Some modifications of Stokes' formula that account for truncation and potential coefficient errors

 Stokes' formula from 1849 is still the basis for the gravimetric determination of the geoid. The modification of the formula, originating with Molodensky, aims at reducing the truncation error outside a spherical cap of integration. This goal is still prevalent among various modifications. In contrast to these approaches, some least-squares types of modification that aim at reducing the truncation error, as well as the error stemming from the potential coefficients, are demonstrated. The least-squares estimators are provided in the two cases that (1) Stokes' kernel is a priori modified (e.g. according to Molodensky's approach) and (2) Stokes' kernel is optimally modified to minimize the global mean square error. Meissl-type modifications are also studied. In addition, the use of a higher than second-degree reference field versus the original (Pizzetti-type) reference field is discussed, and it is concluded that the former choice of reference field implies increased computer labour to achieve the same result as with the original reference field. Received: 14 December 1998 / Accepted: 4 October 1999     

局部和全局边界条件的组合

时域局部人工边界是以行波概念为基础的,原则上不能用于模拟零频分量（消减运动）。Ｗｏｌｆ提出了能同时模拟零频分量和行波的双渐近－多向透射边界。本文指出,在这一组合中的双渐近边界的高频渐近项是不合理的,还查能降低模拟精度。据此,本文提出一种概念清楚、简便实用的组合方案－多次射透－静力边界,并通过数值试验对此方案进行检验。     

Darcys Law Expressed by Chemical Index

Ｉｎ 18 5 6 ,ＨｅｎｒｙＤａｒｃｙｐｕｂｌｉｓｈｅｄｈｉｓｌａｗ ,ｔｈｅＤａｒｃｙ’ｓｌａｗ ,ｅｘｐｒｅｓｓｅｄｂｙｈｙｄｒａｕｌｉｃｉｎｄｅｘｔｈｒｏｕｇｈａｌｏｎｇ ｔｅｒｍｅｘｐｅｒｉｍｅｎｔｏｆｗａｔｅｒｐｅｒｍｅａｔｉｏｎｉｎｍｕｌｔｉ ｍｉｎｅｒａｌｍｅｄｉｕｍ (Ｘｕ ,1986 ) ,ｗｈｉｃｈｎｏｔｏｎｌｙｍｅｔｔｈｅｕｒｇｅｎｔｎｅｅｄｏｆｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｓｏｃｉａｌｅｃｏｎｏ ｍｙａｎｄｐｒａｃｔｉｃｅｆｏｒｃａｌｃｕｌａｔｉｏｎｏｆｗｅｌｌｗａｔｅｒｑｕａｎｔｉｔｙａｔｔ…     

From Celsius to Chaos to Cyclones: Using Temperature-Conversion Equations to Introduce Advanced Mathematical Concepts in Earth Science Courses

The Fahrenheit-to-Celsius temperature-conversion equation is a basic component of many introductory earth science courses. Despite its simplicity, it presents a challenge to students and instructors alike because residents of the United States are unfamiliar with the Celsius scale. By solving for the point at which these two temperature scales are equal, it is possible to use the equations for temperature conversion as a springboard to more advanced topics. It is demonstrated that temperature-conversion equations and chaotic equations can be solved using identical numerical and graphical techniques. As a result, the fundamental concepts of chaos theory and numerical methods can be introduced to students in the context of the simplest equations in the earth sciences. These solution methods are applied to the quantitative theory of the extratropical cyclone as an example of the utility and broad scope of this educational approach.     

中国登陆热带气旋与太平洋海表温度的关系

根据1951～2000年中国登陆热带气旋与厄尔尼诺年、拉尼娜年的关系分析,得到了一些重要认识：(1) 在厄尔尼诺年,中国登陆热带气旋数偏少;(2) 厄尔尼诺事件强度越大,中国登陆热带气旋数越少;(3) 厄尔尼诺事件的结束时间若超过5月1日,那么次年中国登陆热带气旋数偏少;(4) 中国登陆热带气旋数的特多年主要集中在拉尼娜年;(5) 在拉尼娜次年,中国登陆热带气旋数偏少;(6) 中国登陆热带气旋强度越大,在厄尔尼诺年出现机会越少;(7) 在厄尔尼诺年,中国初旋偏迟,终旋偏早。同时对其机理进行了探讨。     

半圆型结构冰压力的物理模拟试验研究

利用DUT-1非冻结合成模型冰开展1:25冰对半圆型构件的物理模拟试验研究. 首先用简单的斜面构件的物理模拟试验检验了整体试验装置和技术设备的可靠性, 然后以同样比尺进行2种冰厚在5个不同水位条件的系列试验, 获得了模型冰排在半圆型构件前的破碎堆积现象和作用于构件上的水平和垂直作用力过程.结合实测模型冰物理和力学指标, 通过优化组合, 拟合出半圆型防波堤冰荷载的试验公式. 这些公式包含了冰对半圆型结构的弯曲破坏作用力、挤压破坏作用力及爬坡和堆积作用力.     

圆形建筑物倾斜观测的新方法

基于全站仪和光电测距仪,本文提出了圆形建筑物倾斜观测的新方法,并推导出了相应的计算公式。     

关于风浪预报公式和风区宽度的注记

从定常波的风浪波高随风距成长的预报公式出发 ,在一定条件下 ,导出各波向上风浪波高分量与该波向上的风距之间的关系 ,以便在不规则风区上推算风浪波高和平均波向 ;同时 ,对风区宽度作了定量化的分析。     

Corrected Formula of Bed Resistance Coefficient for Plane Numerical Simulation of Tidal Current

By means of a logarithm law for the velocity profile,a corrected formula of bed resistancecoefficient,which involves many factors such as gradient of still water depth,variation of surfaceelevation,flow direction,and so on,is derived from the 3D governing equations of tidal current by aver-aging over the whole water depth.Theoretical analysis and application have shown that the 2D plane tidalcurrent numerical model would be more reasonable and could be applied to steep bottom topographywhen the corrected bed resistance coefficient is used,therefore the results of reproduction simulation andengineering calculation would be more scientific and reasonable.