Rotational instability of a horizontal shear flow in a stratified rotating fluid

The rotational instability of a thermally stratified, viscous, conducting, rotating fluid is investigated by means of linearized perturbation equations. It is assumed that the basic horizontal flow is vertically uniform and that the horizontal shear is confined in a thin layer. By solving a simplified boundary value problem as a model of rotational instability in the sea, we have shown that the vertical wave length of the neutral disturbance is of order 10 times as large as the laminar Ekman layer thickness, and that this scale is proportional to (L/N)^1/3, whereL is the width of the shear layer andN is the Brunt-Vaisala frequency.     

波浪作用下方箱-水平板浮式防波堤时域水动力分析

在线性化势流理论范围内求解方箱-水平板浮式防波堤的波浪绕射和辐射问题,从时域角度分析了浮式防波堤的水动力特性.采用格林函数法将速度势定解问题的控制微分方程变换成边界上的积分方程进行数值求解,浮式防波堤的运动方程采用四阶Runge-Kutta方法求解.对不同层数水平板的浮式防波堤的波浪透射系数、运动响应和锚链受力进行了计算分析,结果表明方箱相对宽度对方箱-水平板浮式防波堤的波浪透射作用有重要的影响,透射系数随着方箱相对宽度的增加而减小.对于方箱加二层水平板的浮式防波堤,在本研究的计算条件下,当方箱相对宽度从0.110增加至0.295时,透射系数从0.88减小至0.30.水平板有利于增加浮式防波堤对波浪的衰减作用,但随着水平板层数从0增加至2,这种波浪衰减作用增加的程度趋弱.方箱-水平板的浮式防波堤的运动量小于单一方箱防波堤的运动量.与此对应,方箱-水平板防波堤的锚链受力小于单一方箱防波堤的锚链受力.     

Numerical study of a round buoyant jet under the effect of JONSWAP random waves

This paper presents a numerical study on the hydrodynamic behaviours of a round buoyant jet under the effect of JONSWAP random waves. A three-dimensional large eddy simulation (LES) model is developed to simulate the buoyant jet in a stagnant ambient and JONSWAP random waves. By comparison of velocity and concentration fields, it is found that the buoyant jet exhibits faster decay of centerline velocity, wider lateral spreading and larger initial dilution under the wave effect, indicating that wave dynamics improves the jet entrainment and mixing in the near field, and subsequently mitigate the jet impacts in the far field. The effect of buoyancy force on the jet behaviours in the random waves is also numerically investigated. The results show that the wave effect on the jet entrainment and mixing is considerably weakened under the existence of buoyancy force, resulting in a slower decay rate of centerline velocity and a narrower jet width for the jet with initial buoyancy.     

Floating pontoon breakwaters

The hydrodynamic properties of a pair of long floating pontoon breakwaters of rectangular section are investigated theoretically. The structures are partially restrained by linear symmetric moorings fore and aft. The fluid motion is idealized as linearized, two-dimensional potential flow. The breakwater motions are assumed to be two-dimensional, in surge, heave and pitch. The solution for the fluid motion is obtained by the boundary integral equation method using an appropriate Green's function. Numerical results are presented that illustrate the effects of the various wave and structural parameters on the efficiency of the breakwaters as barriers to wave action. It is found that the wave reflection properties of the structures depend strongly on their width, draft and spacing and the mooring line stiffnesses, while their excess buoyancy is of lesser importance.     

Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.     

PSME model of parametric excitation of two-layer liquid in a tank

Internal waves driven by external excitation constitute important phenomena that are often encountered in environmental fluid mechanics. In this study, a pseudospectral σ-transformation model is used to simulate parametric excitation of stratified liquid in a two-layer rectangular tank. The σ-transformation maps the physical domain including the liquid free surface, the interface between the liquid layers, and the bed, onto a pair of fixed rectangular computational domains corresponding to the two layers. The governing equation and boundary conditions are discretised using Chebyshev collocation formulae. The numerical model is verified for two analytical sloshing problems: horizontal excitation of constant density liquid in a rectangular tank, and vertical excitation of stratified liquid in a rectangular tank. A detailed analysis is provided of liquid motions in a shallow water tank due to excitations in the horizontal and the vertical directions. Also, the effect of pycnocline on the wave motions and patterns is studied. It is found that wave regimes and patterns are considerably influenced by the pycnocline, especially when the excitation frequency is large. The present study demonstrates that a pseudospectral σ-transformation is capable to model non-linear sloshing waves in a two-layer rectangular tank.     

