The Expansion of the Distance Between Two Arbitrary Gravitating Points as Applied to Specific Models of Celestial Bodies

For the complete system of biharmonic functions a suitable representation in spheroidal coordinates is found. It is used for expanding the distance between two arbitrary gravitating points and its inverse quantity in appropriate series. Such expansions can be of interest and useful in a number of problems of celestial mechanics and stellar dynamics.     

河口海岸三维水流数值模型中几种垂向坐标模式研究述评

回顾了近年来国内外河口、近岸海域三维斜压水流数值模式研究的进展,着重讨论了不同垂向坐标下三维水流模式的发展状况以及存在的问题。地形拟合坐标(σ坐标)模式可以很好地拟合床面地形和自由面,已在物理海洋学中被广泛使用。但在地形变化剧烈,尤其在密度层结效应明显的海域,σ坐标模式中的水平压强梯度力误差会引起伪密度流。寻求高精度的数值模式以及更加有效的拟合坐标变换将是值得努力的方向。     

Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems

This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild-slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the confonnal system. The computational results show that the confonnal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical confonnal grid system.     

Baroclinic Buoyancy-Inertia Joint Stability Parameter

At present, the barotropic buoyant stability parameter has been derived from a vertical virtual displacement of a water parcel. The barotropic inertial stability parameter in the eccentrically cyclogeostrophic, basic current field was derived in 2003 from a horizontal cross-stream virtual displacement of a parcel. By expressing acceleration of a parcel due to a virtual displacement, which is arbitrarily sloping within a vertical section across the basic current, in terms of natural coordinates, we derived the vertical component of baroclinic buoyant stability parameter B ₂ ², the horizontal component of baroclinic inertial stability parameter I ₂ ², the baroclinic joint stability parameter J ², its buoyant component B ² and its inertial component I ². B ² is far greater than I ₂ ², and when neglecting relative vorticity except for vertical shear, a downward convex curve of J ² plotted against the slope of a virtual displacement follows a trend of B ² curve. If a parcel displaces along a horizontal surface or an isopycnal surface, however, B ² vanishes, and J ² becomes equal to I ². Actual parcel is apt to displace not only along the bottom slope, but also along the sea surface and an isopycnal interfacial surface, which is approximately equivalent to an isentropic surface, preferred by lateral mixing and exchange of momentum. Such actual displacement makes B ² vanishing, and grants I ² an important role. The present analysis of I ² examining effects due to curvature and horizontal and vertical shear vorticities are useful in deepening our understanding of baroclinic instability in actual oceanic streams.     

Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth

Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.     

长江口三维潮流数值计算及动力分析

采用三维动力学数学模型对长江口潮流场进行了计算，对长江口潮流流态在一个潮周期内逐时进行了分析，并对长江口南支盐水倒灌从动力学角度进行了初步探讨。计算结果表明：文中模型较好地重演长江口潮流场，可以用于大型复杂河口工程实际中的潮流场的计算和分析。     

GPS、GLONASS、GALILEO三大系统间时间系统以及坐标系统的转换

在当今的三大定位导航系统中,它们各自用着自己的时间标准和坐标框架,这使得我们在进行多样数据处理与数据融合时很不方便。这就需要我们对此三个系统的时间系统以及坐标系统进行有效的转换,本文就是基于这样的需求,详细介绍并分析了此三大系统中各自的时间系统与坐标系统,通过对多方资料的综合、推证与计算,综合得出GPS、GLONASS以及GALILEO三大系统间的时间转换方法及坐标转换模型与公式。而且,这些转换公式与方法所得出的结果是完全能满足绝大多数用户的精度需求的。     

GPS/GLONASS定位系统融合的坐标转换研究

GPS和GLONASS卫星定位系统分别采用WGS-84和PZ-90坐标系。为统一两种卫星定位成果,欧、美、俄于20世纪90年代各自求出两坐标系之间的转换参数。目前三种参数尚未统一,对GPS/GLONASS联合定位造成较大影响。本文针对国外介绍PZ-90和WGS-84坐标系相互转换时常用的转换模型及三种不同转换参数进行比较分析。分别选用地面GPS参考站坐标和GLONASS卫星轨道坐标,用三种坐标转换参数进行转换,对转换结果差异及其对单点定位和相对定位精度造成的影响进行全面分析比较,得出一些有益结论。     

Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.