本文采用理论和数值方法研究高超声速三维边界层流动的稳定性和感受性问题。本文首先应用高精度离散方法发展了基本流求解和稳定性分析工具，并在此基础上开展了以下研究： 本文从理论上证明，在线性稳定性分析的框架下，背景流为二维平行流的，任意的小扰动都可以表示为边界层中的离散谱模态和连续谱模态的组合。其中，离散谱模态主要分布在边界层内，连续谱模态主要反映为边界层外的快/慢声波、涡波和熵波。

The stability and receptivity analyses of hypersonic three-dimensional boundary layers are investigated numerically and theoretically. High-order discrete methods have been used to establish basic flow and stability solvers with both high-fidelity and efficiency. After careful validations and verifications of the present solvers, we perform the following analyses. Firstly, in the framework of linear stability theory, we analytically achieve the linearized perturbation equation’s solution under the assumption of two-dimensional parallel flows over a flat boundary layer. It has been proved that any small perturbations in two-dimensional parallel flows can be expressed as the combination of discrete modes and continuous modes. The discrete modes are mainly distributed inside the boundary layer, while the continuous modes are reflected as slow/fast acoustic waves, entropy waves and vorticity waves. Then, hypersonic attachment-line instabilities over blunt bodies have been investigated. The attachment-line instabilities exhibit three-dimensional TS wave features near the attachment line, and crossflow instability features further downstream if the sweep Mach number is low(?𝑠 < 3). However, the global modes of attachment-line instabilities display the characteristics of inviscid instability in the attachment line’s vicinity and three-dimensional Mack modes further downstream if the sweep Mach number is highenough(?𝑠 > 4). For the first time, a theoretical explanation for the transition occurring earlier is given as the sweep Mach number is above 5. Moreover, relative complete behaviours of the attachment-line instabilities, over a swept parabolic body, to sweep Mach number are presented. In addition, the traditional receptivity theory, based on local theory, has been extended to solve complex multidimensional hypersonic problems with the help of adjoint equations and biorthogonal eigenfunction systems. A general theory for receptivity problem has been established and performed on hypersonic flows over swept blunt bodies. In the hypersonic flow over a swept blunt body, the receptivity analyses indicate that the global modes of attachment line are the most responsive to external forces and surface perturbations applied in the vicinity of the attachment line, regardless of the sweep angles, although the global modes cover a large region further away from the attachment line. This finding indicates that the leading edge control might be effective for the hypersonic flows over swept blunt bodies. Finally, the global stability analysis has been performed on a three-dimensional boundary layer formed by a hypersonic flow over a flat plate’s smooth roughness. Because of the lift-up mechanism, typical streak structures are formed in the flow field after encountering the roughness. Both Sinuous and Varicose secondary instabilities are presented after streaks’ formation, and the competition between these two instabilities is observed. The Varicose mode dominates the flow immediately behind the roughness, but its growth rate decreases fast. After some distance away from the roughness, the Sinuous mode dominates the flow and finally becomes the only unstable mode further downstream.