 and 2007, 21 samples and more than 200-km sub-bottom data as well as 80-km near shore side-scan sonar data were gotten, which gave an initial image of the boundaries of the Taiwan Shoal and revealed the internal structure of the sand waves in this area. The results showed that the major component of the sediment samples was sand, and sand waves occurred everywhere in this area, which closely followed the range of the Taiwan Shoal as we know. The western boundary of the Taiwan Shoal thus reaches the 30 m isobaths near the shore, and as a result, its area potentially covers approximately 12 800-14 770 km². The sand waves have different shapes under the complex ocean dynamics, and the height of sand waves in the near shore is usually smaller than that in the Taiwan Shoal. The number of sand waves ranged from 1-5 per kilometer, with more waves in the isobath-intensive area, suggesting the importance of topography for the formation of sand waves. The stratigraphic structure under the seabed has parallel bedding or cross bedding, and large dipping groove bedding can be seen locally in different parts, which may be the result of terrestrial deposition since the Late Pleistocene.     

The role of bottom friction in models of nonbreaking tsunami wave runup on the shore

The role of bottom friction in the runup of nonbreaking long waves on the shore is analyzed. The case of the normal incidence of monochromatic waves is considered. The relief of the model region consists of an even horizontal bottom area conjugated with a flat slope. The energy dissipation is estimated as the work of bottom friction forces over the wave field obtained using the known analytical solution based on the Carrier-Greenspan transforms. Estimates of energy losses for waves whose periods are typical for tsunami waves have been obtained. The energy dissipation is shown to be not concentrated in the shore line area as a rule. The question about the practicability of using partially reflecting boundary conditions on the coast to take into account the bottom friction in large-scale models of tsunami propagation is considered.     

辽东湾觉华岛附近海域海底地形地貌及沉积物分布特征分析

为对辽东湾觉华岛附近海域海底工程地质环境进行系统评估,利用高分辨海底声学探测设备获取调查海区的精密水深地形数据,利用筛析法、激光粒度仪实验法确定沉积物类型及粒度参数特征,最终综合分析得到研究区海底地形地貌及沉积物分布特征。研究发现,目标海域测量水深介于4~22m之间,平均水深15m左右,海底地形平坦,整体表现为平缓的近岸缓坡,地貌以近岸粉砂淤泥质浅滩地貌为主,局部发育微型海底沙波;海底浅地层第一声学反射界面清楚连续,可全区追踪,穿透深度0.5~5m不等,沉积物厚度相对稳定;表层沉积物中值粒径普遍较小,沉积物类型东区以粉砂和砂质粉砂为主,西区以砂质粉砂为主;表层沉积物组分和粒度参数的空间变化规律较为复杂,分析认为其主要受到沉积物物源以及辽东湾内往复流、沿岸流的影响。。     

长江口及其邻近海区环流和温、盐结构动力学研究IV 盐度结构

盐度的数值模拟结果表明: 一年四季长江口及其邻近海区的盐度分布均为近岸低, 外海高,近岸与外海盐差大。冬季近岸和外海的上层盐度呈垂直均匀分布, 陡坡及外海的底层出现层化; 近岸特别是长江口及其以南近岸盐度的水平变化显著, 外海变化缓慢。春季在长江口以北, 近岸至外海的表层至近底层盐度呈垂直均匀分布, 近岸至外海的底层存在一个向北延伸的盐舌; 长江口及其以南近岸和外海的表层至次表层盐度呈垂直均匀分布, 在近岸稍远的表层至次表层形成盐跃层, 其强度自近岸至外海和自表层至底层逐渐减弱; 在陡坡区的底层盐度几乎呈均匀分布, 并保持高盐特征。夏季除长江口及其以南近岸浅水区盐度呈垂直均匀分布外, 其它区域盐度均出现剧烈分层, 在长江冲淡水区形成强盐跃层, 其强度自表层至底层迅速减弱, 陡坡至外海的底层盐度大致呈均匀分布且保持高盐特征。秋季长江口以北近岸浅水区表层盐度低且出现层化, 表层以下盐度高且呈垂直均匀分布; 近岸以远自表层至底层呈垂直均匀分布, 在外海上层盐度低且呈垂直均匀分布, 而底层盐度高并出现分层;长江口及其以南近岸浅水区盐度呈垂直均匀分布, 陡坡区出现层化, 其盐度为表层低, 底层高; 层化自表层至底层逐渐增强, 并随陡坡至外海的减弱, 上层又逐渐变为垂直均匀分布。     

Reflection of long internal waves of small amplitudes from an underwater slope

The dynamics of long waves in the vicinity of a transition point of a two-layer flow into a single-layer one is studied within the linear theory of shallow water. The analogy between this problem and the classical problem of surface wave runup on the shore is shown. Conditions for breaking internal waves on a slope are discussed.     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

