On the problem of boundary conditions in isentropic coordinates

The main advantages of constant potential enthalpy as a vertical coordinate are weaker horizontal velocity gradients in frontal regions and a higher vertical resolution. A disadvantage is the intersection of isentropes with the ground and folding of these surfaces. A numerical model is proposed to overcome the difficulties imposed by the intersection of isentropes with the ground. The model contains a physical and computational domain. The top and bottom surfaces of the computational domain are isentropes whereas the physical domain of the flow confined above by a free surface of constant pressure, and the bottom of this domain is the surface of the earth. In the present study the top surfaces of these two domains coincide (θ _T, P_Tare constants in space and time). The model was tested for the study of frontogenesis and cyclogenesis and integrated for 7 days. The results correspond to enstrophy-conserving finite difference scheme.     

微机大地测量数据库系统的数据模型化

本文论述了微机大地测量数据库系统的数据模型化问题,所设计的概念模式与大地测量实际具有较高的模拟精确度,逻辑设计考虑了模式的优化和DB的性能要求。文中对分块存贮方法的利弊进行了较深入的讨论,并提出了克服弊端的相应措施。     

Theory of anisotropic dynamic ray tracing in ray-centred coordinates

A 4×4-propagator matrix formalism is presented for anisotropic dynamic ray tracing, including the propagation across curved interfaces. The computations are organised in the same way as in ervený's well-known isotropic propagator matrix formalism. Attention is paid to cases where double eigenvalues of the Christoffel matrix result in unstable expressions in the dynamic ray tracing system, but where geometrical spreading is well-behaved.     

Digital astro-geodetic camera system for the measurement of the deflections of the vertical: tests and results

This study introduces the new results of a novel low-cost digital zenith camera system operated in Turkey that uses astronomical and geodetic instrumentation. Currently, it is possible to determine deflections of the vertical (DoV) components by using a vast amount of information gathered from geo-referenced star images, tilt measurements, and Global Navigation Satellite System technology. This new design of an astro-geodetic camera system is used for calculating DoV components with 12 independent solutions on a test station in Istanbul, and additional observations were performed to investigate the external accuracy of the system on a test network. A specific leveling method is developed to align system toward the zenithal direction. The final results of the observations on a test station located in Istanbul indicate that the accuracy of the system is about ±0.19 arc-seconds in latitude and ±0.28 arc-seconds in longitude determination. The system has been further tested on a network with 4 control points that have averagely 20?km baselines. At the test network, the root mean square of the average value of the vertical deflections is calculated as ±0.36 arc-seconds. Furthermore, DoV components are compared with the values that are calculated using global geopotential models.     

Inertial Instability of Arbitrarily Meandering Currents Governed by the Eccentrically Cyclogeostrophic Equation

Using natural coordinates, we have derived a criterion for the inertial instability of arbitrarily meandering currents. Such currents, governed by the eccentrically cyclogeostrophic equation, are adopted as the basic current field for the parcel method. We assume that any virtual displacement which is given to a water parcel moving in the basic field has no influence on this field. From the conservation of mechanical energy for a virtual displacement we derive an inertial instability frequency ω _m = [(f + 2u/r)Z]^0.5 for the eccentrically cyclogeostrophic current, where f is the Coriolis parameter, u the velocity (always positive), r the radius of curvature of a streamline (negative for an anticyclonic meander), and Z the vertical component of absolute vorticity. If ω _m ² is negative, the eccentrically cyclogeostrophic current becomes unstable. Although the conventional, centrifugal instability criterion, derived from the conservation of angular momentum in a circularly symmetric current field, has a certain meaning for a monopolar vortex, it contains a radial shear vorticity that is difficult to use in arbitrarily meandering currents. The new criterion ω _m ² contains a lateral shear vorticity that is applicable to arbitrarily meandering currents. Examining instabilities of concentric rings with radii of 50–100 km, we consider reasons why the anticyclonic supersolid rotation has been very much less frequently observed than the cyclonic supersolid rotation, despite a prediction of some common stability and a rapid change in radial velocity gradient for the former. Classifying eccentric streamlines into the large and small curvature-gradient types, we point out that the large-gradient curvature in anticyclonic rings is apt to be unstable. This revised version was published online in July 2006 with corrections to the Cover Date.     

