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arXiv · 2608.30840

Real Schur Flow Acoustic Directivity and Helicity Effects within

Pan Xu·Jian-Zhou Zhu·Min Zhu
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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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Pan Xu, Jian-Zhou Zhu, Min Zhu. 2026-08-31. Real Schur Flow Acoustic Directivity and Helicity Effects within. https://arxiv.org/abs/2608.30840

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