The 2D second-mode is a potent instability in hypersonic boundary layers (HBLs). We study its linear and nonlinear evolution, followed by its role in transition and eventual breakdown of the HBL into a fully turbulent state. Linear stability theory (LST) is utilized to identify the second-mode wave through FS-synchronization, which is then recreated in linearly and nonlinearly forced 2D direct numerical simulations (DNSs). The nonlinear DNS shows saturation of the fundamental frequency, and the resulting superharmonics induce tightly braided ``rope-like'' patterns near the generalized inflection point (GIP). The instability exhibits a second region of growth constituted by the fundamental frequency, downstream of the primary envelope, which is absent in the linear scenario. Subsequent 3D DNS identifies this region to be crucial in amplifying oblique instabilities riding on the 2D second-mode ``rollers''. This results in lambda vortices below the GIP, which are detached from the ``rollers'' in the inner boundary layer. Streamwise vortex-stretching results in a localized peak in length-scales inside the HBL, eventually forming haripin vortices. Spectral analyses track the transformation of harmonic peaks into a turbulent spectrum, and appearance of oblique modes at the fundamental frequency, which suggests that fundamental resonance is the most dominant mechanism of transition. Bispectrum reveals coupled nonlinear interactions between the fundamental and its superharmonics leading to spectral broadening, and traces of subharmonic resonance as well.
Linear Instability of Shock-Dominated Laminar Hypersonic Separated Flows
采用动力学直接模拟蒙特卡罗（DSMC）方法研究了双楔高超声速氮分子绕流中激波/边界层相互作用（SWBLI）系统的展向自激均匀扰动。流动的过渡努森数和单位雷诺数分别为3.4 x 10 $^{-3}$和5.2 x 10 $^4$ m $^{-1}$。由于上楔面产生的马赫数为7的分离（弓形）激波下游存在着强烈的热不平衡。线性不稳定性机制预计使预先计算的二维基流在展向扰动下可能不稳定。具体的目的是评估不稳定模式的增长率，波长，位置，和起源的展向周期性流动结构，以及在这种相互作用中存在的特征频率。
Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar-turbulent separatrix
本文用直接数值模拟的方法研究了滑移面对平面Poillille流层流-湍流分界线的影响。湍流寿命，湍流持续的可能性，研究过渡流与各种滑移长度。与无滑移情况相比，滑移面降低了持续湍流的可能性，并且随着滑移长度的增加，可能性进一步降低。采用纳维-斯托克斯方程的非线性行波解（也称为精确相干解），对滑移面对湍流转捩的影响进行了确定性分析。使用了两个解族，称为P3和P4，因为它们的下分支解嵌入层流和湍流的吸引盆的边界上（Park & Graham 2015）。此外，它们表现出不同的流动结构-P3和P4分别表示为核心模式和临界层模式。滑移面对解的影响通过摩擦力演化、线性增长率和过渡轨迹的相空间投影来观察。滑移面改变过渡动力学的核心模式，但相当大的临界层模式。最重要的是，滑移面促进不同的过渡动力学-早期和旁路样过渡的核心模式和延迟和H-/K型的临界层模式的过渡。时空和象限分析的基础上，它被发现，滑移面促进流行的强壁向运动（掠样事件）靠近涡核通道中心附近，诱导早期过渡，而持续的喷射事件存在于该地区的$Λ$形涡核靠近临界层，导致延迟过渡。
