大气运动基本方程组的稳定性分析

Stability for the Basic System of Equations of Atmospheric Motion

以分层理论提供的基本方法分析大气运动基本方程组的拓扑学特征;证明局地直角坐标系中的大气运动基本方程组在无穷可微函数类中是稳定方程;给出局部解意义下使方程组典型定解问题适定的充要条件;讨论大气动力学中有关“以过去推测未来”以及当涉及应用问题时如何修改定解条件和下垫面的选择等问题;指出在通常假设下,基本方程组中的3个运动方程和连续方程完全决定了这个方程组的性质.

The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory; It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric moron was stable equations in infinitely differentiable function class; In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution was well posed were also given. Such problems as something about ＂speculating future from past＂ in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed; It is also pointed out that trader the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.