解Klein-Gordon方程的基于光滑分片Lagrange型插值的Galerkin方法

构造1种光滑的分片Lagrange型插值多项式空间,并在此空间中利用Galerkin法对非线性Klein-Gordon(NKG)方程进行求解.并分析数值格式的稳定性和收敛性,进行数值实验.数值结果表明格式精确有效.     

海洋平台输液管道振动流特性研究

该文研究了海洋平台输液管道振动流的行为特性。依据振荡流体力学基本原理 ,建立了输液管道非定常、不可压缩、粘性振动流的物理模型和数学模型。推导出了关于流场速度、压力系数的微分方程组 ,得到了不同条件下流动的速度和压力分布。结果表明流体诱发的海洋平台输液管道振动流的行为特性受管道结构形状及流体性质的影响。比较等截面管道的变分解和数值解 ,说明本文所选用的方法用于研究海洋平台输液管道振动流是有效的。     

几类特殊的矩阵多项式

本文讨论几类特殊的矩阵多项式,先介绍几个基本概念,然后证明。对这几类特殊的矩阵多项式,与之相应的L—值问题可转化为低次的代数多项式求根问题。最后,使用“投影尺度”建立了L—值的摄动定理。     

求解代数Riccati方程的一些数值方法评述

在过去的三十多年中 ,代数 Riccati方程的数值求解一直是数值代数界和控制论界关注的重要课题。作者简要评述几种用于求解代数 Riccati方程的有代表性的数值方法。     

几类特殊的矩阵多项式

本文讨论几类特殊的矩阵多项式，先介绍几个基本概念。然后证明。对这几类特殊的矩阵多项式，与之相应的L-值问题可转化为低次的代数多项式求根问题。最后．使用“投影尺度”建立了L-值的摄动定理。     

人工神经网络在潮汐数值预报中的应用

潮汐数值预报经过了几十年的发展,但是其预报精度并不能让人十分满意,本文试图将传统的潮汐数值预报模式与近年来发展迅速的人工神经网络相结合并改进潮汐数值预报的精度。文章建立了一个神经网络系统,采用潮汐数值模式的输出结果作为网络输入,潮位观测资料作为输出,用建立的神经网络进行训练,结果表明人工神经网络可以明显地改进潮汐数值预报的精度。     

影响连云港的几次显著温带风暴潮过程分析及其数值模拟

本文建立一个温带风暴潮模式,包括海上边界层风场模式和风暴潮数值模式.利用建立的温带风暴潮模式,模拟了影响连云港的几次显著温带风暴潮过程,结果表明,本模式所采用的海上边界层风场模式和风暴潮数值模式是匹配的,能够满足海洋工程中的风暴潮数值计算的需要,甚至可以成为日常温带风暴潮数值预报的有用手段.     

一种区域似大地水准面模型拟合方法分析

GPS技术结合(似)大地水准面模型,可快速高精度的获取测点正常高,因此精化区域(似)大地水准面成为各国家和地区建立现代高程基准的重要任务。利用GPS水准进行区域似大地水准面拟合,通过实验比较分析了二次多项式、三次多项式、多面函数、移动曲面模型,论证了各自模型的特点,实验结果表明:对于地势较平坦的实验区,以上几种方法拟合的区域似大地水准面精度都在4cm以内,都能满足一般工程应用的精度要求,其中移动曲面模型拟合的实验区似大地水准面最佳。     

一种区域似大地水准面模型拟合方法分析

GPS技术结合(似)大地水准面模型,可快速高精度的获取测点正常高,因此精化区域(似)大地水准面成为各国家和地区建立现代高程基准的重要任务。利用GPS水准进行区域似大地水准面拟合,通过实验比较分析了二次多项式、三次多项式、多面函数、移动曲面模型,论证了各自模型的特点,实验结果表明:对于地势较平坦的实验区,以上几种方法拟合的区域似大地水准面精度都在4cm以内,都能满足一般工程应用的精度要求,其中移动曲面模型拟合的实验区似大地水准面最佳。     

