Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint
Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint
复制标题
DOI：
10.1017/jfm.2023.1043
复制
发表时间：
2023-12
影响因子：
3.7
通讯作者：
Runjie Song;Ming Dong;Lei Zhao
中科院分区：
文献类型：
--
作者：
Runjie Song;Ming Dong;Lei Zhao
摘要边界层转捩到湍流的非线性阶段中的基本共振（FR）出现在主导的平面不稳定模式达到有限振幅时，与主导模式相同频率的低振幅斜行模式，连同静止条纹模式，在所有傅立叶分量中经历最强的放大。这可能是触发高超音速边界层自然转捩的最有效手段。在本文中，我们的目的是揭示在弱非线性框架下的大雷诺数渐近技术的基础上的FR的内在机制。研究发现，谐振频率基本上是由平面主模、条纹模和斜模组成的三重共振。在边界层的主要部分，基本模式和条纹模式的非线性相互作用种子的倾斜模式的增长，而倾斜模式和基本模式的相互作用驱动的滚动组件（横向和横向速度）的条纹模式，这导致了一个更强的放大条纹模式的流向分量由于提升机制。这种渐近分析清楚地表明，条纹模和斜模的无量纲增长率与基模的无量纲振幅$（\bar {\displaystyle\bar {10}^{-1}）$是同一数量级的，并且条纹模的振幅比斜模的振幅大O（\bar {\displaystyle\bar {10}^{-1}）$。条纹模态和斜模态的流向速度、展向速度和温度的主层解随着接近壁面而变得奇异，因此下面出现粘性壁层。壁层产生出流速度的主层的解决方案，包括导致改进的渐近理论，其准确性通过比较在中等雷诺数和二次不稳定性分析（SIA）在足够高的雷诺数的非线性抛物稳定性方程（NPSE）的计算确认。
Abstract The fundamental resonance (FR) in the nonlinear phase of the boundary-layer transition to turbulence appears when a dominant planar instability mode reaches a finite amplitude and the low-amplitude oblique travelling modes with the same frequency as the dominant mode, together with the stationary streak modes, undergo the strongest amplification among all the Fourier components. This regime may be the most efficient means to trigger the natural transition in hypersonic boundary layers. In this paper, we aim to reveal the intrinsic mechanism of the FR in the weakly nonlinear framework based on the large-Reynolds-number asymptotic technique. It is found that the FR is, in principle, a triad resonance among a dominant planar fundamental mode, a streak mode and an oblique mode. In the major part of the boundary layer, the nonlinear interaction of the fundamental mode and the streak mode seeds the growth of the oblique mode, whereas the interaction of the oblique mode and the fundamental mode drives the roll components (transverse and lateral velocity) of the streak mode, which leads to a stronger amplification of the streamwise component of the streak mode due to the lift-up mechanism. This asymptotic analysis clearly shows that the dimensionless growth rates of the streak and oblique modes are the same order of magnitude as the dimensionless amplitude of the fundamental mode $(\bar {\epsilon }_{10})$, and the amplitude of the streak mode is $O(\bar {\epsilon }_{10}^{-1})$ greater than that of the oblique mode. The main-layer solution of the streamwise velocity, spanwise velocity and temperature of both the streak and the oblique modes become singular as the wall is approached, and so a viscous wall layer appears underneath. The wall layer produces an outflux velocity to the main-layer solution, inclusion of which leads to an improved asymptotic theory whose accuracy is confirmed by comparing with the calculations of the nonlinear parabolised stability equations (NPSEs) at moderate Reynolds numbers and the secondary instability analysis (SIA) at sufficiently high Reynolds numbers.