石岛地震台远震记录反演研究

利用石岛地震台的远震体波记录,采用旋转相关函数法和接收函数法分别反演了台站下方介质的各向异性特征和速度结构.(1)对震中距25°~35°且记录良好的5次地震的ScS震相,采用旋转相关函数法反演了岩石圈的剪切波分裂参数.对深源地震的反演结果表明,石岛地震台快波偏振方向为N94°E,这意味着西沙附近处于近东西向微偏南的拉张或地壳下方的地幔流方向为近东西微偏南,西沙地区地壳是过渡性的,其底部的驱动力主要来自与欧亚板块运动一致的物质流.快慢波时间延迟为1.3 s,估算各向异性层厚度为100 km左右.(2)对震中距20°~60°的9次远震P波波形三分向记录,采用接收函数法反演了地壳和上地幔的S波速度结构.反演结果表明,石岛地震台下方地壳分为3层:约5 km以上有一速度梯度带,S波速度从1.5 km/s逐渐增加到3.5 km/s,其间有若干小的分层;在5~16 km的平均速度为3.8 km/s左右,其间有若干小的分层;在16.0~26.5 km的速度为3.6 km/s左右,这是一个明显的低速层;莫霍面埋深为26.5 km,莫霍面以下平均速度为4.7 km/s,也有若干小的分层,尤其是在莫霍面之下有一个明显的低速层.根据转换波到时分析和速度剖面左右摆动现象,认为反演结果中的小分层可能是不真实的,但在16.0~26.5 km的低速层的真实程度还是较高的,表明下地壳具有一定的塑性.     

Hamiltonian description of shear and gravity shear waves in an ideal incompressible fluid

Methods of studying the dynamics of wave disturbances in st;ratified shear flows of an ideal incompressible fluid are considered. The equations governing the motions of interest represent Hamilton equations and are derived by writing the velocity field in terms of Clebsch potentials. Equations written in terms of semi-Lagrangian variables are integrodifferential equations, which make it possible to consider both continuous and discontinuous solutions, as well as the cases where the parameters of the undisturbed medium are step functions. Two dynamic systems are presented. The first, canonical system of equations is most suitable for describing gravity waves in a shear flow in the case where the undisturbed medium is characterized by sharp gradients of density and flow velocity. The simplest model in which disturbances obey this system of equations is the well-known Kelvin-Helmholtz model. The second dynamic system describes, in particular, gravity-shear waves and, in the case of a homogeneous medium, shear waves in a two-dimensional flow. This system is most suitable for studying the dynamics of disturbances in models with sharp gradients of vorticity. On the basis of the approach developed in this study, the problem of the dynamics of disturbances in a flow with a continuous distribution of vorticity in a finite-thickness layer is solved. If the thickness of this layer is small compared to the characteristic wavelength and the gradient of the undisturbed vorticity in this layer is large, the solution has the form of a mode whose frequency is close to the frequency of the shear wave on a vorticity jump that would be obtained by letting the layer’s thickness approach zero. The results obtained allow, in particular, the estimation of the range of validity of finite-layer approximations for models with smooth profiles of flow and density. In addition, these results can be interpreted as the basis for the development of nonlinear aspects of the theory of hydrodynamic stability.     

The effects of a porous-elastic seabed on interfacial wave propagation

A theoretical model for the decay of progressive interfacial gravity waves propagating above a porous bed is developed assuming potential flow in a two-layer system with a free surface and a sharp interface. A new wave dispersion relation for two-layer flow above a quasi-static porous seabed is derived and investigated. The solutions for the nonlinear wave profile are derived using a perturbation method and the effects of geometric and flow parameters including bed characteristics, depth ratios and the densities of the two fluids are studied and discussed. Comparisons with existing analytical solutions for viscous interfacial wave attenuation over a rigid bed demonstrate the relative importance of the porous bed as a mechanism for wave decay. It is shown that the influence of a porous seabed on wave propagation is significant when the depth of the lower layer, normalised by the wavenumber, is less than π.     

