Rays, multipoles, and caustics

Speaker's Name: John Chapman
Speaker's Affiliation: University of Keele
Speaker's Research Theme(s): Applied Mathematics,
Abstract:
This presentation is based on the paper Near-field scattering by the method of locally subsonic waves. Proc. R. Soc. A 480: 20230720 (2024). https://doi.org/10.1098/rspa.2023.0720. In this, a technique is developed for determining the sound field scattered by a compact body when it is close enough to an acoustic source to be in its near field. The approach is based on the fact that large regions of many near fields may be well approximated at each point in space by a subsonic plane wave (also called an inhomogeneous plane wave, or an evanescent wave). Such a wave is defined by the property that in one direction it propagates with subsonic phase speed, while in a perpendicular direction it has exponential amplitude variation. Hence by defining a canonical problem, compact scattering of a subsonic plane wave, and solving it, we are able to give a unified analytical treatment of many near-field scattering problems. Our approach draws on the formulae of Rayleigh scattering (as applied to an incident field with complex wavenumber) and the asymptotic theory of the wave equation. For an arbitrary three-dimensional multipole, we determine in full detail how its subsonic wave structure depends on the spherical harmonic parameters (m, n), and show that our approach has a very large region of validity.

Venue: UP-Maths A17