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Bi-orthogonal decomposition for slow acoustic pulse receptivity simulation of hypersonic boundary layer over a blunt cone

Published online by Cambridge University Press:  19 November 2025

Zihao Zou Open the ORCID record for Zihao Zou [Opens in a new window] ,
Simon He  and
Xiaolin Zhong
Zihao Zou*
Affiliation:
University of California, Los Angeles, CA 90095, USA
Simon He
Affiliation:
University of California, Los Angeles, CA 90095, USA
Xiaolin Zhong
Affiliation:
University of California, Los Angeles, CA 90095, USA
*
Corresponding author: Zihao Zou, zzou1@ucla.edu
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Abstract

The conventional $\textrm{e}^N$ laminar-to-turbulent transition-prediction method focuses on the relative growth rate, called the $N$ factor, and neglects receptivity. To improve predictions, Mack (1977) proposed the amplitude method to incorporate receptivity, nonlinear effects and broadband characteristics. Currently, the lack of accurate receptivity coefficients, estimates of initial disturbance amplitudes at the lower-branch neutral position, referred to as branch I (where the imaginary part of the spatial wavenumber is zero), hinders the application of the amplitude method. Although experimental- and numerical-receptivity analyses have been conducted previously, they rely on correlations or indirect approaches. For the purpose of direct evaluation, this study applies bi-orthogonal decomposition to direct numerical simulation (DNS) data of a hypersonic boundary layer over a blunt cone, extracting initial amplitudes of instability modes. The decomposition framework incorporates both boundary-layer and entropy-layer modes, enabling direct evaluation of receptivity coefficients at branch I. The decomposed modal amplitudes show reduced multimode interference and the receptivity coefficients have been computed to have fewer oscillations. With an overall greater magnitude, the receptivity coefficients suggest a possible earlier transition location than the previous numerical study by He & Zhong (2023 J. Spacecr. Rockets, vol. 60, no. 6, pp. 1927–1938). Additionally, a discrete entropy-layer mode is recovered, contributing to instability development alongside modes F and S. These findings support the use of bi-orthogonal decomposition as a practical tool for receptivity analysis and enhancement of the amplitude method in transition prediction.

JFM classification

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

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JFM Papers
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Journal of Fluid Mechanics , Volume 1023 , 25 November 2025 , A29
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© The Author(s), 2025. Published by Cambridge University Press

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