一种有限区域海表温度预报模式——II.物理学部分

首先阐述预报模式的物理学方程的内容,它包括海-气的热量交换、云的诊断关系、夹卷和抽吸等几方面,皆以参数化形式给出;在数值积分方面重点讨论了阻尼惯性振荡的数值方法;为了检验模式的预报性能,最后给出几例数值实验以及试预报结果。     

Sea-structure interaction for tripod-type steel gravity platform

The paper deals with a numerical integrated procedure to calculate the effects of the interaction between sea waves and a tripod-type steel gravity platform. The main aspects to be taken into account for a reliable wave loading analysis of such a new type of platform are emphasized. Among them, the field perturbation effect due to the large bodies presence is analysed. Finally, some principal results in terms of structure global loads obtained by the numerical integrated procedure are presented.     

Spurious instabilities of long planetary waves in a two-and-a-half layer model subtropical gyre ocean with a wind-driven steady circulation

In a number of flows that support coupled free-waves, instability results when free-wave dispersion relations calculated without the coupling cross or approach one another. The propagation of long planetary wave perturbations of a two-and-a-half layer model subtropical gyre is one such oceanographically important instance. This note points out that, for a baroclinically unstable two-and-a-half layer model subtropical gyre, numerically aliased long wave dispersion relation plots display extra crossings that are artifacts of the discretization, and these may lead both to spurious numerical instabilities and to numerical misrepresentation of actual instabilities. Paradoxically, the numerical instability may in some instances manifest itself more strongly as the numerical resolution is improved. The aliasing mechanism may be related to the zone of small scale activity found in the southwestern corner of a time dependent model subtropical gyre in the numerical perturbation experiments of (Dewar, W., Huang, R., 2001. Adjustment of the ventilated thermocline. J. Phys. Oceanogr. 13, 293–309). Similar multilayer models are often discussed in the literature, so that the results may be widely useful.     

Sea surface scattering and propagation loss: review, update, andnew predictions

Sea-surface-scattering loss estimates based on perturbation methods are reviewed. The perturbation method has been known to be quite accurate for estimating low-frequency acoustic wave scattering loss. The author compares models that are based on the perturbation methods of H.W. Marsch (1961) and F.G. Bass (1960). Predictions based on numerical integration in a complex domain are presented and compared to previous predictions     

关于具二次约束最小二乘问题的敏度分析

本文系统地研究具二次约束最小二乘问题的敏度分析。首先给出长期方程唯一正根的上界和下界；然后证明割线法用于计算拉格朗日乘子时全局收敛；最后给出解的扰动界。     

On the parabolic equation method in internal wave propagation

A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numerical experiments on propagation of an incident plane wave over a circular-type shoal are presented in comparison with the analytical result, based on Born approximation.     

失稳背景流下对称型海洋内波的生成演变

本文采用无海底地形但考虑海洋跃层和剪切背景流的二维非静力准不可压缩方程组的数值模式,开展失稳垂向剪切背景流下线性和非线性对称型海洋内波生成演变的数值实验,并对结果进行分析、比较和讨论。研究结果表明,线性内波强度随积分时间始终呈指数增长,并有内波的对称不稳定;而非线性内波强度则在发展期呈准线性增长,最终进入稳定期。线性增长比非线性增长要快得多,非线性效应具有维稳作用。对该线性和非线性对称型内波,在跃层附近位密度扰动均有大值中心,即其为跃层所俘获,这与实际观测相一致;流函数与位密度扰动两者均有很好配合,位密度扰动的正、负中心分别相应于流函数的上升、下沉运动,表明有从海底向上的斜对流发生,且以跃层为顶盖。对线性内波来说,随积分时间增加,其波形大体不变,其正、负振幅也大体相同,并有符号相反原地增长的两个倾斜环流圈,而在它们之间则有较强倾斜上升流。非线性内波波形随积分时间改变,倾斜环流圈数目也在增加,最终形成负环流强于正环流的结果,并导致流函数、位密度扰动水平梯度剧增,其可视为间断。     

