运动物体生成内波的一类非线性谱方程组

本文给出了由运动物体所生成内波的基本方程组和对应的谱方程组。该方程组的线性部分是一具有体积源 (其下简称为体源 )的 Sturm- Liouville本征值问题 ,而它的非线性部分是由体源与线性波场相互作用的谱表示。在这类强迫方程的源项中包含了 10类内波谱 ,这些谱最终均可利用内波的振幅谱表示。本文给出了线性波场波要素的谱表示和运动物体生成内波的非线性谱方程可解性的讨论。为了检验所得到的谱方程组 ,文中又进行了该谱方程组线性部分的数值计算。     

Numerical Simulation of Waves Generated by Seafloor Movements

Waves generated by vertical seafloor movements are simulated by use of a fully nonlinear two-dimensional numerical wave tank. In the souree region, the seafloor lifts to a designated height by a generation function. The numerical tests show that the linear theory is only valid for estimating the wave behaviors induced by the seafloor movements with a small amplitude, and the fully nonlinear numerical model should be adopted in the simulation of the wave generation by the large amplitude seafloor movements. Without the background surface waves, many numerical tests on the stable maximum elevations η0^max are carried out by beth the linear theory and the fully nonlinear model. The results of two models are compared and analyzed. For the fully nonlinear model, the influences of the amplitudes and the horizontal lengths on η^max are stronger than that of the characteristic duration times. Furthermore, results reveal that there are significant differences be- tween the linear theory and the fully nonlinear model. When the influences of the background surface waves are considered, the corresponding numerical analyses reveal that with the fully nonlinear model the η0^max near-linearly varies with the wave amplitudes of the surface waves, and the η0^max has significant dependences on the wave lengths and the wave phases of the surface waves. In addition, the differences between the linear theory and the fully nonlinear model are still obvious, and these differences are significantly affected by the wave parameters of the background surface waves, such as the wave amplitude, the wave length and the wave phase.     

分层海洋中运动物体生成的内波

该文提供分层海洋中运动物体生成内波的理论、数值和实验研究的背景资料的综述 ,并给出理论研究的 Green函数、正交模态模式和极点回避等方法的评述。数值研究给出数值求解Wronsky行列式的源求解方法及介绍直接差分计算含源内波方程和积分方程的方法。有关源致内波的实验研究 ,作者介绍物体在分层流水槽运动时生成内波的两个典型实验及其主要实验结果。最后评述船舶在海洋表面处生成表面波的研究方法 ,以此指导水下 Rankine卵形体生成内波的实验研究。     

Efficient Generation of Freak Waves in Laboratory

In the present study,Kriebel's method is improved to generate freak waves in laboratory.The improved method superposes a random wave train with two transient wave trains to simulate freak wave events in a wave tank.The freak waves are more nonlinear than what generated with Kriebel's method of the same energy.It can also generate freak waves to satisfy all the qualifications of the adopted definition with less energy than Kriebel's and can hardly influence the significant wave height.     

2-D Composite Model for Numerical Simulations of Nonlinear Waves

—A composite model,which is the combination of Boussinesq equations and Volume of Fluid(VOF)method,has been developed for 2-D time-domain computations of nonlinear waves in a large re-gion.The whole computational region Ω is divided into two subregions.In the near-field around a struc-ture,Ω_2,the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulenceclosure model of k-εequations and numerically solved by the improved VOF method;whereas in thesubregion Ω_1(Ω_1=Ω-Ω_2) the flow is governed by one-D Boussinesq equations and numerically solvedwith the predictor-corrector algorithm.The velocity and the wave surface elevation are matched on thecommon boundary of the two subregions.Numerical tests have been conducted for the case of wave propa-gation and interaction with a wave barrier.It is shown that the composite model can help perform efficientcomputation of nonlinear waves in a large region with the complicated flow fields near structures taken in-to account.     