Modeling wave�Ccurrent bottom boundary layers beneath shoaling and breaking waves

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.     

Longitudinal dispersion in wave-current-vegetation flow

The flow, turbulence, and longitudinal dispersion in wave-current flow through submerged vegetation are experimentally examined. Laboratory experiments are carried out by superimposing progressive waves on a steady flow through simulated submerged vegetation. The resultant wave-current-vegetation interaction shows strong interface shear with increase in the velocity due to the wave-induced drift. The increase in turbulence in the region of vegetation is found to be about twice higher than in the no-wave case due to the additional mixing by wave motions. Solute experiments are conducted to quantify the wave-current-vegetation longitudinal dispersion coefficient (WCVLDC) by the routing method and by defining length and velocity scales for the wave-current-vegetation flow. An empirical expression for the WCVLDC is proposed. Although the increase in vertical diffusivity is observed as compared with bare-bed channels, the shear effect is stronger, which increases the value of the WCVLDC. The study can be a guideline to understand the combined hydrodynamics of waves, current, and vegetation and quantify the longitudinal dispersion therein. Published in Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 50–67, January–February, 2009.     

Second-order random interfacial wave solutions for two-layer fluid with a free surface

1 Introduction Interfacial waves travelling along the interface between two fluids of different densities can be often observed in subsurface layers of the ocean since the upper subsurface layer is warmer over much of the o- cean (Umeyama, 2002). They are…     

Mass transport in a two-layer wave boundary layer

The transport of a chemical species under the pure action of surface progressive waves in the benthic boundary layer which is loaded with dense suspended sediments is studied theoretically. The flow structure of the boundary layer is approximated by that of a two-layer Stokes boundary layer with a sharp interface between clear water and a heavy fluid. The simplest model of constant eddy diffusivities is adopted and the exchange of matter with the bed is ignored. For a thin layer of heavy fluid, whose thickness is comparable to the surface wave amplitude and the Stokes boundary layer thickness, effective transport equations are deduced using an averaging technique based on the method of homogenization. The effective advection velocity is found to be equal to the depth-averaged mass transport velocity, while the dispersion coefficient can be shown to be positive definite. Explicit expressions for the transport coefficients are obtained as functions of fluid properties and flow kinematics. Physical discussions on their relations are also presented.     

Inversion of teleseismic waves at Shidao Seismographic Station

1 IntroductionThe temporary Shidao seismographic station,the farthest one from China s Mainland (except Tai-wan Province) supported by a national fundamentalresearch project for the study of the evolution ofcontinental margin, is located at Shidao island(…     

Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid

The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered.     

Numerical simulation of wave-induced laminar boundary layers

The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.     

Flow under standing waves: Part 1. Shear stress distribution,energy flux and steady streaming

The conditions for energy flux, momentum flux and the resulting streaming velocity are analysed for standing waves formed in front of a fully reflecting wall. The exchange of energy between the outer wave motion and the near bed oscillatory boundary layer is considered, determining the horizontal energy flux inside and outside the boundary layer. The momentum balance, the mean shear stress and the resulting time averaged streaming velocities are determined. For a laminar bed boundary layer the analysis of the wave drift gives results similar to the original work of Longuet–Higgins from 1953. The work is extended to turbulent bed boundary layers by application of a numerical model. The similarities and differences between laminar and turbulent flow conditions are discussed, and quantitative results for the magnitude of the mean shear stress and drift velocity are presented. Full two-dimensional simulations of standing waves have also been made by application of a general purpose Navier–Stokes solver. The results agree well with those obtained by the boundary layer analysis. Wave reflection from a plane sloping wall is also investigated by using the same numerical model and by physical laboratory experiments. The phase shift of the reflected wave train is compared with theoretical and empirical models.     

