完整Coriolis力作用下近惯性波的数学模型及其动力学机制研究

大气及海洋运动对人类的影响一直是科学家关注的热点问题，揭示其动力学机制对实际预报等有重要意义。本项目是在申请者前期对完整Coriolis力作用下大尺度Rossby波动力学理论研究基础上，进一步研究Coriolis参数水平分量对中尺度近惯性波动的影响。一方面，从地球流体力学基本方程组出发，通过尺度分析法等数理方法构建完整Coriolis力作用下近惯性波动数学模型，包括线性及非线性模型；另一方面，利用正交模等方法研究具有垂向加速的线性近惯性波频散关系及传播机制，通过导数展开等弱非线性法及数值模拟研究非线性模型，获得非线性近惯性波演变所满足的非线性发展方程，借助解析及数值求解，与实际观测现象进行比较进而揭示其波动力学机制。有望完善线性惯性波理论、建立相应非线性波理论及解释Coriolis参数水平分量对短、长期波动现象动力学影响，揭示相应物理机制，从而完善“传统近似”之不足。

The influence of atmospheric or oceanic motion on human beings has always been a hot issue of concern to scientists. It is important to reveal the mechanism of atmospheric and oceanic motion for practical prediction. This project, based on the obtained theories of large scale Rossby wave mechanics under complete Coriolis force during the applicant's former investigations, is mainly on the studies of the effects on mesoscale near-inertial waves from the horizontal component of Coriolis parameter. On the one hand, both the linear and nonlinear mathematical model for near-inertial waves with complete Coriolis force are obtained by using methods of scales analysis etc. from the primitive equations of Geophysical Fluid Mechanics. On the other hand, the obtained linear model including the acceleration of vertical velocity is investigated by using normal mode analysis, the dispersion relation and wave propagating mechanics are given. The nonlinear model is discussed by using weak nonlinear methods, such as the derivative expansions, numerical simulations, the nonlinear equations are derived to simulate the evolution of nonlinear near-inertial waves, and solve them by analytical or numerical method. It is significant to advance the linear theories and to work up the nonlinear theories of near-inertial waves, and it will explain the mechanical effects on short or long term weather events from the horizontal component of Coriolis parameter, much more physical nature of the motion is further revealed. It will both improve the deficiency of the "traditional approximation" and provide more reasonable theoretical basis.