具有小密度差的两层流体中运动点源的二阶内波解

在具有自由面的两层流体中，运动点源生成的Kelvin船波存在两种模式，即表面波模式和内波模式。当上、下层流体密度比趋于1时，由内波模式计算的界面波幅趋于无穷大，这与实验事实相违背。为克服此困难，在自由面和界面作小波幅运动的假设，引入一个小密度差参数。研究了运动点源在无粘、不可压且具有小密度差的两层有限深流体中生成的高阶波动。首先利用摄动方法推导了各阶小参数满足的边值问题；其次，给出了小密度差情形下的可解性条件。证明了在密度比趋于1的极限情形，不存在导致界面波幅无穷大的内波模式；最后，利用Phillips的非线性共振相互作用理论，构造了具有自由面的两层有限深流体中Kelvin船波系的二阶一致有效波动解，并证明了该解在深水情形下退化为Newman关于均匀流体中自由面的二阶波动解。     

EXPERIMENTAL INVESTIGATION ON THE EVOLUTION OF INTERNAL SOLITARY WAVE OVER A RIDGE AND ITS ACTING FORCES ON A SUBMERGED SLENDER BODY

内孤立波沿山脊地形传播过程中的结构变化使得影响海洋结构物及水下航行器安全的不确定因素增加,用大型重力式分层流试验水槽系统研究内孤立波过山脊地形及其对细长潜体作用力特性,可有效提高对其危害性机理的认识.为此,利用电导率探头阵列,结合染色标识方法,测量内孤立波演变特性,同时利用三分量传感器测量水下细长体模型受力特性.研究结果表明：山脊地形显著改变下凹型内孤立波结构,表现为坡前波幅增大,坡顶背风波面抬升,坡后波长变长;内波结构变化直接影响细长体受力特性,表现为坡前向下作用力明显增强,坡顶向上作用力突显,坡后作用力持续时间变长;细长体受力特性变化影响其运动趋势,坡前下沉运动增强、朝山脊方向纵荡运动显著.     

过山脊内孤立波演变及其对细长潜体的作用力特性

内孤立波沿山脊地形传播过程中的结构变化使得影响海洋结构物及水下航行器安全的不确定因素增加,用大型重力式分层流试验水槽系统研究内孤立波过山脊地形及其对细长潜体作用力特性,可有效提高对其危害性机理的认识.为此,利用电导率探头阵列,结合染色标识方法,测量内孤立波演变特性,同时利用三分量传感器测量水下细长体模型受力特性.研究结果表明:山脊地形显著改变下凹型内孤立波结构,表现为坡前波幅增大,坡顶背风波面抬升,坡后波长变长;内波结构变化直接影响细长体受力特性,表现为坡前向下作用力明显增强,坡顶向上作用力突显,坡后作用力持续时间变长;细长体受力特性变化影响其运动趋势,坡前下沉运动增强、朝山脊方向纵荡运动显著.     

内孤立波作用下潜深对潜体运动响应和载荷特性的影响研究

内孤立波常发生于海洋密度跃层, 因其峰高谷深、携带能量巨大, 在传播过程中会导致跃层上下的海水流动呈现剪切状态, 并引起突发性的强流. 潜体在水下悬停时极有可能会遭遇内孤立波, 由于内孤立波的流场特性, 置于跃层上下的悬浮潜体所产生运动响应和水动力载荷变化不尽相同, 甚者会出现掉深现象. 为探究潜深对波体耦合作用的影响, 基于不可压缩N-S方程和mKdV理论, 采用速度入口造波, 结合重叠网格技术和流固耦合方法, 建立了分层流中内孤立波耦合水下潜体多自由度运动的数值模型, 通过该模型分析了不同潜深下悬浮潜体的运动响应和载荷特性. 结果表明: 在内孤立波作用下, 位于密度跃层上方和跃层中的潜体顺着波的前进方向运动, 先下沉后抬升, 位于跃层下方的潜体则会逆流持续下沉; 潜体与波面的垂向距离越小, 对其纵荡、垂荡和速度的影响越显著, 而位于密度跃层中的潜体在分界面处沿着波形运动, 其运动响应和载荷变化受影响较小; 潜体在跃层上、下流体中所受水平力的方向相反, 水平力峰值小于垂向力峰值, 且位于跃层下方的潜体一直受到低头力矩, 最终导致掉深.      