近岸海浪模式在中国东海台风浪模拟中的应用--数值模拟及物理过程研究

较为详细地介绍了基于能量平衡方程的第三代近岸海浪数值模式SWAN（Simulation Waves Nearshore）及其包含的物理过程（风生浪、底摩擦、白浪耗散、深度诱导波破碎、非线性波－波相作用等），并利用该模式对影响杭州湾－长江口沿岸海域的一次台风浪过程进行了模拟研究：模式所需风场由藤田台风风场模型嵌入对应台风特征等压线，并对相应时段的NCAR／NCEPT资料、单站资料进行同化后提供；利用自嵌套的方式提供波谱边界条件；模式模拟的结果与实际海浪观测资料相符较好，在此基础上，研究了底摩擦、深度诱导波破碎、三波相互作用等物理过程联合对近岸台风浪的影响，初步认识了它们在近岸台风浪生成、传播过程中的重要作用。     

青岛外海潮致第二模内孤立波的观测研究

根据在青岛附近海域开展的现场观测数据介绍了一种可能的新的第二模内孤立波的产生机制。温度链观测数据显示在2 h内孤立波特征由显著的第一模内孤立波变为了显著的第二模内孤立波。所观测到的第二模内孤立波的波面起伏和它的垂直结构同KdV(Korteweg-de Vries)方程的理论结果吻合良好,对应涨潮引起的内波非线性系数、频散系数以及Ursell数的变化和第二模内孤立波的产生相匹配。这些结果表明,所观测到的第二模内孤立波可能是由于涨潮导致的局地层结快速变化引起的。进一步分析表明,局地层结快速变化可能由潮汐推动黄海冷水团边缘锋面移动引起。     

Solitary wave propagation influenced by submerged breakwater

The form of Boussinesq equation derived by Nwogu （1993） using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, water depth was divided into five layers with six layer interfaces to simulate velocity at each layer interface. Besides, a physical experiment was carried out to validate numerical model and study solitary wave propagation.“Water column collapsing”method （WCCM） was used to generate solitary wave. A series of wave gauges around an impervious breakwater were set-up in the flume to measure the solitary wave shoaling, run-up, and breaking processes. The results show that the measured data and simulated data are in good agreement. Moreover, simulated and measured surface elevations were analyzed by the wavelet transform method. It shows that different wave frequencies stratified in the wavelet amplitude spectrum. Finally, horizontal and vertical velocities of each layer interface were analyzed in the process of solitary wave propagation through submerged breakwater.     

Transformation of the Indonesian Throughflow Water by Vertical Mixing and Its Relation to Tidally Generated Internal Waves

Numerical experiments with two-dimensional nonhydrostatic model have been performed to investigate tidally generated internal waves at the Dewakang sill at the southern Makassar Strait where two large-amplitude “bumps” of relatively shallow water exist. We investigate the effect of these features on vertical mixing, with emphasis on the transformation of the Indonesian throughflow (ITF) water properties. The result shows that large-amplitude internal waves are generated at both bumps by the predominant M₂ tidal flow, even though the condition of the critical Froude number and the critical slope are not satisfied. The internal waves induce such vigorous vertical mixing in the sill region that the vertical diffusivity attains a maximum value of 6 × 10⁻³ m²s⁻¹ and the salinity maximum and minimum core layers characterizing the ITF thermocline water are considerably weakened. Close examination reveals that bottom-intensified currents produced mainly by the joint effect of barotropic M₂ flow and internal tides generated in the concave region surrounding both bumps can excite unsteady lee waves (Nakamura et al., 2000) on the inside slopes of the bumps, which tend to be trapped at the generation region and grow into large-amplitude waves. Such generation of unsteady lee waves does not occur in case of one bump alone. Trapping and amplification of the waves in the sill region induce large vertical displacements (∼60 m) of water parcels during one tidal period, leading to strong vertical mixing there. Since the K₁ tidal currents are relatively weak, large-amplitude internal waves causing intense vertical mixing are not generated. This revised version was published online in July 2006 with corrections to the Cover Date.     

非线性波传播的新型数值模拟模型及其实验验证

以一种新型的Boussinesq型方程为控制方程组,采用五阶Runge-Kutta-England格式离散时间积分,采用七点差分格式离散空间导数,并通过采用恰当的出流边界条件,从而建立了非线性波传播的新型数值模拟模型.通过对均匀水深水域内波浪传播的数值模拟说明,模型能较好地模拟大水深水域和强非线性波的传播.通过设置不同的入射波参数来进行潜堤地形上波浪传播的物理模型实验,并将数值解与物理模型实验结果进行了比较.     