近岸沿岸流及污染物运动的数值模拟

基于双曲型缓坡方程和近岸浅水方程对近岸波浪斜向入射破碎所生成的沿岸流及污染物在沿岸波流作用下的运动进行了数值模拟,并对数值模拟结果进行了验证分析。数值模拟结果表明,在相近工况参数下,随着入射波高的增大,沿岸流流速和平均水面升高值均明显增大;随着岸坡坡度的增加,沿岸流流速和平均水面升高值明显增大;随着入射波浪周期的增大,平均水面升高值明显增大。在沿岸缓坡区域,由斜向入射波浪破碎所产生的沿岸流对污染物的运动起着不可忽略的影响。     

Experimental study of long wave generation on sloping bottoms

Low-frequency waves generated on steep (1:10) and mild (1:40) slopes by six series of bichromatic wave groups are studied experimentally. The shorelines for both slopes are replaced by horizontal reaches of small depth. This reduces the reflection of long waves near the shoreline significantly, which for the first time makes possible the explicit observation of outgoing breakpoint forced long waves. The breakpoint and released bound long wave mechanisms on the different slopes are compared. Generally, the breakpoint forced long waves dominate the low-frequency wave field on the steep slope, while the released bound long waves are found to be more significant on the mild slope. Two parameters indexing the effectiveness of the breakpoint mechanism are compared and the normalized slope tends to give more realistic results. Shoaling of bound long waves is analyzed and the shallow-water equilibrium limit ~ h^−5/2 exhibits a good prediction of the variation of the bound long waves on both slopes.     

Laboratory study of random wave slamming on a piled wharf with different shore connecting structures

Impact pressures from random waves on the underside of a wharf deck were measured in a laboratory wave channel. Three different types of shore connecting structures were considered: open-piled, permeable slope and impermeable slope wharves. The experiments were carried out with significant wave heights ranging from 10 cm to 20 cm, spectral peak periods ranging from 1.0 s to 2.0 s, and the relative clearance of the model with respect to significant wave heights ranging from 0.1 to 0.4. The characteristics of the wave impact pressures for different shore connecting conditions are investigated, and their statistical distributions along the underside of the models are also determined. Experimental results indicate that the impact pressures depend on parameters such as the significant wave height, the spectral peak period, and the relative length and clearance of the model.     

Topographically trapped waves over the continental shelf and slope

General characteristics of topographically trapped subinertia waves are discussed from the viewpoint of an eigenvalue problem and ray theory. Special attention is paid to the slope parameterS(x) (=(dh/dx)/h, wherex denotes the coordinate perpendicular to the shoreline, increasing seaward, andh(x) is the depth) which is a measure of the strength of the restoring force of the waves. Three cases for theS distribution are considered, in whichS is assumed to be positive at the coast and to tend to zero far from the coast. The first is whereS(x) decreases monotonically towards the open ocean. It is found in this case that waves are trapped near the coast. The second is whereS(x) does not decrease monotonically, but has a maximum. It is concluded that this case may contain two types of waves, i.e., those trapped near the coast and those trapped near the maximum, and the dispersion curves corresponding to different types may nearly intersect, namely, result in “kissing”. The third is whereS(x) has a negative region (corresponding to the presence of a trench). It is found in this case that an infinite sequence of waves is trapped in the negativeS region which propagate with the coast to their left (right) in the northern (southern) hemisphere besides the waves trapped near the coast. The topography in the second case corresponds to a typical continental shelf and a typical continental slope. It is shown by model calculation that trapped waves are present over the continental slope as well as over the continental shelf. Almost the same results are obtained for superinertia waves ifS is replaced by 1/h which is a measure of the restoring force of superinertia waves.     

Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves

In this paper, the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed of 1/15 uniform slope, is experimentally investigated. Flow visualization technique with thin-layered fluorescent dye was first used to observe the variation of the flow structure, and a laser Doppler velocimeter was then employed to measure the horizontal velocity, U.The bottom boundary layer flow is found to be laminar except within a small region near the breaking point. The vertical distribution of the phase-averaged velocity U at each phase is non-uniform, which is directly affected by the mean velocity, . The magnitude of increases from zero at the bottom to a local positive maximum at about z/δ2.02.5 (where z is the height above the sloping bottom and δ is the Stokes layer thickness), then decreases gradually to zero at z/δ6.07.0 approximately, and finally becomes negative as z/δ increases further. Moreover, as waves propagate towards shallower water, the rate of increase in the maximum onshore oscillating velocity component is greater than that of the offshore counterpart except near the breaking point. The free stream velocities in the profiles of the maximum onshore and offshore oscillating velocity components, and are found to appear at z/δ≥6.0. This implies that, if the Stokes layer thickness is used as a length scale, the non-dimensionalized boundary layer thickness remains constant in the pre-breaking zone. Although is greater than and the asymmetry of the maximum free stream velocities (i.e. ) increases with decrease of water depth, a universal similar profile can be established by plotting z/δ versus ( ) or ( ). The final non-dimensional profile is symmetric and unique for the distributions of the maximum onshore and offshore oscillating velocity components within the bottom boundary layer, which are induced by nonlinear, asymmetric shoaling waves crossing the pre-breaking zone.     