分层流体中内波与半潜平台相互作用的模型试验

对密度分层流体中内波与半潜平台的相互作用问题进行了模型试验研究.采用摇板方法进行了内波造波试验,对内波波长、周期和波高进行了测量分析,获得了内波波高和波长与周期之间的相关关系.利用激光和倾角仪方法对半潜平台的纵荡和纵摇运动响应进行了测量分析,获得了平台纵荡运动及纵摇角幅值与内波周期之间的相关关系.结果表明,在半潜平台的设计与应用中,内波对其运动响应的影响是不可忽视的.特别地,发现了在内波周期的某个范围内,半潜平台的纵荡和纵摇都会出现倍频周期运动响应的现象.     

分层流体中内孤立波数值造波方法及其应用

海洋内波是发生在密度分层海水中的波动，对潜艇航行的稳定性和悬停性都有重要影响。本文采用有限体积自适应半结构多重网格法求解Navier-Stokes方程，并用VOF(Volume of Fluid)方法追踪两层流体界面，应用双推板造波法进行内孤立波数值造波，对两层流体中的内孤立波数值造波方法进行研究和探讨。数值模拟结果证...     

Experiments on the interaction of internal waves with the semi-submersible platform in a stratified fluid

对密度分层流体中内波与半潜平台的相互作用问题 进行了模型试验研究. 采用摇板方法进行了内波造波试验,对内波波长、周期和波高进行了 测量分析,获得了内波波高和波长与周期之间的相关关系. 利用激光和倾角仪方法对半潜平 台的纵荡和纵摇运动响应进行了测量分析,获得了平台纵荡运动及纵摇角幅值与内波周期之 间的相关关系. 结果表明,在半潜平台的设计与应用中,内波对其运动响应的影响是不可忽 视的. 特别地,发现了在内波周期的某个范围内, 半潜平台的纵荡和纵摇都会出现 倍频周期运动响应的现象.     

圆柱运动的内波渐近解

本文提供一个二维内波的渐近解法,对水平圆柱在无粘、稳定的密度连续分层流体中任意倾角运动的问题,得到了伴随的色散关系式,结合倾角α=90°圆柱垂直运动情况,给出了圆柱面上的边界条件和无穷远衰减条件。用渐近展开的方法求出內波的渐近解;对内波传布的规律作了讨论并与內波流场显示结果进行了比较,计算结果合理,运用本解法可望在求解分层流体中圆柱任意方向运动的问题,其它形状物体分层绕流的内波问题、非定常色散以及三维的内波问题中得到推广应用。     

二流体系统中界面孤立波的分裂

本文讨论了二流体系统界面上内孤立波的分裂,发现上下层流体密度比对分裂成两个内孤立波的条件没有影响,此时只要孤立波从较深的流体运动到较浅的流体就会发生分裂,但分裂成二个以上孤立波的条件受密度比和上游上下层流体厚度比的影响。     

二流体系统中界面孤立波的分裂

本文讨论了二流体系统界面上内孤立波的分裂,发现上下层流体密度比对分裂成两个内孤立波的条件没有影响,此时只要孤立波从较深的流体运动到较浅的流体就会发生分裂,但分裂成二个以上孤立波的条件受密度比和上游上下层流体厚度比的影响。     

