Information in spinning sound fields

TL;DR

This paper analyzes the information content of spinning sound fields, revealing limits on source identification accuracy and explaining the effectiveness of low-order models in noise control and jet radiation.

Contribution

It introduces a transformation of circular sources into Chebyshev polynomial modes and analyzes their radiative properties using exact and asymptotic methods.

Findings

Higher order modes generate exponentially small fields.

Lower order modes radiate mainly near the source plane.

Results explain ill-conditioning of source identification and low radiation efficiency.

Abstract

The information content of a spinning sound field is analyzed using a combination of exact and asymptotic results, in order to set limits on how accurately source identification can be carried out. Using a transformation of the circular source to an exactly equivalent set of line source modes, given by Chebyshev polynomials, it is found that the line source modes of order greater than the source wavenumber generate exponentially small fields. Asymptotic analysis shows that the remaining, lower order, modes radiate efficiently only into a region around the source plane, with this region shrinking as the mode order is increased. The results explain the ill-conditioning of source identification methods; the successful use of low order models in active noise control; and the low radiation efficiency of subsonic jets.