Generation of random waves in time-dependent extended mild-slope equations using a source function method

We develop techniques of numerical wave generation in the time-dependent extended mild-slope equations of Suh et al. [1997. Time-dependent equations for wave propagation on rapidly varying topography. Coastal Engineering 32, 91–117] and Lee et al. [2003. Extended mild-slope equation for random waves. Coastal Engineering 48, 277–287] for random waves using a source function method. Numerical results for both regular and irregular waves in one and two horizontal dimensions show that the wave heights and the frequency spectra are properly reproduced. The waves that pass through the wave generation region do not cause any numerical disturbances, showing usefulness of the source function method in avoiding re-reflection problems at the offshore boundary.     

基于双层Boussinesq方程的三维波浪数值模型及其验证

Liu等给出的最高导数为2的双层Boussinesq水波方程具有较好的色散性和非线性,基于该方程建立了有限差分法的三维波浪数值模型。在矩形网格上对方程进行了空间离散,采用高阶导数近似方程中的时、空项,时间积分采用混合4阶Adams-Bashforth-Moulton的预报—校正格式。模拟了深水条件下的规则波传播过程,计算波面与解析结果吻合较好,反映出数值模型能很好地刻画波面过程及波面处的速度变化;在kh=2π条件下可较为准确获得沿水深分布的水平和垂向速度,这与理论分析结果一致。最后,利用数值模型计算了规则波在三维特征地形上的传播变形,数值结果和试验数据吻合较好;高阶非线性项会对波浪数值结果产生一定的影响,当波浪非线性增强,水深减少将产生更多的高次谐波。建立的双层Boussinesq模型对强非线性波浪的演化具有较好的模拟精度。     

相同尺度地形与背景流共振生成内孤立波机制

为研究内孤立波的地形和背景流共振机制,用地形和背景流共振机制计算了3个潜标观测的内孤立波(不同模态、不同波长)的流速和传播速度,并与观测到的内孤立波进行比较。潜标观测的第一模态内孤立波(波长分别为6.4和3.3km)都是下凹型内孤立波,2个内孤立波的传播速度约为1.4m/s、最大振幅约为48m,水平流向结构都是上层西北向、下层东南向,波长3.3km 的内孤立波波峰前后有更明显的下降流和上升流。用共振机制计算出的第一模态和第二模态纬向流速的垂向结构与观测相同,最大纬向流速出现的深度与观测一致,分别相差5和12m。用共振机制计算出的内孤立波传播速度与用 KdV 方程计算的传播速度相当,共振机制计算波速为0.66~1.21m/s,KdV 方程计算波速为0.79~1.40m/s。     

浅水中浮体在波浪作用下运动的三维时域计算模型

港口中系泊船在波浪作用下运动问题的本质是浅水波浪与浮体的相互作用。与深水情况不同,浅水问题应当考虑水底、水域边界的影响及浅水波浪自身的特性,单一模型很难实现该模拟过程。为此,建立了Boussinesq方程计算入射波和Laplace方程计算散射波的全时域组合计算模型。有限元法求解的Boussinesq方程能使入射波充分考虑到水底、水域边界的影响和浅水波浪的特性;散射波被线性化,采用边界元法求解,并以浮体运动时的物面条件为入射波和散射波求解的匹配条件。该方法为完全的时域方法,计算网格不随时间变动,计算过程较为方便。通过与实验及其他数值方法的结果进行比较,验证了本模型对非线性波面、浮体的运动都有比较理想的计算结果,显示了本模型对非线性问题具有较好的计算能力。     

非静压波浪模型无反射造波

非静压波浪模型是一种近年来得到迅速发展且有望在工程计算中获得广泛应用的波浪模型。为了在非静压波浪模型中实现无反射造波,在连续性方程中添加了质量源项进行域内源造波,并采用阻尼消波方法进行数值消波。数值算例结果表明,所建立的无反射造波方法可以较好地避免非静压波浪数学模型中的二次反射,实现长时间稳定波浪模拟。     

Numerical Simulation for Refraction-Diffraction of Waves in Water of Slowly Varying Current and Topography

A new numerical finite difference iteration method for refraction-diffraction of waves in waterof slowly varying current and topography is developed in this paper.And corresponding theoretical modelincluding the dissipation term is briefly described,together with some analysis and comparison ofcomputational results of the model with measurements in a hydraulic scale model(Berkhoff et al.,1982).An example of practical use of the method is given,showing that the present model is useful to engineeringpractice.     

