Real Schur Flow Acoustic Directivity and Helicity Effects within

Abstract

The statistical description and acoustic diagnostics of anisotropic turbulence remain challenging. Real Schur flows (RSFs), prototype models of component-wise dimensionally reduced flows (CWDRFs), provide effective platforms for studying such problems. We combine absolute statistical equilibrium with the acoustic analogy to investigate helicity effects on the far-field directivity of sound radiated from three types of CWDRFs: two different RSFs, and a further reduction of them (liberated Schur flow). We evaluate the directivity from the vortex-sound source spectrum which is calculated with the Wick theorem from the absolute equilibirum Gaussian ensemble. Helicity amplifies the dimensional reduction induced anisotropy of the directivity functions across all CWDRFs, with distinct patterns.

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BibTeX

@misc{xu2026real,
  title = {{Real Schur Flow Acoustic Directivity and Helicity Effects within}},
  author = {Pan Xu and Jian-Zhou Zhu and Min Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30840},
  eprint = {2608.30840},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30840},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Real Schur Flow Acoustic Directivity and Helicity Effects within
AU  - Pan Xu
AU  - Jian-Zhou Zhu
AU  - Min Zhu
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30840
UR  - https://arxiv.org/abs/2608.30840
AB  - The statistical description and acoustic diagnostics of anisotropic turbulence remain challenging. Real Schur flows (RSFs), prototype models of component-wise dimensionally reduced flows (CWDRFs), provide effective platforms for studying such problems. We combine absolute statistical equilibrium with the acoustic analogy to investigate helicity effects on the far-field directivity of sound radiated from three types of CWDRFs: two different RSFs, and a further reduction of them (liberated Schur flow). We evaluate the directivity from the vortex-sound source spectrum which is calculated with the Wick theorem from the absolute equilibirum Gaussian ensemble. Helicity amplifies the dimensional reduction induced anisotropy of the directivity functions across all CWDRFs, with distinct patterns.
ER  -

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