Radial cancellation in spinning sound fields

TL;DR

This paper provides an exact analysis of how circular acoustic sources radiate sound, revealing the limited degrees of freedom and applying these insights to noise cancellation and jet noise source identification.

Contribution

It introduces a precise analysis of the radiation properties of circular sources with angular and radial dependence, elucidating the source's radiating part and its implications.

Findings

Number of radiating degrees of freedom is at most k-n.

Low-frequency radiating part is explicitly characterized.

Application to jet noise source identification and noise cancellation.

Abstract

The radiating part of a circular acoustic source is determined on the basis of an exact analysis of the radiation properties of a source with angular dependence $\exp \J n\theta$ and arbitrary radial dependence. It is found that the number of degrees of freedom in the radiated field is no greater than $k-n$, where $k$ is the wavenumber. The radiating part of the source at low frequency is the wavenumber. The radiating part of the source at low frequency is explicitly stated and used to analyze noise cancellation. The results are applied to the identification of sources in jet noise and an explanation for the low order structure of jet noise fields is proposed.