规则波下刚性植物根茎对边界层最大剪切力特性影响研究

基于考虑根茎影响的近岸植物消波实验,对边界层的最大剪切力特性进行了研究。利用前人提出的规则波下含植物水流的边界层流速计算公式,探究了单独根和根茎组合两种植物模型的边界层最大剪切力特性,分析了两种模型的剪切力的沿程变化、植物对剪切力衰减特性的影响,拟合了衰减系数的公式。研究表明,波浪在通过植物带时,剪切力会出现一定幅度增大,随后逐渐降低。植物对剪切力的消减效果随入射波高的增大而增大,且茎有助于根群对边界层最大剪切力的消减作用,其消减系数的范围为0.06~0.61,拟合的公式更加适用于水深较浅的情况。     

拉格朗日描述下三层流体系统中界面内波的三阶渐近解

在流体力学中，描述流体运动有Lagrange方法和Euler方法.Euler方法是通过观测通过空间各固定位置点处流体质点的运动行为来描述流体运动规律，而Lagrange方法是跟踪各个流体质点，通过观测它们在时空运动中所走过的路径来描述流体的运动规律.在数学处理上，Euler方法较Lagrange方法简单，但Lagrange方法可以完全描述流体运动的整个流场的所有特性，而Euler方法却无法描述每个流体质点的运动轨迹.本文，我们研究具有刚性边界的三层流体系统中的界面内波，其中上层流体的密度比下层流体的密度大.通过在界面处引入朗格朗日匹配条件并使用微扰法得到了拉格朗日描述下的界面内波的一阶解、二阶解及三阶解，给出了质量输运速度、波频率、平均水平和质点运动轨迹的解.结果表明对于质量输运速度、波频率、平均水平和质点运动轨迹在界面处会有不连续性，但是我们发现在满足一定的三层流体水深比和密度比条件时这种不连续性将会消失.     

实验室造波条件对内孤立波发展影响的直接数值模拟

内孤立波具有振幅尺度大、能量集中的特点,其引起流场和密度场的迅速变化可能对海洋工程结构物以及水下潜体造成严重威胁。因此研究不同造波条件下生成的内孤立波运动的流场特征具有重要的学术意义和实际应用价值。采用直接数值模拟方法和给定的初始密度场密度跃迁函数,对重力塌陷激发内孤立波的运动过程进行研究,探讨了不同造波条件下,激发产生的内孤立波波型、涡度、振幅和水平速度等流场特征。结果表明:(1)直接模拟数值方法能够模拟内孤立波传播过程中的密度界面波型反转现象;(2)从定性和定量的角度,证实了不稳定内孤立波传播过程中存在能量的向后传递;(3)对于相同的台阶深度(水闸两侧初始密度界面的高度差),初始涡流保持相同,但是随着上下层水深比的减小,其强度下降显著;(4)台阶深度对初始涡流的垂直结构的影响要大于上下层水深比,且台阶深度对内孤立波的振幅、水平速度的影响显著。     

Sand transport under combined current and wave conditions: A semi-unsteady,practical model

For the general purposes of morphodynamic computations in coastal zones, simple formula-based models are usually employed to evaluate sediment transport. Sediment transport rates are computed as a function of the bottom shear stress or the near bed flow velocity and it is generally assumed that the sediment particles react immediately to changes in flow conditions. It has been recognized, through recent laboratory experiments in both rippled and plane bed sheet flow conditions that sediment reacts to the flow in a complex manner, involving non-steady processes resulting from memory and settling/entrainment delay effects. These processes may be important in the cross-shore direction, where sediment transport is mainly caused by the oscillatory motions induced by surface short gravity waves.The aim of the present work is to develop a semi-unsteady, practical model, to predict the total (bed load and suspended load) sediment transport rates in wave or combined wave-current flow conditions that are characteristic of the coastal zone. The unsteady effects are reproduced indirectly by taking into account the delayed settling of sediment particles. The net sediment transport rates are computed from the total bottom shear stress and the model takes into account the velocity and acceleration asymmetries of the waves as they propagate towards the shore.A comparison has been carried out between the computed net sediment transport rates with a large data set of experimental results for different flow conditions (wave-current flows, purely oscillatory flow, skewed waves and steady currents) in different regimes (plane bed and rippled bed) with fine, medium and coarse uniform sand. The numerical results obtained are reasonably accurate within a factor of 2. Based on this analysis, the limits and validity of the present formulation are discussed.     

