A coupled-mode model for the refraction–diffraction of linear waves over steep three-dimensional bathymetry

A consistent coupled-mode model recently developed by Athanassoulis and Belibassakis [1], is generalized in 2+1 dimensions and applied to the diffraction of small-amplitude water waves from localized three-dimensional scatterers lying over a parallel-contour bathymetry. The wave field is decomposed into an incident field, carrying out the effects of the background bathymetry, and a diffraction field, with forcing restricted on the surface of the localized scatterer(s). The vertical distribution of the wave potential is represented by a uniformly convergent local-mode series containing, except of the ususal propagating and evanescent modes, an additional mode, accounting for the sloping bottom boundary condition. By applying a variational principle, the problem is reduced to a coupled-mode system of differential equations in the horizontal space. To treat the unbounded domain, the Berenger perfectly matched layer model is optimized and used as an absorbing boundary condition. Computed results are compared with other simpler models and verified against experimental data. The inclusion of the sloping-bottom mode in the representation substantially accelerates its convergence, and thus, a few modes are enough to obtain accurately the wave potential and velocity up to and including the boundaries, even in steep bathymetry regions. The present method provides high-quality information concerning the pressure and the tangential velocity at the bottom, useful for the study of oscillating bottom boundary layer, sea-bed movement and sediment transport studies.     

黄河三角洲海底土波致再悬浮研究

在现代黄河三角洲采集土样,制备室内水槽试验的底床,施加波浪作用,观测波致悬沙含量的变化规律,分析不同波高、作用时间对单位面积底床再悬浮量的影响,及波浪停止作用后悬浮泥沙的静水沉降规律。研究发现,在水深一定条件下底床再悬浮量呈现随波高增大而增大的特性,两者线性拟合的相关性很好;在一定波高的波浪连续作用下,约5 000~6 000个波周期底床再悬浮过程完成;在波浪作用初始阶段底层悬沙含量与中上层的相差很大,悬沙含量垂线结构呈斜线型,稳定阶段的悬沙浓度垂向结构呈准直线型,底层与表层含沙量比值为0.98~1.25,整个水层含量分布均匀;静水沉降过程中当悬沙含量大于1 g/dm3,悬沙含量(SSC)呈现出随时间指数衰减的规律,悬沙浓度与沉降通量呈线性关系。研究结果对认识黄河水下三角洲泥沙运移规律具有一定的科学意义。     

渤海中部海底恒温层温度及泥温相位随深度变化特征

利用渤海中部两点一年中４个季节泥温观测资料，近似确定两测点海底恒温层泥温分别为１１．０℃和１１．７℃。认国泥温随深度变化可视为一垂向波－泥温波，并利用这一概念分析了泥温相位随深度变化特征，８＾＃，Ａ（Ｂ）平台测点泥温波波长分别为ｌ８＝８ｍ和ｌＡ（Ｂ）＝１０ｍ。研究建议，以０．５ｍ处多年泥温平均值作为海底恒温层温度。     

An environmental assessment in the Strait of Sicily: measurementand analysis techniques for determining bottom and oceanographicproperties

In October 1997, the EnVerse 97 shallow-water acoustic experiments were jointly conducted by SACLANT Centre, TNO-FEL, and DERA off the coast of Sicily, Italy. The primary goal of the experiments was to determine the sea-bed properties through inversion of acoustic data. Using a towed source, the inversion method is tested at different source/receiver separations in an area with a range-dependent bottom. The sources transmitted over a broadband of frequencies (90-600 Hz) and the signals were measured on a vertical array of hydrophones. The acoustic data were continuously collected as the range between the source and receiving array varied from 0.5 to 6 km. An extensive seismic survey was conducted along the track providing supporting information about the layered structure of the bottom as well as layer compressional sound speeds. The oceanic conditions were assessed using current meters, satellite remote sensing, wave height measurements, and casts for determining conductivity and temperature as a function of water depth. Geoacoustic inversion results taken at different source/receiver ranges show sea-bed properties consistent with the range-dependent features observed in the seismic survey data. These results indicate that shallow-water bottom properties may be estimated over large areas using a towed source fixed receiver configuration     

Hybrid Surface Waves from a Harmonic Perturbation Source

The problem of constructing uniform asymptotics of surface perturbations of far fields from a localized harmonic source in the flow of a heavy homogeneous fluid of infinite depth is considered. It is shown that the wave pattern of generated far fields at specific parameters is a system of hybrid wave disturbances that simultaneously possesses the properties of waves of two types: annular (transverse) and wedgeshaped (longitudinal) waves. The properties of the phase structure and wave fronts of the generated fields are studied. Uniform asymptotics of the solutions describing hybrid surface wave disturbances far from a harmonic source are constructed.     

