Internal waves in a rotating stratified spherical shell: asymptotic solutions

Summary. Small amplitude oscillations of a rotating, density-stratified fluid bounded by a spherical shell are examined. No restrictions are placed on the thickness of the shell. The internal mode spectrum is examined in the complete rotation-stratification parameter range including the regime that is appropriate for a plausible stratification distribution in the Earth's fluid core. A mathematical model is derived in terms of an eigenvalue PDE of mixed type. The existence of oscillatory solutions is exhibited in the limits of no rotation and no stratification. The frequency spectrum is extended asymptotically away from these limiting cases. A reduction in the complexity of the PDE for modes oscillating at the inertial frequency is exploited. A variational formulation is constructed in which the stratification parameter is treated as an eigenvalue of the system for fixed wave frequency. The spectral information is again extended asymptotically away from these 'accessible' points. Although the PDE reduces to Laplace's tidal equations (LTE) only under stringent parameter restrictions, it is observed that aspects of the behaviour of low frequency LTE modes are reproduced in the general model.     

Reflection effect in close binaries. II. Distribution of emergent radiation from the irradiated component along the line of sight

We have calculated the effects of irradiation from a point source observed at infinity. Plane-parallel approximation and spherically-symmetric approximations are employed in calculating the self-radiation field for the sake of comparison. It is found that there are considerable changes in the radiation received at infinity between the approximation of plane-parallel stratification and spherical symmetry.     

Interannual variability of low-degree gravitational change, 1980–2002

Time variations in the Earths gravity field at periods longer than 1 year, for degree-two spherical harmonics, C₂₁, S₂₁, and C₂₀, are estimated from accurately measured Earth rotational variations. These are compared with predictions of atmospheric, oceanic, and hydrologic models, and with independent satellite laser ranging (SLR) results. There is remarkably good agreement between Earth rotation and model predictions of C₂₁ and S₂₁ over a 22-year period. After decadal signals are removed, Earth-rotation-derived interannual C₂₀ variations are dominated by a strong oscillation of period about 5.6 years, probably due to uncertainties in wind and ocean current estimates. The model-predicted C₂₀ agrees reasonably well with SLR observations during the 22-year period, with the exception of the recent anomaly since 1997/1998.     

球面四元三角网的复杂拓扑关系计算

针对已有球面四元三角网拓扑关系计算方法不能处理带空洞复杂目标的情况,提出了基于公共三角格网来计算球面四元三角网复杂拓扑关系,该方法能准确判断出带空洞复杂目标的拓扑关系,为全球空间分析和应用提供了新的思路。     

基于QTM的海平面上升分析与模拟

针对海平面上升影响范围分析与模拟这一国际前沿问题,通过研究基于球面四元三角网(QTM)的关键技术问题,包括复杂拓扑关系计算、LOD剖分、球面水淹分析、基于QTM的多分辨率的DEM数据组织方法和分析精度的相关性评定等,以.Net和Direct3D为开发工具,设计开发了基于QTM的海平面上升影响范围评估模型。该研究结果可为全球海平面上升影响的防灾减灾决策提供有效支撑,并推动了球面数据模型和球面格网拓扑分析的理论成果在全球变化预测相关领域的应用进展。     

基于球谐函数模型的电离层预报

据球谐函数模型系数的特点,采用ARMA(p,q)模型对球谐函数模型系数进行预报,由球谐函数模型计算电离层VTEC。提出了针对某一时刻球谐系数进行预报的方法,相比传统按照时刻顺序的预报,预报时间大大延长,预报精度也有所提高。试验结果表明,相比中高纬度地区,低纬度地区预报精度偏低,同时,一天中不同时刻预报结果有所差别,前半天的预报效果明显好于后半天。     

Analysis of the three-dimensional stellar velocity field using vector spherical functions

We apply vector spherical functions to problems of stellar kinematics. Using these functions allows all of the systematic components in the stellar velocity field to be revealed without being attached to a specific physical model. Comparison of the theoretical decomposition coefficients of the equations for a particular kinematical model with observational data can provide precise information about whether the model is compatible with the observations and can reveal systematic components that are not described by this model. The formalism of vector spherical functions is particularly well suited for analyzing the present and future (e.g., GAIA) catalogs containing all three velocity vector components: the propermotions in both coordinates and the radial velocity. We show that there are systematic components in the proper motions of Hipparcos stars that cannot be interpreted in terms of the linear Ogorodnikov-Milne model. The same result is also confirmed by an analysis of the radial velocities for these stars.     

Experimental investigation of the harmonic generation by waves over a submerged plate

Experiments in a wave flume have been performed to analyse the nonlinear interaction between regular gravity waves and a submerged horizontal plate used as breakwater. A new method, based on the Doppler shift generated by a moving probes, has been used to discriminate the incident fundamental mode and the reflected fundamental mode. The relationships of the reflection and transmission coefficients to the wave number at different submergence depth ratios are presented. The accurate discrimination, by this method, of the phase-locked and free modes allows the quantification of the higher harmonics generated by the breakwater and the analysis of the nonlinear interaction between the waves and the submerged plate. The transfer of energy from the fundamental mode to higher harmonics is very large in the cases of small submergence depth ratios. The vortices produced at the edges take part in the production of higher harmonics by interaction with the free surface but involve, at the same time, a dissipation process that increases the efficiency of the breakwater.     

变异函数模型参数的非线性加权总体最小二乘法

针对球状模型和指数模型两种变异函数模型线性化后的系数矩阵具有非线性形式,系数矩阵元素含有随机误差等问题,该文使用非线性加权总体最小二乘法估计变异函数模型参数。以高程异常数据为例,利用变异函数值的点对数定权法和系数矩阵中距离值的方差-协方差传播律定权法迭代解算参数,并与最小二乘法,加权最小二乘法和非线性总体最小二乘法进行对比分析。实验结果表明:非线性加权总体最小二乘法能够得到更高精度的变异函数模型参数。