Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a twolayer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a flat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Ser. D, 47(12):1147-1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth''s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.     

风浪和海洋飞沫对海表面拖曳系数和风廓线的影响

基于埃克曼理论,本文将波致应力和飞沫应力引入到海-气边界层的界面应力中,来研究海表面风浪和海洋飞沫对海-气边界层动量交换的影响,并得到修改后的埃克曼模型的理论解。波致应力是由风浪谱和波增长函数估计,并得到在中低风速下,波致应力、飞沫应力与湍流应力相比,对海表面拖曳系数和风廓线的影响非常小。当风速高于25米/秒时,海洋飞沫通过飞沫应力对海-气界面应力的作用远高于波致应力,以至于波致应力可以忽略。海表面拖曳系数在高风速下,随着风速的增大而减小。通过采用风浪谱的不同波龄,得到海洋飞沫的产生会导致海-气边界层风速的增加。最后,理论解与现场的观察数据进行了对比。对比后的数据表明,在中高风速下,飞沫对海-气边界层的影响远大于表面风浪。     

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…     

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.     

Waves at the sea surface generated by a flow over an underwater obstacle

We study wave perturbations appearing at the surface of a two-layer fluid flowing around an underwater obstacle in the lower layer of the fluid. The obstacle is modeled as a point source. A class of asymptotic solutions was obtained that demonstrate that realistic conditions of the open sea and the given parameters of the source in the neighborhood of the source of hydrodynamic perturbations allow for the formation of two types of surface waves. The waves of the first type only slightly depend on the stratification, and, in the conditions of the real sea, they are almost not observed. The characteristics of the second type of waves were repeatedly recorded in field experiments during radar and optical monitoring of the sea surface.     

Laboratory model of the Obukhov geostrophic vortex

The results of laboratory modeling of geostrophic adjustment in a shallow-water layer in rotating paraboloid are presented. According to the Rossby-Obukhov theory, this process excites nonstationary wave and stationary vortex (geostrophic) components of motion in a rotating fluid. In our experiments, the wave and vortex components were excited by extracting a preliminarily imbedded hemisphere (which made the initial distribution of the depth of the fluid inhomogeneous) from the central area of a rotating vessel with a parabolic base. Under this excitation technique, a prominent cyclonic eddy is formed in the central portion; the structure of this eddy is satisfactorily described within the linear theory of adjustment. Along with the shallow-water experiments, the published experimental data on modeling geostrophic adjustment in a two-layer medium are analyzed. A simple analytic solution to the corresponding problem of the adjustment theory is obtained, and this solution agrees with the experiment.     

内孤立波波致流场数值模拟研究

基于KdV、mKdV理论,利用Fluent计算软件,采用"平板拍击"造波方法,进行内孤立波数值模拟,并与物理实验结果进行对比验证。利用数值模拟结果,分析内孤立波波致流场变化,结果表明:上下层流体中波致水平流速方向相反,均呈现先增加后减小的变化趋势,且波谷经过时刻流速最大;在波谷经过断面处,波致水平流速在上层流体中沿垂向分布无明显变化,在波面以下的下层流体中有衰减趋势,但衰减很小;两层流体界面与波谷之间存在过渡水深范围,水平流速在该水深范围内沿垂向衰减明显,且随内孤立波振幅的增大,过渡水深范围有所增大。     

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.     

非线性流函数在实验风浪场计算中的应用

风作用于水面产生风浪, 其中由于波流紊动产生的动量和能量的交换机制是一个很复杂的过程。风应力一般用来描述这种能量交换, 可以分为3个部分: 水面的剪切力、波生应力以及紊动应力。采用一种有效的非线性波流分离方法——NSFM(Nonlinear Stream Function Method)对波流运动的动量和能量输移进行定性描述。构造能够有效表达非线性波浪的解析流函数, 摄动求解使其满足拉普拉斯方程、动力边界条件和运动边界条件, 结合实验室风浪数据, 分离出波生速度场。通过交叉谱分析, 得到波生雷诺应力在不同风速下对风应力的贡献。结果表明: NSFM对不同工况条件下的风浪的处理具有较高的精度, 模型适应性良好; 且风速越大, 波生应力沿着水深衰减得越快, 且自由面波生应力在动量输移中的比重会逐渐减弱。     

完全非线性深水波的数值模拟

基于势流理论,并结合深水波质点运动从水面向下呈e指数衰减的特性,建立了完全非线性数值变深水槽模型,通过实时模拟活塞式造波机运动来产生波浪.采用时域高阶边界元法进行模拟,利用混合欧拉-拉格朗日方法和四阶Runge-Kutta方法追踪流体瞬时水面,应用镜像格林函数消除了水槽两个侧面的积分,在水槽末端布置人工阻尼层来消除反射...     

Diffraction of Water Waves by A Vertically Floating Cylinder in A Two-Layer Fluid

In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes.     

