作　　者： ; ; ; ;

机构地区： 中国科学院大气物理研究所

出　　处： 《大气科学》 2003年第4期689-711,共23页

摘　　要： 简要介绍中国科学院大气物理研究所七十多年来在理论与计算地球流体力学方面的若干研究及其新的进展。在理论地球流体力学方面,介绍了长波动力学及线性稳定性问题、弱非线性理论及行星波动力学以及用Arnold方法(能量-Casimir方法)研究大气和海洋中各种流体运动的非线性稳定性问题的成果。此外,对扰动演变、扰动和基流相互作用及热带大气动力学中的第二类不稳定条件(CISK)也作了简要的介绍。在计算地球流体力学方面,主要内容包括:用物理观点和数学分析相结合的方法阐述了造成计算紊乱和计算不稳定的机理,论证计算稳定性、算子非负性和能量守恒性之间的密切关系,对国际上流行的瞬时能量守恒的格式找到非线性计算不稳定的特解;设计出一批内部协调并且具有完全总能量守恒的差分格式(包括隐式的、显式的和高精度的),发展了多种经济省时算法等等。此外,对近年来新发展的总能量守恒的半拉格朗日格式,多守恒格式及辛几何算法重点作了介绍。 This survey is concerned with some main results and achievements in theoretical and compu-tational geophysical fluid dynamics obtained by the scientists of the Institute of Atmospheric Physics, Chinese Academy of Sciences. In the field of theoretical geophysical fluid dynamics, the contents are: long-wave dynamics and linear stability problems, weakly-nonlinear theory and planetary-wave dynam-ics, nonlinear stability criteria of atmospheric and oceanic motions established by Arnold method (ener-gy-Casimir method), the evolution of disturbance, the interaction of disturbance and basie state, and the conditional instability of the second kind (CISK) in the tropical atmospheric dynamics. For computa-tional geophysical fluid dynamics, the mechanism of computational disorder and instability is explained from both physical consideration and rnathematical analysis. The close relationship among computational stability, non-negative of operators and energy conservation is discussed. The finding of the nonlinear unstable solution of some internationally popular instantaneous energy conservation schemes and the de-sign of a series of explicit, implicit and high-resolution schemes which are cornpletely squarely conserva-tive and harmonic inside are presented. The development of many economic algorithms is described. Moreover, energy-conserving semi-Lagrangian scheme, multi-conservation scheme and sym-plectic difference scheme developed in recently years are briefly introduced.

关 键 词： 地球流体力学 能量守恒 辛几何算法 经济算法

领　　域： [理学] [理学]