The near-field of spinning sources: Why source identification is hard

An asymptotic analysis is presented for the near field of spinning sources, based on a transformation into cylindrical coordinates centred on a line at a fixed radius from the source axis. This transforms the circular source into an equivalent finite length line source with a source distribution made up of `modes' given as Chebyshev polynomials of the second kind. These `modes' play a role like that of modes in ducts and the analysis shows that their acoustic field propagates or decays depending on whether the mode order is less than, or greater than, wavenumber respectively, similar to the cut-on/cut-off behavior of duct modes. The analysis is used to examine the problem of identifying a source from field measurements. This has a wide range of applications and is recognized to be (very) ill-conditioned. Using the information supplied by the analysis of the source near field, the reasons for this ill-conditioning are explained.