Nonlinear evolution of radiating modes in the presence of sound waves impinging on a supersonic boundary layer: subharmonic resonance
Author(s)
Qin, Fufeng
Wu, Xuesong
Type
Journal Article
Abstract
This paper investigates linear and nonlinear evolution of a radiating mode in a supersonic boundary layer in the presence of an impinging sound wave. Of special interest is the case where the sound wave has wavenumber and frequency twice those of the radiating mode, and so the two share the same phase speed and hence the critical layer. In this case, a radiating mode is sensitive to a small-amplitude sound wave due to effective interactions taking place in their common critical layer. The sound wave influences the development of the radiating mode through the mechanism of subharmonic parametric resonance, which is often referred to as Bragg scattering. Amplitude equations are derived to account for this effect in the two regimes where non-equilibrium and non-parallelism play a leading-order role, respectively. A composite amplitude equation is then constructed to account for both of these effects. These amplitude equations are solved to quantify the impact of the impinging sound wave on linear and nonlinear instability characteristics of the radiating mode. Numerical results show that the incident sound makes the amplification and attenuation of the radiating mode highly oscillatory. With sufficiently high intensity, the impinging sound enhances the radiating mode. For a certain range of moderate intensity, the impinging sound inhibits the growth of the radiating mode and may eliminate the singularity, which would form in the absence of external acoustic fluctuations. The far-field analysis shows that the incident sound alters the Mach wave field of the radiating mode significantly, rendering its pressure contours spiky and irregular.
Date Issued
2025-06-25
Date Acceptance
2025-05-15
Citation
Journal of Fluid Mechanics, 2025, 1013
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
1013
Copyright Statement
© The Author(s), 2025. Published by Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Subjects
AERODYNAMIC NOISE
boundary layer stability
DISTURBANCES
HYPERSONIC FLOW
INSTABILITY WAVES
Mechanics
nonlinear instability
Physical Sciences
Physics
Physics, Fluids & Plasmas
RECEPTIVITY
Science & Technology
STABILITY
STOKES LAYER
Technology
TRANSITION
transition to turbulence
TRIAD
WATER-WAVES
Publication Status
Published
Article Number
A29
Date Publish Online
2025-06-20