四阶奇异边值问题无穷多个正解存在性的一个注记

本文考虑四阶奇异边值问题x( 4 ) =λa(t) f (t,x(t) ) ,0 相似文献   

胶州湾三维变动边界的潮流数值模拟

基于Blumberg等（1986）的河口、陆架和海洋模式，引入变边界处理技术，建立了胶州湾三维变动边界的潮流模型，模型以σ-正交曲线坐标下三维非线性潮波方程为基本方程，引入2.5阶瑞封闭方程组，采用分裂算子法数值求解方程组，利用湍封闭方程求解垂直紊动粘滞系数，采用干湿网格方法模拟潮流漫滩过程，三维变动边界潮流模型计算结果与实测值吻合良好。     

Numerical Simulation of Non-Linear Wave Propagation in Waters of Mildly Varying Topography with Complicated Boundary

In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.     

Second-Order Wave Diffraction Around 3-D Bodies by A Time-Domain Method

A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to establish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping layer is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the method is used to compute the second-order wave forces and run-up on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.     

渐新世/中新世分界的地层学事件

介绍渐新世/中新世分界面(即古近纪/新近纪分界面)附近的浮游有孔虫和钙质超微化石事件及其新年龄。2004年国际地层年代表确定该分界面位于第58长偏心率周期弱振幅处,古地磁事件C6Cn.2n底面,经天文调谐后的年龄为23.03 Ma。发生在该界面附近的生物地层学事件主要是浮游有孔虫Paragloborotalia kugleri的始现面(22.96 Ma)和钙质超微化石Sphenolithus delphix的末现面(23.11 Ma)。在南海北部东沙群岛附近的大洋钻探ODP1148站,渐新世/中新世界面以崩塌沉积物为特征,有明显沉积间断,标志南海当时有较大范围的构造运动。     

High parallelization efficiency in barotropic-mode computation of ocean models based on multi-grid boundary ghost area

In general, barotropic-mode computation requires the largest communication time in ocean models because of its iterative nature, when parallel computation is performed based on regional partitioning. In this study, reduction in the overhead time included in the communication in the parallel computation of the barotropic mode is considered to achieve a high parallelization efficiency of ocean models. We verify that the reduction in the communication frequency based on the multi-grid boundary ghost area reduces the total communication time. We find that this is because the sum of several kinds of overhead time for communication occupies a fairly large part of the total communication time. We discuss the trade-off between the decrease in communication time and the increase in computation time due to increased boundary area in such cases, leading to a determination of a suitable width of the multi-grid boundary that minimizes the total required time. We also discuss the efficiencies of the one- and two-dimensional partitioning of the model domain, when a multi-grid boundary is used. In general, two-dimensional partitioning is more efficient than one-dimensional for large partitioning numbers.     

Depth- and current-induced effects on wave propagation into the Altamaha River Estuary, Georgia

A study of sea surface wave propagation and its energy deformation was carried out using field observations and numerical experiments over a region spanning the midshelf of the South Atlantic Bight (SAB) to the Altamaha River Estuary, GA. Wave heights on the shelf region correlate with the wind observations and directional observations show that most of the wave energy is incident from the easterly direction. Comparing midshelf and inner shelf wave heights during a time when there was no wind and hence no wave development led to an estimation of wave energy dissipation due to bottom friction with corresponding wave dissipation factor of 0.07 for the gently sloping continental shelf of the SAB. After interacting with the shoaling region of the Altamaha River, the wave energy within the estuary becomes periodic in time showing wave energy during flood to high water phase of the tide and very little wave energy during ebb to low water. This periodic modulation inside the estuary is a direct result of enhanced depth and current-induced wave breaking that occurs at the ebb shoaling region surrounding the Altamaha River mouth at longitude 81.23°W. Modelling results with STWAVE showed that depth-induced wave breaking is more important during the low water phase of the tide than current-induced wave breaking during the ebb phase of the tide. During the flood to high water phase of the tide, wave energy propagates into the estuary. Measurements of the significant wave height within the estuary showed a maximum wave height difference of 0.4 m between the slack high water (SHW) and slack low water (SLW). In this shallow environment these wave–current interactions lead to an apparent bottom roughness that is increased from typical hydraulic roughness values, leading to an enhanced bottom friction coefficient.     

Characteristics of the boundary layer at the bottom of a solitary wave

The results of direct numerical simulations of the boundary layer generated at the bottom of a solitary wave are described. The numerical results, which agree with the laboratory measurements of Sumer et al. (2010) show that the flow regime in the boundary layer can be laminar, laminar with coherent vortices and turbulent. The average velocity and bottom shear stress are computed and the results obtained show that the logarithmic law can approximate the velocity profile only in a restricted range of the parameters and at particular phases of the wave cycle. Moreover, the maximum value of the bottom shear stress is found to depend on the dimensionless wave height only, while the minimum (negative) value depends also on the dimensionless boundary layer thickness. Diagrams and simple formulae are proposed to evaluate the minimum and maximum bottom shear stresses and their phase shift with respect to the wave crest.     

机载激光雷达对青岛及周边海域的气溶胶探测

工作波长为532 nm的机载大气环境探测激光雷达AEDAL（Atmospheric Environment Detecting Airborne Lidar）装载在CMS_3807飞机上,于2005年11月7～11日期间在青岛地区及周边海域上空进行了飞行探测.此次实验的目的有两个：验证我国用于大气环境探测的激光雷达技术已经具备从地基向空基乃至天基发展的条件;获得青岛地区及周边海域边界层结构及大气气溶胶时空分布变化的特点.激光雷达的高时空分辨率为获取飞行路径上的边界层结构及气溶胶时空分布提供了可能.为了研究下垫面对边界层及气溶胶时空分布的影响,预定的飞行路径上包含了丰富的地形变化,有城市、丘陵、海区等.通过给出11月8日及11日的探测结果,不仅得到了不同地区边界层结构及气溶胶的时空分布特点,还可以看到冷锋、地形、地面气象场等因素对它们的影响.     

常Q滞弹性介质地震波动数值模拟——时域本构优化逼近

在地震波动模拟中计入常Q滞弹性阻尼,可有效降低模拟波形的误差.就时域有限差分和有限元模拟而言,常基于广义标准线性体建立阻尼介质的时域本构逼近.广义标准线性体由若干标准线性体并联得到,增加标准线性体个数能有效提高模拟精度,但计算量及计算存储将成倍增长.目前尚未有普适的标准线性体个数优化取值方案.本文基于广义标准线性体参数的非线性优化拟合方法,详细分析了时域本构逼近误差的影响因素,清楚揭示了逼近误差仅取决于频带宽度,与频带上下限取值无关这一特性,阐明了构建具有普适性标准线性体个数优化取值方案的可行性.论证了波形模拟精度主要取决于波传播距离与模拟波长的比值以及标准线性体的个数取值.综合考虑上述两个控制因素,结合在波动正反演问题中广为采纳的波形时频误差衡量准则,对不同Q值介质给出了标准线性体个数优化取值表.进一步,本文提出采用不同个数标准线性体以近似不同Q值的阻尼介质时域本构,解决了以往波动数值模拟中统一采用相同个数标准线性体而导致的计算量及计算存储浪费或模拟精度低下等问题,并基于数值实验验证了这一方法的精度.本文工作对推进滞弹性介质波动数值模拟及其在全波形反演问题中的应用具有理论价值和实践意义.