Water wave scattering by bottom undulations in an ice-covered two-layer fluid

The scattering of plane surface waves by bottom undulations in an ice-covered ocean modelled as a two-layer fluid consisting of a layer of fresh water of lesser density above a deep layer of salt water, is investigated here by using a simplified perturbation analysis. In such a two-layer fluid there exist waves of two different modes, one with higher mode propagates along the interface and the other with lower mode propagates along the ice-cover. An incident wave of a particular mode gets reflected and transmitted by the bottom undulations into waves of both the modes so that transfer of wave energy from one mode to another takes place. The first-order reflection and transmission coefficients of two different modes are obtained due to incident waves of again two different modes by employing Fourier transform technique in the mathematical analysis. For sinusoidal bottom topography these coefficients are depicted graphically against the wavenumber. These figures show how the transfer of energy from one mode to another takes place.     

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.     

Global estimates of wind energy input to subinertial motions in the Ekman-Stokes layer

By incorporating the wave-induced Coriolis-Stokes forcing into the classical Ekman model, the wind energy input to the Ekman-Stokes layer is investigated, with an emphasis on the surface wave effects when the direction of Stokes drift deviates from that of wind stress. Theoretical analysis of the kinetic energy balance of the Ekman-Stokes layer shows that the total wind energy input consists of the direct wind energy input and the wave-induced energy input. Details of the direct wind and wave-induced energy input are discussed. Based on the ECMWF ERA-40 Re-Analysis wind stress and surface wave data, the global total wind energy input to subinertial motions in the Ekman-Stokes layer is estimated at 2.19 TW, including 0.26 TW (12%) wave-induced energy input and 1.93 TW (88%) direct wind energy input. The effect of sea-ice coverage on the energy input to the Ekman-Stokes layer is also considered. It is shown that the global total energy input could be overestimated by 0.08 TW (about 4%) without taking the sea-ice coverage into account.     

Mud-Wave Interaction： A Viscoelastic Model

1 .IntroductionThe interaction between waves propagating onthe surface of a body of water andthe bed materialis a long standing coastal problem.The problemis practicallyimportant because the waves can be at-tenuated at a muchfaster rate whenthe bed materi…     

Green functions with pulsating sources in a two-layer fluid of finite depth

The derivation of Green function in a two-layer fluid model has been treated in different ways.In a two-layer fluid with the upper layer having a free surface,there exist two modes of waves propagating due to the free surface and the interface.This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating.The source point is located either in the upper or lower part of a two-layer fluid of finite depth.The derivation is carried out by the method of singularities.This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present.Furthermore,experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results.Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower,for each case.The effect of the density on the internal waves is demonstrated.Also,it is shown how the surface and internal wave amplitudes are compared for both the wave modes.The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.     

The effect of wave-induced radiation stress on storm surge during Typhoon Saomai (2006)

The effects of wave-induced radiation stress on storm surge were simulated during Typhoon Saomai using a wave-current coupled model based on ROMS (Regional Ocean Modeling System) ocean model and SWAN (Simulating Waves Nearshore) wave model.The results show that radiation stress can cause both set-up and set-down in the storm surge.Wave-induced set-up near the coast can be explained by decreasing significant wave heights as the waves propagate shoreward in an approximately uniform direction;wave-induced set-down far from the coast can be explained by the waves propagating in an approximately uniform direction with increasing significant wave heights.The shoreward radiation stress is the essential reason for the wave-induced set-up along the coast.The occurrence of set-down can be also explained by the divergence of the radiation stress.The maximum wave-induced set-up occurs on the right side of the Typhoon path,whereas the maximum wave induced set-down occurs on the left side.     

Generation of internal waves in the region of a bottom ridge with continuously varying height

Internal waves generated by a barotropic wave impinging on a bottom ridge with continuously varying height are studied within the framework of the linear theory of long waves. We consider the case where the diurnal tide travels at an arbitrary angle to the axis of the ridge located in the area of a geostrophic flow caused by tilting of the free sea surface and the interface of a two-layer ocean. We study the dependences of the amplitudes of internal waves on the velocity of the geostrophic flow, the direction of propagation of the barotropic tide, and the geometry of the ridge. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Second-Order Solutions for Random Interfacial Waves Under Steady Uniform Currents

1.Introduction Owingtothesimilaritiesbetweenthesurfacewaveandtheinterfacialwave,itisnaturaltoapply themethodsdevelopedforsurfacewavestothestudyofinterfacialwavesasreviewedbyUmeyama (1998;2000).Recently,Song(2004)derivedsecond ordersolutionsforrandominterfacialwavesat aconstantdepthinatwo layerfluidsystemwitharigidlidusinganexpansiontechnique,analogousto thatusedbyLonguet Higgins(1963)andSharmaandDean(1979),tostudyrandomsurfacewaves. Inthispaper,Song’sresultsareextendedtoamoregeneralcaseoft…     

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.