| Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint | |
| Song RJ(宋润杰); Dong M(董明); Zhao, Lei | |
| Corresponding Author | Dong, Ming([email protected]) ; Zhao, Lei([email protected]) |
| Source Publication | JOURNAL OF FLUID MECHANICS
 |
| 2024-01-08 | |
| Volume | 978Pages:44 |
| ISSN | 0022-1120 |
| 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 ((is an element of) over bar (10)), and the amplitude of the streak mode is O((is an element of) over bar (-1)(10)) 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. |
| Keyword | boundary layer stability transition to turbulence |
| DOI | 10.1017/jfm.2023.1043 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:001142159300001 |
| WOS Keyword | SECONDARY INSTABILITY ; TRANSITION ; STABILITY ; RECEPTIVITY ; EVOLUTION |
| WOS Research Area | Mechanics ; Physics |
| WOS Subject | Mechanics ; Physics, Fluids & Plasmas |
| Funding Project | National Natural Science Foundation of China[11988102] ; National Natural Science Foundation of China[U20B2003] ; National Natural Science Foundation of China[12002235] ; National Science Foundation of China[YSBR-087] ; CAS project for Young Scientists in Basic Research |
| Funding Organization | National Natural Science Foundation of China ; National Science Foundation of China ; CAS project for Young Scientists in Basic Research |
| Classification | 一类/力学重要期刊 |
| Ranking | 1 |
| Contributor | Dong, Ming ; Zhao, Lei |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/94128 |
| Collection | 非线性力学国家重点实验室 |
| Recommended Citation GB/T 7714 | Song RJ,Dong M,Zhao, Lei. Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint[J]. JOURNAL OF FLUID MECHANICS,2024,978:44.Rp_Au:Dong, Ming, Zhao, Lei |
| APA | 宋润杰,董明,&Zhao, Lei.(2024).Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint.JOURNAL OF FLUID MECHANICS,978,44. |
| MLA | 宋润杰,et al."Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint".JOURNAL OF FLUID MECHANICS 978(2024):44. |
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