A General Linear Wave Theory for Water Waves Propagating over Uneven Porous Bottoms

Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green‘s scond identity. This theory can be reduced to a number of the most typical mild-slope equations curreutly in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.     

Shoaling Surface Gravity Waves Cause a Force and a Torque on the Bottom

Freely propagating surface gravity waves are observed to slow down and to stop at a beach when the bottom has a relatively gentle upward slope toward the shore and the frequency range of the waves covers the most energetic wind waves (sea and swell). Essentially no wave reflection can be seen and the measured reflected energy is very small compared to that transmitted shoreward. One consequence of this is that the flux of the wave’s linear momentum decreases in the direction of wave propagation, which is equivalent to a time rate of change of the momentum. It takes a force to cause the time rate of change of the momentum. Therefore, the bottom exerts a force on the waves in order to decrease the momentum flux. By Newton’s third law (action equals reaction) the waves then impart an equal but opposite force to the bottom. In shallow (but finite) water depths the wave force per unit bottom area is calculated, for normal angle of incidence to the beach, to be directly proportional to the square of the wave amplitude and to the bottom slope and inversely proportional to the mean depth; it is independent of the wave frequency. Constants of proportionality are: 1/4, the fluid density and the acceleration of gravity. Swell attenuation near coasts and some characteristics of sand movement in the near-shore region are not inconsistent with the algebraic structure of the wave force formula. Since the force has a depth variation which is significantly faster than that of the dimensions of the particle orbits in the vertical direction, the bottom induces a torque on the fluid particles that decreases the angular momentum flux of the waves. By an extension of Newton’s third law, the waves also exert an equal but opposite torque on the bottom. And because the bottom force on the waves exists over a horizontal distance, it does work on the waves and decreases their energy flux. Thus, theoretically, the fluxes of energy, angular and linear momentum are not conserved for shoaling surface gravity waves. Mass flux, associated with the Stokes drift, is assumed to be conserved, and the wave frequency is constant for a steady medium.     

Seismic amplifications from offshore to shore

The objective of this study is to determine numerical estimations of seismic amplifications of waves traveling from offshore to shore considering the effect of sea floor configurations. According to the Boundary Element Method, boundary elements were used to irradiate waves and density force can be determined for each element. From this hypothesis, Huygens’ Principle is implemented since diffracted waves are constructed at the boundary from which they are radiated and this is equivalent to Somigliana's theorem. Application of boundary conditions leads to determine a system of integral equations of Fredholm type of second kind, which is solved by the Gaussian method. Various numerical models were analyzed, a first one was used to validate the proposed formulation and some other models were used to show various ideal sea floor configurations to estimate seismic amplifications. Once the formulation was validated, basic slope configurations were studied for estimating spectra of seismic amplifications for various sea floor materials. In general terms, compressional waves (P-waves) can produce seismic amplifications of the incident wave in the order of 2–5. On the other hand, distortional waves (S-waves) can produce amplifications up to 5.5 times the incident wave. A relevant finding is that the highest seismic amplifications due to an offshore earthquake are always located near the shore-line and not offshore despite the seafloor configuration.     

琼州海峡白沙门海滩冲淤的遥感分析

琼州海峡白沙门海滩是海口市重要旅游资源,历史研究表明自20世纪60年代以来其一直处于侵蚀退化状态。本文选取1994—2015年的19景Landsat遥感影像提取白沙门海滩水边线并计算海滩坡度,分析海滩冲淤,结果表明:1994—2008年海滩处于冲刷状态,高潮位的水边线平均向岸回退了104.71 m, 低潮位的水边线平均向岸回退了95.49 m,但是2000年附近时段的人工补沙弥补了海滩侵蚀退化;2008—2015年海滩转为淤积状态,高潮位的水边线平均向海前进了34.17 m,低潮位的水边线平均向海前进了25.52 m,海滩淤积可能是海滩东侧的新埠岛围填海工程造成的。     

An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion

In the present paper, by introducing the effective wave elevation, we transform the extended ellip- tic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)’s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly vary- ing topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.