A generalized coordinate ocean model and a comparison of the bottom boundary layer dynamics in terrain-following and in z-level grids

Sensitivity studies with a new generalized coordinate ocean model are performed in order to compare the behavior of bottom boundary layers (BBLs) when terrain-following (sigma or combined sigma and z-level) or z-level vertical grids are used, but most other numerical aspects remain unchanged. The model uses a second-order turbulence closure scheme that provides surface and BBL mixing and results in a quite realistic climatology and deep water masses after 100 year simulations with a coarse resolution (1° × 1°) basin-scale terrain-following grid. However, with the same turbulence scheme but using a z-level grid, the model was unable to produce dense water masses in the deep ocean. The latter is a known problem for coarse resolution z-level models, unless they include highly empirical BBL schemes.A set of dense water overflow experiments with high-resolution grids (10 and 2.5 km) are used to investigate the influence of model parameters such as horizontal diffusivity, vertical mixing, horizontal resolution, and vertical resolution on the simulation of bottom layers for the different coordinate systems. Increasing horizontal diffusivity causes a thinner BBL and a bottom plume that extends further downslope in a sigma grid, but causes a thicker BBL and limited downslope plume extension in a z-level grid. A major difference in the behavior of the BBL in the two grids is due to the larger vertical mixing generated by the turbulence scheme over the step-like topography in the z-level grid, compared to a smaller vertical mixing and a more stably stratified BBL in the sigma grid. Therefore, the dense plume is able to maintain its water mass better and penetrates farther downslope in the sigma grid than in the z-level grid. Increasing horizontal and vertical resolution in the z-level grid converges the results toward those obtained by a much coarser resolution sigma coordinate grid, but some differences remain due to the basic differences in the mixing process in the BBL.     

Dispersion and stability analyses of the linearized two-dimensional shallow water equations in Cartesian coordinates

In the present study, a Fourier analysis is used to develop expressions for phase and group speeds for both continuous and discretized, linearized two-dimensional shallow water equations, in Cartesian coordinates. The phase and group speeds of the discrete equations, discretized using a three-point scheme of second order, five-point scheme of fourth order and a three-point compact scheme of fourth order in an Arakawa C grid, are calculated and compared with the corresponding values obtained for the continuous system. The three-point second-order scheme is found to be non-dispersive with grid resolutions greater than 30 grids per wavelength, while both the fourth-order schemes are non-dispersive with grid resolutions greater than six grids per wavelength. A von Neumann stability analysis of the two- and three-time-level temporal schemes showed that both schemes are stable. A wave deformation analysis of the two-time-level Crank–Nicolson scheme for one-dimensional and two-dimensional systems of shallow water equations shows that the scheme is non- dispersive, independent of the Courant number and grid resolution used. The phase error or the dispersion of the scheme decreases with a decrease in the time step or an increase in grid resolution.     

一般曲线坐标系下波浪传播的数值模拟

在曲线坐标系下,建立了缓变水深水域波浪传播的数值模拟模型.模型适宜于复杂变化的边界形状,克服了各种代数坐标变换的局限性.在建立模型时,将原始的椭圆型缓坡方程的近似型式——依赖时间变化的抛物型方程,作为控制方程,既克服了一般抛物近似方法的缺点,又便利了方程的求解;从开边界条件、不同反射特性的固壁边界条件相统一的表达式出发,对边界条件进行处理;用ADI法数值求解控制方程.对模型的验证表明,数值解与物模实验值吻合良好,模型对于具有复杂边界的工程实际有较强的适应性.     

A Numerical Model of Nonlinear Wave Propagation in Curvilinear Coordinates

For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries,a numerical model is developed in curvilinear coordinates. In the model,the Boussinesq-type equations including the dissipation terms are employed as the governing equations. In the present model,the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables,instead of the usual primitive velocity variables. The introduction of utility velocity variables which...     

CASS 8.0在绘制地质工作部署图坐标转换中应用

针对多金属矿勘探中测点坐标的批量生成过程步骤繁琐的问题,文中提出了一种利用CASS8.0直接生成1:1万高精度磁法勘探测点及1:1万激电中梯探测测点坐标的思路。通过利用现有地形地质图以及专业绘图软件CASS8.0在制图及坐标转换方面的优越性,直接生成可以应用于手持GPS测量仪的数据格式文件和绘制出可以用于野外找点的地形地质图,达到测绘坐标点在地图上快速导入导出的效果。在内蒙古自治区额济纳旗黑鹰山南区铅多金属矿普查项目的工作中,针对工区面积大,地形复杂,在工作部署中,需要布置探测点数量庞大,采用原始方法计算并人工将每个测点坐标输入手持GPS定位仪中的工作量大且极易出错,探测点点位不能根据实际地形合理规避危险区域或者障碍物（悬崖、峭壁等）等问题,通过利用黑鹰山南区铅多金属矿普查区地形地质图及CASS8.0绘图方面的优越性,批量对工作部署图中测点进行定位编号并调整,从CASS8.0导出坐标数据点并导入天宝R4 GPS手持定位仪中的方法,避免了人工输入数据出错的问题,合理规划了探测路线,提高工作效率,保障了工作人员的生命安全,该应用表明,此方法在工作部署图绘制中更加直观、方便,解决大面积比例尺工作部署图坐标导出导入问题,并且效率极高,在工作中取得了较好的效果。