Perturbations of the Kepler Problem in Global Coordinates

The usual action-angle variables for the Kepler Problem (the Delaunay variables) are not globally defined, leaving out some orbits (circular orbits or those lying on the xy-plane). Moreover they are trascendental functions of the physical variables, making it quite difficult to write the perturbed Hamiltonian. The way-out proposed here is to pass to a 8-dimensional rank-6 Poisson manifold, that is, to parametrize the state of the Kepler Problem with two 4-dimensional vectors mutually orthogonal and of equal norm. This revised version was published online in July 2006 with corrections to the Cover Date.     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

A simple analytical model for surface water waves on a depth-varying current

A perturbation analysis is presented in which a series of small amplitude regular waves co-exist with an arbitrarily sheared current, U(z). Assuming that the current velocity is weak, i.e. U(z)/c=O(ε), the solution is extended to O(ε²), where c is the phase velocity and ε=ak the wave steepness. This provides a first approximation to the non-linear wave-current interaction, and allows simple explicit solutions for both the modified dispersion relation and the water-particle kinematics to be derived. These solutions differ from the existing irrotational models commonly used in design and, in particular, highlight the importance of the near-surface vorticity distribution. These results are shown to be in good agreement with laboratory data provided by Swan et. al. [J. Fluid Mech (2001, in press)]. Perhaps more surprisingly, good agreement is also achieved in a number of strongly non-linear wave-current combinations, where the results of the present analytical solution are compared with a fully non-linear numerical wave-current model.     

Water wave scattering by bottom undulations in an ice-covered two-layer fluid

The scattering of plane surface waves by bottom undulations in an ice-covered ocean modelled as a two-layer fluid consisting of a layer of fresh water of lesser density above a deep layer of salt water, is investigated here by using a simplified perturbation analysis. In such a two-layer fluid there exist waves of two different modes, one with higher mode propagates along the interface and the other with lower mode propagates along the ice-cover. An incident wave of a particular mode gets reflected and transmitted by the bottom undulations into waves of both the modes so that transfer of wave energy from one mode to another takes place. The first-order reflection and transmission coefficients of two different modes are obtained due to incident waves of again two different modes by employing Fourier transform technique in the mathematical analysis. For sinusoidal bottom topography these coefficients are depicted graphically against the wavenumber. These figures show how the transfer of energy from one mode to another takes place.     

斜压大气中的地形扰动

本文主要讨论地形对天气系统的影响,研究了斜压大气中地形背风气旋的问题。用小参数法简化基本运动方程,利用青藏高原和落基山脉的实际地形,采用FFT的数值方法,考虑了不同地形、风切变、大气层结等诸因素对地形扰动的影响。结果表明:青藏高原和落基山脉东侧的地形扰动与统计结果较一致;层结对地形扰动的影响较敏感。     

A Fast Algorithm for Solving CNOP and Associated Target Observation Tests

Conditional Nonlinear Optimal Perturbation （CNOP） is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector （LSV） to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function （EOF）. The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System （GRAPES）, an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity （target） area is evaluated through two observing system simulation experiments （OSSEs）. The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors （ARPEs） in the verification region are reduced significantly compared with the ＂true state,＂ when the initial conditions （ICs） in the sensitivity area are replaced with the ＂observations.＂ The decrease of the ARPEs can be achieved for even longer prediction times （e.g., 72 h）. Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon＇s initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.     

四川“9.22”暴雨过程的波包分布及传播特征

利用NCEP/NCAR再分析资料,通过波包传播的诊断方法,对2008年9月22—27日我国川西地区持续性暴雨过程期间波包传播和积累进行了分析与研究,分析表明,波包分布及传播能明显反映出降水过程的发生、维持和结束特征。波包的大值区域与强降水区域基本一致,强降水过程基本上产生于波包扰动能量积累的高值时段或处于高位相阶段。波包值的经向和纬向传播特征表明9月22—27日川西地区持续性暴雨过程主要受西太平洋副热带高压、偏北地区和高原地区的弱冷空气、孟湾和南海向盆地输送水汽的两条水汽通道以及台风"黑格比"的共同作用。     

影响热带气旋路径的敏感性试验与研究

针对热带气旋观测中的敏感区域问题,用数值模拟的方法,以GRAPES-TCM为试验模式,对登陆中国的2个热带气旋“派比安”与“圣帕”进行了敏感性试验,并通过模拟其他4个热带气旋路径对试验结果进行了验证.结果显示,初始场的不确定性导致了热带气旋路径的不确定性,但初始场中涡旋场的变化对路径几乎没有影响,环境场中位于涡旋外、距...     

两种样本生成方法对DRP-4DVar同化方法性能影响的比较及分析

降维投影四维变分同化方法(DRP-4DVar)利用历史预报的集合来统计背景误差协方差,并将分析变量投影到样本空间下求解代价函数,因而集合样本的质量对DRP-4DVar同化方法的性能有着重要影响.文中尝试使用三维变分(3DVar)控制变量的扰动方法来产生集合样本,并与原来的历史预报扰动方法做比较.历史预报扰动样本具有随流...     

LEO卫星轨道设计中的主要摄动源影响评估

对地球低轨道卫星 (LEO)轨道设计中的摄动力模型进行了分析 ,并估计了其量级。然后针对用于GPS无线电掩星的LEO卫星轨道设计对掩星地面测点稳定性的要求 ,对力学模型进行了取舍 ,同时估计了各摄动力模型对轨道设计目标的影响