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On the receptivity of first and cross-flow modes in hypersonic sharp wing flows

Published online by Cambridge University Press:  15 October 2025

Jiachen Lu Open the ORCID record for Jiachen Lu [Opens in a new window] ,
Ken Chun Kit Uy Open the ORCID record for Ken Chun Kit Uy [Opens in a new window] ,
Rui Zhao Open the ORCID record for Rui Zhao [Opens in a new window]  and
Chihyung Wen Open the ORCID record for Chihyung Wen [Opens in a new window]
Jiachen Lu
Affiliation:
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, PR China
Ken Chun Kit Uy
Affiliation:
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, PR China
Rui Zhao*
Affiliation:
School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, PR China
Chihyung Wen
Affiliation:
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, PR China
*
Corresponding author: Rui Zhao, zr@bit.edu.cn
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Abstract

A long-standing conceptual debate regarding the identification and independence of first Mack and cross-flow instabilities is clarified over a Mach 5.9 sharp wing at zero angle of attack and varying sweep angles. Their receptivity of the boundary layers to three-dimensional slow acoustic and vorticity waves is investigated using linear stability theory, direct numerical simulation and momentum potential theory (MPT). Linear stability theory demonstrates that the targeted slow mode appears as the oblique first mode at small sweep angles ($0^\circ$ and $15^\circ$) and transitions to the cross-flow mode at larger sweep angles ($30^\circ$ and $45^\circ$). Direct numerical simulation indicates that both the oblique first mode and cross-flow mode share identical receptivity pathways: for slow acoustic waves, the pathway comprises ‘leading-edge damping–enhanced exponential growth–linear growth’ stages. For vorticity waves, it consists of ‘leading-edge damping–non-modal growth–linear growth’ stages. Momentum potential theory decomposes the fluctuation momentum density into vortical, acoustic and thermal components, revealing unified receptivity mechanisms: for slow acoustic waves, the leading-edge damping is caused by strong acoustic components generated through synchronization. The enhanced exponential growth stage is dominated by steadily growing vortical components, with acoustic and thermal components remaining at small amplitudes. For vorticity waves, leading-edge disturbances primarily consist of vortical components, indicating a distinct mechanism from slow acoustic waves. Non-modal stages originate from adjustments among MPT components. Vortical components dominate the linear growth stage for both instabilities. These uniform behaviours between first Mack and cross-flow modes highlight their consistency.

JFM classification

Boundary Layers: Boundary layer receptivity Compressible Flows: Hypersonic Flow Boundary Layers: Boundary layer stability

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JFM Papers
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Journal of Fluid Mechanics , Volume 1021 , 25 October 2025 , A18
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© The Author(s), 2025. Published by Cambridge University Press

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