The Problem for Consideration of the Spatial Variation of Gravitational Acceleration in the Atmospheric Motion
在大气运动中考虑重力加速度空间变化的问题

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.