Achievements in Geophysical Fluid Dynamics
地球流体力学的研究与进展

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.