Small perturbation method of high-frequency bistatic volumescattering from marine sediments

The first-order small perturbation method (Born approximation), as frequently applied to high-frequency scattering from marine sediments, is critically reviewed, tested for accuracy and extended. The sediment is modeled as an acoustic-fluid half space with random fluctuations in density and compressibility. Several cases of volume scattering from typical marine sand and mud sediments are presented to illustrate the effects of two important assumptions: (1) the effects of assuming the density and compressibility fluctuations are proportional, and (2) half-space effects. By relaxing the assumption that the sediment density and compressibility are proportional, the bistatic scattering cross section is significantly altered. The effects of properly modeling the sediment as a random half space (as opposed to an infinite continuum) are also discussed. In the context of first-order perturbation theory, half-space effects manifest themselves as a “modified” spectra for density and compressibility fluctuations. It is shown that, for lossy sediments and for scattering near the specular direction, half-space effects are significant and cannot be neglected. This result is significant because current models of sediment volume scattering do not include half-space effects. In addition to the theoretical model, exact numerical simulations are used to evaluate the accuracy of the perturbation model for a limited number of cases     

海浪初始谱误差演变初步分析

为了分析海浪初始场误差对于短期预报的影响,导出了海浪谱能量平衡方程的初始扰动谱线性演化方程,据此分析了数值实践中扰动谱的增长和衰减过程;在特定条件下,将初始扰动谱线性演化方程做了简化,依此考虑扰动谱持续时效问题。分析结果表明,初始谱误差是以指数形式增长或衰减的,即使在衰减情况下。持续时效也至少有1～2d的量级,初始场精度是影响海浪短期预报准确度的一个重要因素。     

垂向湍流扩散系数的不确定性对深层叶绿素最大值现象模拟的影响

深层叶绿素最大值(Deep Chlorophyll Maximum, DCM)现象的数值模拟是研究海洋表层生态系统和全球碳循环的重要组成部分之一。但是由于自身的复杂性和观测的局限性,数值模式中物理参数的不确定性给模拟结果带来了一定程度的误差。其中,垂向湍流扩散系数(vertical turbulence diffusion)是模式所包含的物理参数中很难直接通过观测来确定的参数,它在模式中的来源和取值往往具有很大的不确定性。本文通过条件非线性最优(参数)扰动(Conditional nonlinear optimal perturbation related toparameter, CNOP-P)方法,研究了垂向湍流扩散系数的不确定性对模式模拟结果的影响。我们发现,垂向湍流扩散系数对 DCM 模拟产生最大影响的 CNOP 型扰动位于生产力层的上半部分。并且,去掉生产力层内湍流扩散系数的误差,模式模拟的改进程度最高达到了 80%。可见,垂向湍流扩散对生态系统的发展和保持起着极其重要的作用,改进垂向湍流扩散系数的不确定性,对 DCM 的数值模拟有着重要意义。     

浅水分潮对海岸潮致地下水波动特征的影响

基于一维Boussinesq方程,在斜坡海岸边界条件中考虑了半日潮及其浅水分潮的综合作用,应用摄动法得到了方程的二阶解。通过与现场实测资料和数值解的比较,分析了浅水分潮对海岸潮致地下水波动特征的影响。分析结果显示,考虑浅水分潮后,方程数值解能较好地反映实测的潮致地下水波动基本特征;方程各阶摄动解虽与现场实测数据有一定误差,但基本上能反映其波动的趋势性特征。研究结果表明,浅水分潮对海岸潮致地下水波动振幅及其超高值的影响比较显著,也能较好地改善相位上的偏移,因此在对海岸潮致地下水波动特征进行研究分析时,应该考虑浅水分潮的作用。