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On the mechanism of dual tones in transitional flow around a heptagonal cylinder

Published online by Cambridge University Press:  05 January 2026

Xuqi Zhang Open the ORCID record for Xuqi Zhang [Opens in a new window] ,
Lian Gan  and
Yu Liu Open the ORCID record for Yu Liu [Opens in a new window]
Xuqi Zhang
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology , Shenzhen, Guangdong 518055, PR China
Lian Gan
Affiliation:
Department of Engineering, Durham University, DH1 3LE, Durham, UK
Yu Liu*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology , Shenzhen, Guangdong 518055, PR China
*
Corresponding author: Yu Liu, liuy@sustech.edu.cn
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Abstract

The dual-tone transition phenomenon and its formation mechanism in the flow around a heptagonal cylinder (side number $N= 7$) are experimentally investigated in depth over a range of free-stream velocities corresponding to Reynolds numbers of the order of $10^4$–$10^5$. Dual tone in this context refers to the emergence of two dominant peaks in the far-field acoustic spectrum when a flow in transition regime passes over a polygonal cylinder in principal orientations. The dual-tone phenomenon is also observed in an $N = 9$ cylinder in the face orientation and an $N = 11$ in the corner orientation, which contrasts with all the other polygonal cylinders of $N\in {\mathbb{Z}}[3,12]$ systematically investigated in the present study, where only a single tonal peak dominates the spectrum, similar to the Aeolian tone observed in the circular cylinder in the subcritical regime. The emergence of the dual tone is found to be responsible for the reduction of far-field noise. Continuous wavelet transform analysis reveals that the occurrence of the two competing tones in the time domain can be empirically modelled by Gaussian distributions. Additional proper orthogonal decomposition based phase averaging using time-resolved planar particle image velocimetry enables coherent vortex structure identification for the two quasi-stable shedding modes, which are responsible for the formation of the two tones. Near-wall flow and pressure fluctuation analysis further confirms that the two tones originate from stochastic shear-layer separation–reattachment switching, thereby generating two patterns of dipole sound sources through distinct vortex formation pathways.

JFM classification

Acoustics: Aeroacoustics Acoustics: Noise control Vortex Flows: Vortex shedding

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1026 , 10 January 2026 , A37
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Copyright
© The Author(s), 2026. Published by Cambridge University Press

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