中纬度地形重力波稳态结构及其在平流层大气中的初级不稳定性研究

New stationary model needs first to be developed for the mountain gravity waves (MGWs) generated through the mid-latitude air flows over ridges at the central Asia channels. Study is then focused on two role problems about these stationary waves, i.e., the ill-posedness exists in reconstruction of their wave structures, as well as the transient instability analysis with a technique likes the optimal perturbations for those stationary waves. As for the first problem, the ill-posedness is expected to be settled through the boundary integrals for those elliptic equations of a specified stationary model, which are suggested to be used in building the regularized solutions for corresponding inverse-boundary value problems (IBVPs). Numerical schemes for reconsturction of those stationary MGWs are then capable to be redesigned under an unified elliptic framework. As for the second problem, technique of the optimal perturbations are suggested to be developed according to the generalized stability theory and/or the theoy of conditonal nonliear optiaml perturbations (CNOP). As proofed by observations, the MGWs entering the mid-latitude stratosphere have unstable dynamics. The instability are analysed in detail through the optimal perturbations to their stationary structures in conjunction with results fetched by method based on the traditional linear theory of instability, i.e., method of the normal modes (NMs). Dynamics of the primary stability transition for MGWs entering the stratosphere are revealed according to the spatial distributions, amplitude increments, and the wave packet informations of those unstable modes, which are fetched with the help of the wavepacket decompostion techniques. It can also be expected that (1) the localizations and the sporadic trends of the MGWs' instability would be characterized in this study, (2) a paradigm for the integral study of the middle atmospheric gravity wave dynamics in combination with corresponding wave origin dyanmics in troposphere would also be presented in this study, and (3) theory pursuants and prediction methods needed by forecasting of the mid-latitude MGWs disasters could also be inspired through this study.

建立适合于中纬度地形、大气层结与环流结构条件的地形重力波稳态模型。运 用椭圆型方程边界积分性质实现模型逆边值问题（IBVPs）正则化计算，在统一椭圆理论框 架下发展地形重力波稳态结构重构方法，解决目前普遍存在的模型不适定性问题，获取客观、真实的地形重力波稳态结构及波模信息。针对地形重力波在中纬度平流层大气动力学性质不稳定的观测事实，运用广义稳定性理论和条件非线性最优扰动理论（CNOP）发展基于地形重力波稳态解的最优扰动分析技术,结合线性稳定性理论的标准模分析方法，研究中纬度地形重力波进入平流层大气的初级不稳定性问题。通过考察不稳定模态的波包结构、振幅增长和空间分布，进一步揭示平流层大气地形重力波稳定性转捩的动力学机制。探讨中纬度平流层大气地形重力波初次转捩的局地性与偶发性规律，探索中层大气领域与波源相结合的重力波不稳定性问题研究途径，为中纬度地形重力波灾变天气预报提供分析方法和理论依据。

地形重力波在平流层大气中的转捩引起复杂的大气动力学效应，该过程形成的高低空转子对航空安全危害严重。准确预报该转子形成的位置、强度和结构信息，对于防范和规避这类危险十分必要。我国大部分地区处于中纬度西风急流环境中，山脉地形多覆盖于中西部地区和国家“一带一路”国家战略关键地位置上，对于这些位置上由地形引起的大气重力波转捩研究显得尤其重要。本研究课题围绕建立适合于中纬度地形、大气层结与环流结构条件的地形重力波稳态模型；在统一椭圆理论框架下发展地形重力波稳态结构重构方法解决模型不适定性问题；发展基于地形重力波稳态解的最优扰动分析技术,结合线性稳定性理论的标准模分析方法，研究中纬度地形 重力波进入平流层大气的初级不稳定性问题等主要目标开展研究工作，取得了一系列研究成果， 主要体现在：（1）系统分析了历史上关于大振幅地形重力波研究方法中存在的局限，有针对性的发展了整体谱方法、半空间上的Riemann映射、多维Chebyshev谱乘子等关键技术；（2）用稳态的Schrodinger方程取代传统大振幅地形重力波研究中的Helmholtz方程，开启了研究地形重力波非静力效应的新途径；（3）打破了传统地形重力波解析分析和数值模拟研究只在有限区域中展开的做法，首次实现了该系统在半无穷平面上的求解，解决了地形重力波求解中长期面临的解不惟一问题，为解释地形重力波的大气中的折射、反射、干涉、衍射、和波导形成提供了自恰的研究工具；（4）利用多维谱乘子初步实现了在谱空间上的零点分析，为转子问题的研究提供了有力工具，有望发展出实用的高低空转子预报系统。本研究成果可发展高低空阵风和风切变环境预报分析工具方面有潜在价值。 由于转捩的动力学机制研究一直因缺少科学的手段，该研究领域近年来进展缓慢，本研究课题在理论方法上开展原始创新，对于改变该领域研究现状有重要价值，为（1）中纬度平流层大气地形重力波初次转捩的局地性与偶发性规律，（2）探索中层大气领域与波源相结合的重力波 不稳定性问题研究途径，（3）为中纬度地形重力波灾变天气预报提供分析方法和理论依据等三个方向的进一步探讨提供了理认技术基础。