Conditions of the propagation of internal gravity waves through wind structures from the troposphere to the ionosphere

We consider the propagation of large-scale internal gravity waves (IGWs) from the troposphere through vertically inhomogeneous wind structures to the ionosphere heights on the basis of an analysis of beam trajectories. We selected different versions of the initial parameters and numerically studied the specific peculiarities of the behavior of beam trajectories related to the location of layers with horizontal and vertical reflection and a critical layer on the pathway of the waves. It was shown that, for sufficiently large-scale IGWs, their propagation from the troposphere to ionosphere heights is possible. We found the characteristic times when the waves generated in the troposphere reach ionosphere heights. We revealed strong variations in these times when the initial parameters of the problem changed. We determined the typical values of the horizontal displacement (relative to the generation source) of the wave packets when they reach the ionosphere.     

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.     

三维物体上二阶波浪绕射的实时模拟

采用二阶时域理论对非线性波浪在任意三维物体周围的绕射问题进行了研究，对自由表面边界条件进行Taylor级数展开，应用摄动展开可以建立相应的边值问题，而且此边值问题的计算域不随时间变化，运用基于B－样条的边界元方法求解每一时刻的波浪场，二阶自由表面边界条件在时间上进行数值积分，在自由表面加了一个人工阻尼层以避免波浪的反射，速度势分解为已知的入射势和未知的散射势，初始条件采用二阶Stokes波浪场，通过加入物体表面边界条件，得到散射势在时间和空间上的发展，本文对圆柱所受规则波的二阶波浪力和波浪爬高进行了计算，数值结果表明此理论计算准确，效率高，数值稳定。     

Propagation of a solitary wave over rigid porous beds

The unsteady two-dimensional Navier–Stokes equations and Navier–Stokes type model equations for porous flows were solved numerically to simulate the propagation of a solitary wave over porous beds. The free surface boundary conditions and the interfacial boundary conditions between the water region and the porous bed are in complete form. The incoming waves were generated using a piston type wavemaker set up in the computational domain. Accuracy of the numerical model was verified by comparing the numerical results with the theoretical solutions. The main characteristics of the flow fields in both the water region and the porous bed were discussed by specifying the velocity fields. Behaviors of boundary layer flows in both fluid and porous bed regions were also revealed. Effects of different parameters on the wave height attenuation were studied and discussed. The results of this numerical model indicate that for the investigated incident wave as the ratio of the porous bed depth to the fluid depth exceeds 10, any further increase of the porous bed depth has no effect on wave height attenuation.     

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。     

Full-range equation for wave boundary layer thickness

Full-range equation covering all the flow regimes in a wave boundary layer is proposed for the boundary layer thickness. The results are compared with the available experimental data and good agreement has been found. In case of wave boundary layers, there are three definitions of boundary layer thickness in use. Therefore, the full-range equation is derived for three of the definitions. The findings of this study may be useful in calculating suspended sediment transport in coastal environments and studying wave–current combined motion.     

Experimental and numerical investigation of viscous effects on solitary wave propagation in a wave tank

Two-dimensional depth-averaged Boussinesq-type equations were presented with the consideration of slowly varying bathymetry and effects of bottom viscous boundary layer. These Boussinesq-type equations were written in terms of the horizontal velocity components evaluated at an arbitrary elevation in the water depth and the free surface displacement. The leading order effects of the bottom boundary layer were represented by a convolution integral in the depth-integrated continuity equation. To test the validity of the theory, a set of laboratory experiments was performed to measure the viscous damping and shoaling of a solitary wave propagating in a wave tank. The time histories of the free surface profiles were measured at several locations along the centerline of the flume. To compare these laboratory data with theoretical results, the two-dimensional Boussinesq-type equations were integrated across the wave tank, resulting in a set of one-dimensional equations, while the side-wall boundary layers were properly considered. The agreement between the experimental data and numerical results was very good. The bottom shear stress formula was also given and its impact on the sediment transport rate was discussed.     

