在大气运动中考虑重力加速度空间变化的问题

给出了在旋转坐标系中考虑重力加速度g的空间变化的大气控制方程组,并证明了大气总质量和总能量的守恒性,以及和取常值g时得到的结果相一致的动、位能和动、内能之间的转换关系.还讨论了在球坐标系中应用方程组时可能出现的困难,给出了在高度近似下在该系中考虑g的空间变化的方案,它可以用来建立完全弹性的非静力模式.

The Problem for Consideration of the Spatial Variation of Gravitational Acceleration in the Atmospheric Motion

A set of controlling equations for the atmospheric motion in the rotational coordinate system is presented, inclusive of the spatial variation of gravitational acceleration. It can be shown that the total atmospheric mass and energy are conservative, and the conversion between kinetic energy and internal energy, and that between kinetic energy and potential energy are similar to those in the case of constant g. Then discussions are made on the problems possibly encountered in the application of the aforementioned results in the spherical coordinates and subject to high approximations, a scheme with the spatial variation of g is suggested. With the scheme a set of controlling equations written in the height terrain following coordinates is given, on the basis of which a fully elastic nonhydrostatic model could be constructed.