Approximate meridional leaky ray amplitudes for tilted cylinders: End-backscattering enhancements and comparisons with exact theory for infinite solid cylinders

Abstract

Leaky waves propagating on cylinders in (or close to) a meridional plane have been found to significantly enhance the high-frequency acoustic visibility of the ends of tilted cylinders [G. Kaduchak et al., J. Acoust. Soc. Am. 100, 64–71 (1996)]. The meridian of interest is in the plane containing the incident wave vector and the cylinder’s axis. A ray model for this enhancement is developed along with a ray model for a canonical test case: scattering by an infinite circular cylinder. To isolate a single high-frequency leaky wave contribution, numerical examples are shown for generalized Rayleigh waves on a solid circular cylinder. Partial wave series (PWS) calculations show that the meridional Rayleigh wave contribution is maximized when the tilt angle is close to the flat-surface coupling angle. The ray model approximates the superposition of leaky waves excited by the incident acoustic wave as a simple integral that accounts for the phase shift and attenuation for propagation from each illuminated surface point to a surface point of interest. While the model gives the spatial evolution of the leaky wave amplitude as would be measured by acoustic imaging, it also approximates the far-field amplitude. Important features of the canonical PWS calculation are reproduced by the model. The far-field magnitude of the end contribution can be larger than for reflection off a rigid sphere having the same radius as the cylinder. The end is assumed to be flat and perpendicular to the cylinder’s axis.