An experimental investigation of plunging breaker boundary layers in the transformation zone

Experimental investigation is made on the boundary layers of the transformation zone (i.e. the region between the last symmetrical wave profile depth and the breaking point) of plunging breakers propagating on a smooth beach with 1/12 uniform slope. Using a laser anemometer, the particle velocities are measured at four verticals along the transformation zone for three different steepnesses of waves within the plunging breaker range. The boundary layer flow in the transformation zone is found mostly of turbulent character and vertical distribution of particle velocities does not seem to conform to the classical law of the wall distribution given for steady-flow boundary layers. The results show that free-stream particle velocities, in the boundary layer of the breaker under the crest phase, increase considerably as the wave progresses towards the breaking point. The boundary layer thickness, defined as the velocity-affected region, remains constant throughout the transformation zone but it decreases with increasing deep-water wave steepness for the particular beach slope tested.     

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。     

Progress on Nonlinear-Wave-Forced Sediment Transport Simulation

In this paper, we report on the use of a numerical wave tank (NWT), based on fully nonlinear potential flow (FNPF) equations, in driving simulations of flow and sediment transport around partially buried obstacles. The suspended sediment transport is modeled in the near-field in a Navier-Stokes (NS) model using an immersed-boundary method and an attached sediment transport simulation module. Turbulence is represented by large eddy simulation (LES). The NWT is based on a higher order boundary element method (BEM), with an explicit second-order time stepping. Hence, only the NWT boundary is discretized. The solution for the velocity potential and its derivatives along the boundary is obtained in the BEM, which subsequently provides a solution at any required internal point within the domain. At initial time, the NS-LES model domain is initialized with the 3-D velocity field provided by the NWT and driven for later time by the pressure gradient field obtained in the NWT. Incident wave fields, as specified in the NWT to drive sediment transport, can be arbitrary. Applications are presented here for single frequency waves, such as produced by a harmonic piston wavemaker in the laboratory, and modulated frequency wave groups. The feasibility of coupling the irrotational flow and NS solutions is demonstrated.     

Dual pontoon floating breakwater

The hydrodynamic properties of a dual pontoon floating breakwater consisting of a pair of floating cylinders of rectangular section, connected by a rigid deck, is investigated theoretically. The structure is partially restrained by linear symmetric moorings fore and aft. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a two-dimensional rigid body undergoing surge, heave and pitch motions. The solution for the fluid motion is obtained by the boundary integral equation method using an appropriate Green's function. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. It is found that the wave reflection properties of the structure depend strongly on the width, draft and spacing of the pontoons and the mooring line stiffness, while the excess buoyancy of the system is of lesser importance.     

内波吸引子的数值模拟

密度稳定层结的流体中产生的内波沿着由内波固有频率、流体浮力频率等因素所确定的特征线(或内波射线)传播。边界上的反射不改变内波的频率,从而也不改变反射后的内波特征线与重力方向所成的夹角。侧边界倾斜的封闭容器内,内波能量沿特征线传播的过程中经侧壁、表面和底面的反射可能会集中在一个封闭的轨道上,形成内波吸引子。该现象已经得到水槽试验、线性理论和数值试验的验证。本文利用非线性非静压的环流模式MITgcm,模拟了二维封闭区域中(1,1)-吸引子和(2,1)-吸引子的形成过程,并讨论初值条件对它们的影响。稳定的(1,1)-吸引子其极限环两侧流速出现很强的剪切流。当减小地形的坡度时,由于线性因素的增加,吸引子的结构不变,但吸引子厚度在相空间中的收缩速度加快。对于(2,1)-吸引子,由于轨道所成的两个环中间的节点耗散了部分能量,吸引子的收敛速度较慢。节点处,流体速度始终为0,但存在强烈混合,流体浮力频率呈现振幅较大的周期变化。     

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.     

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…