Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid

TL;DR

This paper provides an analytical solution for the acoustic scattering of a Bessel beam by a rigid spheroid, analyzing how shape, beam angle, and frequency affect scattering in underwater acoustics.

Contribution

It introduces a formal analytical method using PWSE for spheroid scattering of Bessel beams, including numerical results and directivity patterns for various parameters.

Findings

Oscillatory backscattering patterns due to wave interference.

Dependence of scattering on aspect ratio, beam angle, and frequency.

3D directivity patterns showing axisymmetric scattering.

Abstract

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (\theta = \pi) in the near-field and the backscattering form function in the far-field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam \beta, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) due to the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the near and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.