层结流体中完整Coriolis力作用下波动力学理论若干问题研究

This project, based on the obtained theories of wave mechanics with complete Coriolis force in barotropic fluid, is mainly on the studies of some problems of wave mechanics with complete Coriolis force in more realistic and reasonable stratified fluid. On the one hand, starting from the basic equations of geophysical fluid dynamics, a potential vorticity conservation equation for stratified fluid with complete Coriolis force is obtained by using methods of perturbation expansions; a series of mathematical models are established through derivative expansion method, and operator theories when complete Coriolis force and multiple physical factors are considered; meanwhile, homotopy perturbation method, Adomian decomposition method and numerical calculation are used for the corresponding mathematical models. Then we can study the influence of the Coriolis force and the physical factors in order to explain the nonlinear fluctuation and some weather events. On the other hand, starting from the basic equations, mathematical model of the evolution of the nonlinear near inertial waves are derived with complete Coriolis force in stratified fluid. The influence of Coriolis force on its motion is studied by means of analytical and numerical solutions, and the physical nature of the motion is further revealed. It will provide an important theoretical basis for the research and application of marine physics, atmospheric dynamics, numerical weather prediction and weather events.

本项目是在申请者对正压流体中完整Coriolis力作用下的波动力学理论研究的基础上，进一步研究更为真实的层结流体中完整Coriolis力作用下波动力学理论的若干问题。一方面，从地球物理流体动力学的基本方程组出发，通过摂动展开法等得到完整Coriolis力作用下层结流体的位涡守恒方程；采用导数展开法、算子理论建立完整Coriolis力及多物理因素作用下的层结流体运动的一系列数学模型；利用同伦摂动法、Adomian分解法及数值计算求解相应数学模型，进而研究完整Coriolis力及物理因素的影响，解释非线性波动及某些天气事件现象等若干问题。另一方面，从基本方程组出发，导出完整Coriolis力作用下的层结流体非线性近惯性波演变所满足的数学模型，通过解析与数值求解研究Coriolis力对其运动的影响，揭示其运动的物理本质。为海洋物理、大气动力、数值天气预报及天气事件的研究及应用提供理论依据。

大气及海洋运动对人类生活及生存有着重要的影响，无论是定性、定量理解及揭示大气及海洋运动的动力学机制还是对于实际天气及气候预报、乃至对于防灾减灾等提供必要的理论依据保障，具有重要理论价值。本项目主要探究了地形、基本流、Coriolis参数对于非线性波动的动力学机制影响。我们研究了径向、纬向及时间缓变地形对于Rossby孤立波的生成、演化及衰退过程的影响；探讨了纬向切变基本流作用下的高维非线性Rossby孤立波模型，定性及定量解释了波动的物理机制；Coriolis参数分量对于大尺度Rossby孤立波、非线性近惯性波波动机制影响表明Coriolis参数水平分量具有移频效应。本项目对于揭示大气及海洋的波动机制提供了必要的理论模型及依据，项目成果以学术论文形式发表，同时对于大气动力学学科的发展也起到了一定的丰富与深入。