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Interactions between oblique second mode and oblique waves in a high-speed boundary layer

Published online by Cambridge University Press:  19 October 2023

Teng Zhou Open the ORCID record for Teng Zhou [Opens in a new window] ,
Zaijie Liu Open the ORCID record for Zaijie Liu [Opens in a new window] ,
Yuhan Lu Open the ORCID record for Yuhan Lu [Opens in a new window]  and
Chao Yan Open the ORCID record for Chao Yan [Opens in a new window]
Teng Zhou
Affiliation:
National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, PR China
Zaijie Liu
Affiliation:
National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, PR China
Yuhan Lu
Affiliation:
National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, PR China
Chao Yan*
Affiliation:
National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, PR China
*
†Email address for correspondence: yanchao@buaa.edu.cn
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Abstract

Interactions between oblique second mode and oblique waves at a high-speed boundary at Mach 4.5 are studied using linear stability theory, nonlinear parabolized stability equations (NPSE) and direct numerical simulation (DNS). Parametric analysis based on the NPSE suggests that the oblique second mode can amplify both the oblique first and second modes, with the former experiencing a higher amplification. Our analysis reveals that the mean-flow distortion and difference mode contribute to this enhancement, with the latter exerting a key influence through the parametric resonance process. Kinetic energy transfer analysis demonstrates that the oblique waves gain energy from the mean flow, rather than from the oblique second mode. Furthermore, we find that the mechanism underlying the interaction between a pair of second oblique waves and a single oblique wave is similar to that between an oblique second mode and an oblique wave, as the steady modes generated by the pair of oblique second modes have a limited impact on the oblique wave. Finally, DNS confirms the validity of two transition paths proposed in this study based on the NPSE results. The first path suggests that a pair of low-amplitude second oblique waves alone are insufficient to cause oblique breakdown, but the introduction of a pair of low-amplitude damping first oblique modes could lead to boundary layer breakdown. The second path involves the formation of a domino-like effect through the combination of different types of oblique waves with the appropriate parameters. These two nonlinear paths can lead to a fully developed turbulent boundary layer.

JFM classification

Compressible Flows: Compressible boundary layers Instability: Transition to turbulence Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , A27
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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