INTERNAL SOLITARY WAVE LOADS EXPERIMENTS AND ITS THEORETICAL MODEL FOR A CYLINDRICAL STRUCTURE

在大型重力式密度分层水槽中, 对内孤立波与圆柱型结构的相互作用特性开展了系列实验. 基于两层流体中 内孤立波的KdV,eKdV和MCC理论, 建立了圆柱型结构内孤立波载荷的理论预报模型, 给出了该载荷理论预报模型中3类内孤立波理论的适用性条件.研究表明, 圆柱型结构内孤立波水平载荷包括水平Froude-Krylov力、附加质量力和拖曳力3个部分, 可以由Morison公式计算, 而内孤立波垂向载荷主要为垂向Froude-Krylov力, 可以由内孤立波诱导动压力计算.系列实验结果表明, 附加质量系数可以取为常数1.0, 拖曳力系数与内孤立波诱导速度场的雷诺数之间为指数函数关系, 而且基于理论预报模型的数值结果与系列实验结果吻合.     

分层流体中内孤立波在台阶上的反射和透射

基于匹配渐近展开和格林函数的方法，研究了两层流体系统中内孤立波在台阶地形上透射、 反射及其分裂的演化特征. 通过保角变换和求解奇异Fredholm积分方程，获得了反映地形 效应对Boussinesq方程影响的约化边界条件，藉此建立了KdV演化方程的``初值'问题， 根据散射反演理论获得了反射波和透射波的解析表达式. 分析结果表明：上下流体层的厚度 比、密度比以及台阶高度对于反射和透射波振幅及其分裂具有显著的影响. 尤其当上层流体 厚度小于下层厚度时，由于存在临界点，在其附近反射波的幅值随台阶高度的演化由单调增 变为单调减，透射波的幅值由单调减变为单调增；上台阶的反射波与入射波反相，其最大幅 值可达到入射波的数倍；此外，下台阶反射波也可发展为单支孤立波，它区别于单层流体中 反射波仅为衰减的振荡波列.     

基于势流理论的内孤立波与立管作用数值研究

内孤立波是一种发生在水面以下的在世界各个海域广泛存在的大幅波浪, 其剧烈的波面起伏所携带的巨大能量对以海洋立管为代表的海洋结构物产生严重威胁, 分析其传播演化过程的流场特征及立管在内孤立波作用下的动力响应规律对于海洋立管的设计具有重要意义. 本文基于分层流体的非线性势流理论, 采用高效率的多域边界单元法, 建立了内孤立波流场分析计算的数值模型, 可以实时获得内孤立波的流场特征. 根据获得的流场信息, 采用莫里森方程计算内孤立波对海洋立管作用的载荷分布. 将内孤立波流场非线性势流计算模型与动力学有限元模型结合来求解内孤立波作用下海洋立管的动力响应特征, 讨论了内孤立波参数、顶张力大小以及内部流体密度对立管动力响应的影响. 发现随着内孤立波波幅的增大, 海洋立管的流向位移和应力明显增大. 由于上层流体速度明显大于下层, 且在所研究问题中拖曳力远大于惯性力, 因此管道顺流向的最大位移发生在上层区域. 顶张力通过改变几何刚度阵的值进而对立管的响应产生明显影响. 对于弱约束立管, 内部流体的密度对管道的流向位移影响较小.      

Internal wave computations using the ghost fluid method on unstructured grids

Two‐layer incompressible flows are analysed using the ghost fluid method on unstructured grids. Discontinuities in dynamic pressure along interfaces are captured in one cell without oscillations. Because of data reconstructions based on gradients, the ghost fluid method can be adopted without additional storages for the ghost nodes at the expense of modification in gradient calculations due to the discontinuity. The code is validated through comparisons with experimental and other numerical results. Good agreements are achieved for internal waves generated by a body moving at transcritical speeds including a case where upstream solitary internal waves propagate. The developed code is applied to analyse internal waves generated by a NACA0012 section moving near interfaces. Variations of the lift acting on the body and configurations of the interfaces are compared for various distances between the wing and the interface. The effects of the interface are compared with the effects of a solid wall. Copyright © 2004 John Wiley & Sons, Ltd.     