Experimental study of the fine structure of the wind field near a rough surface

The air-flow velocity field near the water surface is studied in the zone of wind-wave intensification. Caused by a periodic separation of eddies, a nonzero time-averaged value of the wind velocity in the near-water streamline is detected at the leading slope of the wave. The distribution of pressure along the wave with allowance for the vertical velocity shear and disturbances produced by eddies and a periodic deceleration of the viscous layer was calculated with the aid of the Cauchy-Lagrange integral. This procedure made it possible to calculate the growth rate of the wave amplitude, whose value was found to be close to its experimental value at the initial stage of acceleration.     

Approximate wave force analysis on rectangular caissons

An approximate analytical analysis is demonstrated in this research note to obtain the approximate wave forces on rectangular caissons fixed vertically on the sea-bed. A data plot has been depicted to show the effect of linear forces for the case of rectangular caissons and that for the case of square caissons.     

Investigation of conditions for the generation and propagation of low-frequency disturbances in the troposphere

Low-frequency disturbances responsible for the excitation of torsional oscillations—variations in the zonal mean flow intensity with a characteristic scale of 15–20 days—propagating along the meridian at mid and low latitudes of both hemispheres are investigated [1]. As data observed over the eastern parts of continents and the western parts of oceans are processed with the lag correlation statistics, traveling waves intersecting the eastern parts of continents from northwest to southeast and then returning to the north along the ocean coasts are identified. In this case, trains of anomalies oriented in the zonal direction periodically appear and are destructed in the western parts of continents. The simulation of the propagation of disturbances in the quasi-geostrophic approximation made it possible to explain the specific features of lag correlation statistics over continents by the dispersion of two-dimensional Rossby waves from traveling sources. The turnover of disturbances over Asia and wave trains to the west from the pole were reproduced. Torsional oscillations caused by the dispersion of two-dimensional Rossby waves have a characteristic form of inclined bands in the latitude-time diagram, whose steepness is controlled by the velocity of displacement of the vorticity source along the meridian.     

Wave pattern induced by a moving atmospheric pressure disturbance

A moving low atmospheric pressure is a main feature of tropical cyclones, which can induce a system of forced water waves and is an important factor that cause water level rise during a storm. A numerical model based on the nonlinear shallow water equations is applied to study the forced waves caused by an atmospheric pressure disturbance moving with a constant velocity over water surface. The effects of the moving speed, the spatial scale and the central pressure drop of the pressure disturbance are discussed. The results show that the wave pattern caused by a moving low-pressure is highly related with its moving speed. The wave pattern undergoes a great change as the moving speed approaches the wave velocity in shallow water. When the moving speed is less than the wave velocity, the distribution of water surface elevation is nearly the same as that of the pressure disturbance, and the maximum of the water surface elevation is located at the center of pressure. When the moving speed is larger than the wave velocity, a triangle shaped wave pattern is formed with a depression occurs in front of the pressure center, and the maximum of the water surface elevation lags behind the center of pressure. As the moving speed increases, the maximum of the water surface elevation firstly increases and then decreases, which reaches a peak when the moving speed is close to the wave velocity. The maximum of water surface elevation is approximately in proportion to the central pressure drop, and slightly affected by the spatial scale of pressure disturbance. Both the central pressure drop and the spatial scale of the pressure disturbance do not significantly affect the forced wave pattern. However, a clear difference can be noticed on the ratio of the maximum water surface elevation in moving pressure situation to that in static situation, when the moving speed is close to the wave velocity. A pressure disturbance with smaller spatial scale and smaller central pressure drop will give a larger ratio when the moving speed is close to the wave velocity.     

Froude-Krylov force coefficients for bodies of rectangular section in the vicinity of the free-surface and sea-bed

A two-dimensional linear diffraction solution for submerged bodies of rectangular section is utilized to calculate the Froude-Krylov force coefficients for the case when the body is located close to the free-surface or sea-bed. Numerical results are presented for the Froude-Krylov force coefficients for a range of wave and structural parameters. It is found that the force coefficients in these situations may be significantly different than those for the same body located away from these boundaries.     

Capillary-Gravitational Waves of Finite Amplitude on the Surface of a Homogeneous Liquid

The method of multiple scales is used to deduce equations for three nonlinear approximations of the capillary-gravitational disturbances of the free surface of a layer of a homogeneous liquid of constant depth. In these equations, the space-time variations of the wave profile in the expression for the velocity potential on the liquid surface are taken into account. On this basis, we construct asymptotic expansions up to the quantities of the third order of smallness for the velocity potential and elevations of the liquid surface induced by running periodic waves of finite amplitude. Furthermore, we analyze the dependences of the amplitude-phase characteristics of wave disturbances on the surface tension, depth of the liquid, and the length and steepness of waves of the first harmonic. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 25–34, September–October, 2005.     

Interaction of Surface Waves in a Basin with Floating Broken Ice

The multiscale method is used to obtain asymptotic expansions up to the quantities of the third order for the elevations of the surface of the basin and the velocity potential of motion of liquid particles in the wave disturbances formed in the process of nonlinear interaction of periodic running waves of the first and second harmonics in a homogeneous ideal incompressible liquid of constant finite depth covered with broken ice. The dependences of the amplitude-phase structure of disturbances on the ice thickness, depth of the basin, and the parameters of interacting harmonics are investigated. We estimate the error of evaluation of the characteristics of the formed vertical displacement of the surface of the basin and nonlinear mass transfer introduced by neglecting the curvature of the wave profile in the expression for the velocity potential in deducing the kinematic and dynamic surface boundary conditions for nonlinear approximations.     

