Relation between the landing-launching coefficient and the attenuation of surface waves propagating around an elastic cylindrical object

Abstract

One approach for developing a physical understanding of the scattering of sound from elastic objects in water is to use the Sommerfeld–Watson transformation (SWT). Following the works of Überall etal., it is known that elastic objects resonances are due to a phase matching of the surface waves propagating around the scatterer. What is more, resonance widths are related to surface waves attenuation, thereby showing the close link between resonance and surface waves propagation phenomena. According to the geometrical theory of diffraction, surface waves are also characterized by a landing coefficient and a launching one, both identical in the present case. This landing–launching coefficient calculated from the SWT gives an indication, as resonance widths and surface waves attenuation, on the coupling between the object and the surrounding fluid. The purpose of this work is to determine an analytical relation between the landing–launching coefficient and the attenuation of surface waves. This relation comes from an identification between the Breit–Wigner approximation of resonances and the Mittag–Leffler expansions related to surface waves contribution. Thereafter, a method of identification of the background introduced by Flax etal. in the acoustic scattering theory has been developed.