Phase velocity spectrum of internal waves in a weakly-stratified two-layer fluid

The problem of steady-state internal waves in a weakly stratified two-layer fluid with a density that is constant in the lower layer and depends exponentially on the depth in the upper layer is considered. The spectral properties of the equations of small perturbations of a homogeneous piecewise-constant flow are described. A nonlinear ordinary differential equation describing solitary waves and smooth bores on the layer interface is obtained using the Boussinesq expansion in a small parameter.     

Wave drag of an ellipsoid of revolution rapidly moving in a horizontal direction in a uniformly stratified fluid

The problem of the wave drag of ellipsoids moving in a uniformly stratified ideal fluid is considered by means of modeling the bodies by surface distributions of mass sources. Analytical results are obtained using the distributions known from the theory of a uniform fluid, which make it possible to describe the emission of internal waves by rapidly moving ellipsoids of revolution (spheroids) in the limit of large Froude numbers. An asymptotically simplified form of the dependence of the wave drag on the Froude number and the spheroid axis ratio is found. In the particular case of a sphere, the result confirmed earlier by Greenslade by making comparisons with a numerical calculation and experimental data is obtained.     

分层流体中内孤波的研究进展

综述了分层流体中内孤波的理论分析和符号运算的研究进展状况,系统介绍了应用背景、实验报道、理论分析和符号运算的结果以及有待进一步研究的问题      

Comparisons of CIP,compact and CIP‐CSL2 schemes for reproducing internal solitary waves

Six different models were evaluated for reproducing internal solitary waves which occur and propagate in a stratified flow field with a sharp interface. Three stages were used to compute internal solitary waves in a stratified field: (1) first‐phase computation of momentum equations, (2) second‐phase computation of momentum equations, which corresponds to computing the Poisson's equation, and (3) density computation. The six models discussed in this paper consisted of combinations of four different schemes, a three‐point combined compact difference scheme (CCD), a normal central difference scheme (CDS), a cubic‐polynomial interpolation (CIP), and an exactly conservative semi‐Lagrangian scheme (CIP‐CSL2). The residual cutting method was used to solve the Poisson's equation. Three tests were used to confirm the validity of the computations using KdV theory; i.e. the incremental wave speed and amplitude of internal solitary waves, the maximum horizontal velocity and amplitude, and the wave form. In terms of the shape of an internal solitary wave, using CIP for momentum equations was found to provide better performance than CCD. These results suggest one of the most appropriate scheme for reproducing internal solitary waves may be one in which CIP is used for momentum equations and CCD to solve the Poisson's equation. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical modeling of the generation of internal waves by uniform stratified flow over a thin vertical barrier

Numerical simulations of two‐dimensional stratified flow past an obstacle (thin vertical strip) were performed at relatively low Reynolds numbers. A finite differences solver was adopted to simultaneously solve Navier–Stokes equations together with transport equations for salinity (stratifying agent), and the standard Smagorinsky turbulent closure scheme was called in whenever necessary to account for turbulence. The emphases were on the evaluation of code for unsteady stratified flow applications as well as identification of transient and steady internal‐wave processes during flow past obstacles. Simulations were compared with laboratory experiments, where observations were made using a high resolution Schlieren technique and conductivity probes. Blocking was observed upstream of the obstacle, surrounded by near‐zero frequency internal waves, the phase lines of which joined those of lee waves through a transition zone in the proximity of the obstacle. This pattern was preceded by initial transients of the starting flow in which propagating internal waves played a dominant role. Confluence of isopycnals passing over/under the obstacle in the wake led to interesting flow phenomena, including the radiation of internal waves. The numerical simulations were in good agreement with observations, except that some phenomena could not be captured due to resolution issues of either numerical or experimental techniques. The efficacy of the code in point for stratified flow calculations with relevance to the atmosphere and oceans was confirmed. Copyright © 2011 John Wiley & Sons, Ltd.