(Why) Jets quantise trapped acoustic modes
Abstract
High-subsonic turbulent jets trap acoustic modes in their potential core. The modes lie in narrow frequency bands that are O(0.1)-wide in Strouhal number, St. By studying a Mach 0.9, Reynolds number 106 jet, this work confirms an earlier hypothesis: each band is made up of O(10) discrete frequencies, ΔSt ∼ O(0.01) apart. To resolve them, we collect O(100 000) snapshots from dedicated schlieren experiments and large-eddy simulations (LES), and apply spectral proper orthogonal decomposition (SPOD). Our SPOD algorithm uses sine tapers and enforces the jet's rotational and reflectional symmetries. For both the schlieren and the LES, the trapped SPOD modes are bounded in the St-x and St-k planes, where x and k are respectively the axial coordinate and wavenumber. The bounds quantise the modes in St, x, and k, such that the nxth mode in St has nx antinodes along x and k. We then predict trapped modes with local, global, modal, and non-modal stability theories. We find evidence of a competition between modal and non-modal stability. From only the theoretical bounds, we build a simple in-phase standing-wave resonance model that predicts the quantised global-mode frequencies.
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BibTeX
@misc{yeung2026jets,
title = {{(Why) Jets quantise trapped acoustic modes}},
author = {Brandon Yeung and Michael N. Stavropoulos and Vincent Jaunet and Peter Jordan and Oliver T. Schmidt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07414},
eprint = {2610.07414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07414},
}
RIS
TY - UNPB
TI - (Why) Jets quantise trapped acoustic modes
AU - Brandon Yeung
AU - Michael N. Stavropoulos
AU - Vincent Jaunet
AU - Peter Jordan
AU - Oliver T. Schmidt
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07414
UR - https://arxiv.org/abs/2610.07414
AB - High-subsonic turbulent jets trap acoustic modes in their potential core. The modes lie in narrow frequency bands that are O(0.1)-wide in Strouhal number, St. By studying a Mach 0.9, Reynolds number 10^6 jet, this work confirms an earlier hypothesis: each band is made up of O(10) discrete frequencies, ΔSt ∼ O(0.01) apart. To resolve them, we collect O(100 000) snapshots from dedicated schlieren experiments and large-eddy simulations (LES), and apply spectral proper orthogonal decomposition (SPOD). Our SPOD algorithm uses sine tapers and enforces the jet's rotational and reflectional symmetries. For both the schlieren and the LES, the trapped SPOD modes are bounded in the St-x and St-k planes, where x and k are respectively the axial coordinate and wavenumber. The bounds quantise the modes in St, x, and k, such that the n_xth mode in St has n_x antinodes along x and k. We then predict trapped modes with local, global, modal, and non-modal stability theories. We find evidence of a competition between modal and non-modal stability. From only the theoretical bounds, we build a simple in-phase standing-wave resonance model that predicts the quantised global-mode frequencies.
ER -