Radial cancellation in spinning sound fields

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.Comment: Submitted to Journal of Fluid Mechanic