A THREE-DIMENSIONAL WIENER-HOPF TECHNIQUE FOR GENERAL BODIES OF REVOLUTION - PART 1: THEORY

This work, the first of two parts, presents the development of a new analytic solution of acoustic scattering and/or radiation by arbitrary bodies of revolution under heavy fluid loading The approach followed is the construction of a three-dimensional Wiener-Hopf technique with Fourier transforms that operate on the finite object's arclength variable (the object's practical finiteness comes about, in a Wiener-Hopf sense, by formally bringing to zero the radius of its semi-infinite generator curve for points beyond a prescribed station). Unlike in the classical case of a planar semi-infinite geometry, the kernel of the integral equation is non-translational and therefore with independent wavenumber spectra for its receiver and source arclengths. The solution procedure begins by applying a symmetrizing spatial operator that reconciles the regions of (+) and (-) analyticity of the kernel's two-wavenumber transform with those of the virtual sources. The spatially symmetrized integral equation is of the Fredholm 2(nd) kind and thus with a strong unit "diagonal" - a feature that makes possible the Wiener-Hopf factorization of its transcendental doubly-transformed kernel via secondary spectral manipulations. The companion paper [1] will present a numerical demonstration of the new analysis for canonical problems of fluid-structure interaction for finite bodies of revolution.