摘要
针对以往大气动力学方程和气候动力学方程数学研究所使用模式的不足之处，本文作了改进，使数学模型更接近于实际情况。这些包括，（１）取大气上界气压为零，而非某个正的（小）常数；（２）消除了整层无辐散近似，从而使地面气压为直接的预报量，但在地面气压预报方程中加入了水平湍流扩散项（平滑）；（３）对大气运动的内热源的辐射传输过程和水汽相变过程作了合理的处理，而非看作已知的外强迫，用适当的方法可以用解析函数较好地逼近这些过程。另外还提出合理的边界条件。我们的目的是要证明这样提出的初—边值问题的解的存在性，以后还可研究其基本性质和长期行为。
With elimination of some approximations or assumptions which exist in the past mathematic models of weather and climate dynamics for mathematical analyses, a new mathematic model for modern mathematical analyses is developed in this paper. This model is closer to those which are applied to the practical predictions of weather and climate. (a) Its top is selected at p (pressure)=0 rather than p>0; (b) the model includes an explicit prediction of surface pressure with horizontal smoothing operator (representing the turbulent diffusion of density), and eliminates the approximation of verticially integrated nondivergence; and (c) the heating is caused by internal sources depending on the atmospheric motion rather than by an external one, and the internal heating function due to the phase change of water vapor is approximated by some properly analytical functions suitable for mathematical analyses. The corespondent boundary and initial conditions are also proposed. This paper is to prove the existence of solution to the problem (equations plus boundary and initial conditions). The general structure and long-term behaviors of the model are to be investigated in the next step.
出处
《大气科学》
CSCD
北大核心
1998年第4期408-417,共10页
Chinese Journal of Atmospheric Sciences
关键词
动力学模型
数学分析
气候动力学
大气动力学
atmospheric dynamics climate dynamics boundary condition existence of solution
