Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint

doi:10.1017/jfm.2023.1043

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	Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint
	Song RJ(宋润杰); Dong M(董明); Zhao, Lei
通讯作者	Dong, Ming(dongming@imech.ac.cn) ; Zhao, Lei(lei_zhao@tju.edu.cn)
发表期刊	JOURNAL OF FLUID MECHANICS
	2024-01-08
卷号	978 页码:44
ISSN	0022-1120
摘要	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.
关键词	boundary layer stability transition to turbulence
DOI	10.1017/jfm.2023.1043
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:001142159300001
关键词[WOS]	SECONDARY INSTABILITY ; TRANSITION ; STABILITY ; RECEPTIVITY ; EVOLUTION
WOS研究方向	Mechanics ; Physics
WOS类目	Mechanics ; Physics, Fluids & Plasmas
资助项目	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
项目资助者	National Natural Science Foundation of China ; National Science Foundation of China ; CAS project for Young Scientists in Basic Research
论文分区	一类/力学重要期刊
力学所作者排名	1
RpAuthor	Dong, Ming ; Zhao, Lei
引用统计
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/94128
专题	非线性力学国家重点实验室
推荐引用方式 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.
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.