不规则波浪数值水槽的造波和阻尼消波

利用MAC(marker and cell)法直接数值求解连续方程和N-S方程.为模拟不规则波长时段连续造波及消除波浪遇结构物后形成的二次反射,采用了源造波法.对开敞边界,采用了海绵阻尼消波和Sommerfeld条件相结合的处理方式.     

Internal generation of waves: Delta source function method and source term addition method

In this study, we investigate two internal wave generation methods in numerical modeling of time-dependent equations for water wave propagation, i.e., delta source function method and source term addition method, the latter of which has been called the line source method in literatures. We derive delta source functions for the Boussinesq-type equations and extended mild-slope equations. By applying the fractional step splitting method, we show that the delta source function method is equivalent to the source term addition method employing the energy velocity. This suggests that the energy velocity should be used rather than the phase velocity for the transport of incident wave energy in the source term addition method. Finally, the performance of the delta source function method is verified by accurately generating nonlinear cnoidal waves as well as linear waves for horizontally one-dimensional cases.     

0908号台风“莫拉克”影响期间福建西沙湾海域台风浪的数值模拟

联合SWAN模型和改进的椭圆型缓坡方程,结合考虑台湾海峡地形效应的改进藤田公式风场模型,建立了台湾海峡及近岸波浪场的数值嵌套模式.边界采用波谱离散驱动,模拟了0908号台风“莫拉克”期间台湾海峡波浪场的演变和崇武西沙湾浅水台风浪传播的物理过程.以实测数据进行单点验证表明,整个模拟过程风速的平均绝对误差为3.38 m/s,波高的平均绝对误差为0.30 m,计算结果较好地反映海峡内波浪对台风的响应过程.“莫拉克”台风登陆台湾岛时,台湾海峡有效波高最大值为5.0m;台风中心进入台湾海峡后,海峡东北部为巨浪到狂涛,有效波高最大值可达10.5 m.接近福建崇武沿岸时,偏E向台风浪向西沙湾内近岸传播,发生浅化、破碎、反射、绕射等变形现象,有效波高最大不足2 m,最小仅为0.2m,波向趋于SE向,波峰线则趋于与峡湾岸线平行;崇武闽台贸易码头附近,大部分波浪受到阻挡作用发生反射,少部分发生绕射,使得码头以北水域波浪较小,有效波高仅为0.2 ～0.6 m,对湾内避风坞起到较好的保护作用.     

Numerical simulations using momentum source wave-maker applied to RANS equation model

For Navier-Stokes equation model using the VOF scheme, Lin and Liu (Lin, P. and Liu, P.L.-F. (1999). Internal wave-maker for Navier-Stokes equations models. J. Waterw. Port Coast. Ocean Eng., 125 (4), 207–215.) developed an internal wave-maker method for which a mass source function of the continuity equation was used to generate target wave trains. Using this internal wave-maker method, various numerical experiments have been conducted without any problems due to waves reflected by a wave-maker. In this study, an internal wave-maker method using a momentum source function was proposed. Various numerical simulations in two and three dimensions were performed using the momentum source wave-maker applied to the RANS equation model in a CFD code, FLUENT. To verify their applicability in 2 dimensions, the computational results obtained using the momentum source wave-maker in a channel of constant depth were compared with the results obtained by using the mass source wave-maker and with the analytical solutions. And the results of the present numerical simulations of hydraulic experiments, which represent nonlinear waves on a submerged shoal and breaking waves on a plane beach, were compared with measurements. The comparisons showed good agreements between them. To see their applicability into 3-dimensional cases, the present results in a basin of constant depth were compared with the analytical solutions, and they agreed well with each other. In addition, vertical variation of longshore current was presented by using the 3-dimensional simulation results.