Kelvin-Stuart猫眼流和剪切流的稳定性研究

流体的稳定性理论主要研究流体运动稳定的条件和失稳后流体的演化规律。以无粘性不可压缩的理想平面流体为研究对象，本项目主要采用微分算子谱分析的方法研究无穷长管道内Kelvin-Stuart猫眼流和受科里奥利力影响下剪切流的一些稳定性问题，具体包括：1.无穷长管道内Kelvin-Stuart猫眼流在同周期和调制扰动下的线性和非线性稳定性；2.受科里奥利力影响下Couette流附近非水平稳态解对空间正则性的敏感度及退化剪切流附近单向行波解族的个数；3.受科里奥利力影响下Sinus流的非线性稳定性及其附近行波解的谱稳定性。本项目不仅可以丰富和发展无穷维哈密顿系统的稳定性理论，而且在大尺度流体动力学的应用研究中起着重要作用。

The theory of fluid stability mainly studies the conditions for stability of fluid motion and the law of fluid evolution after instability. Taking the inviscid and incompressible ideal plane fluid as the research object, in this project, we mainly use the method of spectral analysis of differential operator to study some problems of stability of the Kelvin-Stuart cat’s eyes flow in an infinite channel and the shear flow under the influence of the Coriolis force, including: 1.Linear and nonlinear stability of Kelvin-Stuart cat’s eyes flow in an infinite channel under the co-periodic and modulational perturbations;2.Sensitivity of non-parallel steady-state solutions near Couette flow to regularity of the space and the number of unidirectional traveling wave families near degenerate shear flow under the influence of Coriolis force;3.Nonlinear stability of Sinus flow and spectral stability of its nearby traveling wave solutions under the influence of Coriolis force. This project can not only enrich and develop the stability theory of the infinite dimensional Hamiltonian system, but also play an important role in the application research of dynamics of large-scale fluids.