论文标题
第二种模式不稳定性的线性,非线性和过渡方式
Linear, nonlinear and transitional regimes of second mode instability
论文作者
论文摘要
2D第二模式是高超音速边界层(HBL)的有效不稳定性。我们研究了其线性和非线性进化,然后研究其在HBL到完全湍流状态的过渡和最终崩溃中的作用。线性稳定性理论(LST)用于通过FS同步识别第二模式波,然后在线性和非线性强制2D直接数值模拟(DNSS)中重新形成。非线性DNS显示了基本频率的饱和度,所得的超野兽会在广义拐点(GIP)附近引起紧密编织的``绳子样''模式。不稳定性表现出第二个生长区域,该区域由基本包膜的基本频率(在线性场景中不存在)构成。随后的3D DNS确定该区域对于在2D第二模式``Rollers''上放大倾斜的不稳定性至关重要。这导致GIP下方的Lambda涡流,并从内部边界层中的``滚筒''分离。流向涡流拉伸会导致HBL内部长度尺度的局部峰,最终形成Haripin涡流。光谱分析跟踪谐波峰向湍流的转化,以及在基本频率下的倾斜模式的出现,这表明基本共振是过渡的最优势机制。双光谱揭示了基本及其超野兽学之间的非线性相互作用,从而导致光谱扩大,以及次谐波共鸣的痕迹。
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.