Effect of dispersion on impulsive waves

The generation and propagation of surface waves resulting from suddenly created disturbances over water surfaces is investigated. The initial boundary conditions defining the disturbance are given either by a velocity of the free surface, an initial elevation of the free surface or a pressure impulsively applied on the free surface. It is shown that the corresponding three forms of solutions are related by a simple time derivative. Linear solutions are obtained in the cases where the wave motion is assumed to be nondispersive, mildly dispersive and fully dispersive, as well as in the case where the motion is given by the method of stationary phase. Criteria are established to indicate the limit of validity of each method.     

A study on kinematics characteristics of freak wave

Based on the 3rd-order Stokes wave theory, the speed of freak waves is formulated in terms of the period and the wave height. Finite modified wave steepness gives rise to a significant enhancement of the nonlinear contributions to the freak wave speed in comparison with the 3rd-order Stokes wave theory. For a fix modified wave steepness, the estimated amplification of the nonlinear contributions due to the deviation from the 3rd-order Stokes wave theory is 0.22～0.99. In addition, the velocity and acceleration fields are also documented in detail. In the present simulation, the horizontal velocities are smaller than the wave speed, and the freak wave exhibits a maximal horizontal velocity up to 37% of the wave speed and a maximal vertical acceleration up to about 20% of the gravitational acceleration.     

The Mathematical and Parameterized Expressions for Wave Induced Excess Flow of Momentum

Wave induced excess flow of momentum(WIEFM)is the averaged flow of momentum over a wave period due to wave presence,which may also be called 3-D radiation stress.In this paper,the 3-D current equations with WIEFM are derived from the averaged Navier-Stokes equations over a wave period,in which the velocity is separated into the large-scale background velocity,the wave particle velocity and the turbulent fluctuation velocity.A concept of wave fluctuating layer(WFL)is put forward,which is the vertical column from the wave trough to wave ridge.The mathematical expressions of WIEFM in WFL and below WFL are given separately.The parameterized expressions of WIEFM are set up according to the linear wave theory.The integration of WIEFM in the vertical direction equals the traditional radiation stress(namely 2-D radiation stress)given by Longuet-Higgins and Stewart.     

Wave Currents Generated by a Moving Load in a Liquid Covered with Ice

We study horizontal wave currents generated in a liquid of finite depth by a load of constant intensity moving over the floating ice cover and analyze the dependences of the space structure of the field of wave velocities on the characteristics of the ice cover and the velocity of motion of the load. It is shown that the velocity of wave currents caused by flexural waves can increase with the velocity of motion of the load, whereas the wave currents caused by the gravity waves decay monotonically. The ice compression increases the velocity of horizontal wave currents.     

Sediment macrobenthos off eastern Waiheke Island,Hauraki Gulf,New Zealand

Aspects of sea-bed structure and benthic-macroinvertebrate species composition, distribution, richness and diversity in coastal waters off eastern Waiheke Island, Hauraki Gulf, are reported. In contrast to the sole historical account of sea-bed community structure from this same region, no widely distributed assemblages of species are recognised throughout it; no two sites share the exact same complement of species; and almost all sites are less than 80% similar in their taxonomic composition, most considerably so. Species richness and diversity are reported to vary with substratum type and depth, and spatially; species occurring within muds are the least diverse and species rich, followed by those of muddy gravels, and then gravels; many taxa prove common to the three substratum types; and dominance of taxa is recognised to decrease with an increase in substratum complexity, from muds to gravels, and species richness. With the exception of invasive marine species, apparent changes in the composition of assemblages throughout this region over the eight-decade period that data span are considered artefacts of the way in which such assemblages were historically defined. We recommend historical accounts of sea-bed community distributions throughout Hauraki Gulf be interpreted with caution, especially when attempting to use such schematic depictions to determine whether changes have occurred in assemblage composition.     

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.     

浅化波浪层流边界层流速分布特性的数值分析

建立了同时考虑波致雷诺应力和时均水平压强梯度影响的二阶波浪边界层数学模型,模型计算得到的浅化波浪层流边界层内瞬时流速剖面、振荡速度幅值和时均流速剖面均与水槽实验数据吻合较好,在此基础上探讨了浅化波浪边界层流速分布特性及其影响机制。随着波浪的浅化变形,边界层内时均流速剖面"底部向岸、上部离岸"的变化特征越来越明显。这是二阶对流项引起的波致雷诺应力和离岸回流引起的时均水平压强梯度共同作用的结果,在床面附近由波致雷诺应力占主导作用并趋于引起向岸流动,在上部区域由时均水平压强梯度占主导作用并趋于引起离岸流动。