Strong near-inertial oscillations in geostrophic shear in the northern South China Sea

With observational data from three Acoustic Doppler Current Profiler (ADCP) moorings, we detected strong near-inertial oscillations (NIO) in the continental shelf region of the northern South China Sea in July 2008. The amplitude of the near-inertial current velocity is much greater than that of diurnal and semi-diurnal tides. The power of the NIOs is strongest in the intermediate layer, relatively weak in the surface layer, and insignificant in the near-bottom layer. The spectral analysis indicates that the NIOs have a peak frequency of 0.0307 cph, which is 2% lower than the local inertial frequency, i.e., a red-shift. The near-inertial wave has an upward vertical phase velocity, which involves a downward group velocity and energy flux. The estimated vertical phase velocity is about 43 m day⁻¹, corresponding to a vertical wave length of about 58 m. The horizontal scale of the NIOs is at least hundreds of kilometers. This NIO event lasted for about 15 days after a typhoon’s passage. Given the northeastward background flow with significant horizontal shear, both Doppler shift and shear flow modulation mechanisms may be responsible for the red-shift of the observed NIOs. For the shear flow mechanism, the observed negative background vorticity and the corresponding effective Coriolis frequency reduce the lower limit of admissible frequency band for the NIOs, causing the red-shift. Meanwhile, the mooring area with the broadened frequency band acts as a wave-guide. The trapping and amplification effects lead to the relatively long sustaining period of the observed NIOs.     

The “slip law” of the free surface

A “slip law” connects the excess velocity or “slip” of a wind-blown water surface, relative to the motion in the middle of the mixed layer, to the wind stress, the wind-wave field, and buoyancy flux. An inner layer-outer layer model of the turbulent shear flow in the mixed layer is appropriate, as for a turbulent boundary layer or Ekman layer over a solid surface, allowing, however, for turbulent kinetic energy transfer from the air-side via breaking waves, and for Stokes drift. Asymptotic matching of the velocity distributions in inner and outer portions of the mixed layer yields a slip law of logarithmic form, akin to the drag law of a turbulent boundary layer. The dominant independent variable is the ratio of water-side roughness length to mixed layer depth or turbulent Ekman depth. Convection due to surface cooling is also an important influence, reducing surface slip. Water-side roughness length is a wind-wave property, varying with wind speed similarly to air-side roughness. Slip velocity is typically 20 times water-side friction velocity or 3% of wind speed, varying within a range of about 2 to 4.5%. A linearized model of turbulent kinetic energy distribution shows much higher values near the surface than in a wall layer. Nondimensional dissipation peaks at a value of about eight, a short distance below the surface.     

Forced convection accompanying wind waves

Wind-wave tunnel experiments reveal, by use of techniques of the flow visualization, that wind waves are accompanied by the wind drift surface current with large velocity shear and with horizontal variation of velocity relative to the wave profile. The surface current converges from the crest to a little leeward face of the crest, making a downward flow there, even though the wave is not breaking. Namely, wind waves are accompanied by forced convections relative to the crests of the waves. Since the location of the convergence and the downward flow travels on the water surface as the crest of the wave propagates, the motion as a whole is characterized by turbulent structure as well as by the nature of water-surface waves. In this meaning, the term of real wind waves is proposed in contrast with ordinary water waves. The study of real wind waves will be essential in future development of the study of wind waves.