The Scattering of a Scalar Wave by a Slender Body of Revolution

Scattering of an arbitrary scalar wave with a fixed wave number incident upon a slender body of revolution is studied. The scattered wave is represented as the superposition of waves due to point singularities distributed along a portion of the axis of the body and lying inside the body. The boundary condition, which may be either Dirichlet or Neumann, leads to an integral equation for the densities of the singularity distributions. The complete uniform asymptotic expansion of the singularity densities, as well as the extent of the distributions, is obtained with respect to the slenderness ratio of the body by using and modifying the methods of Handelsman and Kelley (J. Fluid Mech., 28 (1967), p. 131) and Geer (J. Fluid mech., 67 (1975), p. 817). The examples of a plane wave either axially or obliquely incident upon the body are presented. The far field behavior of the scattered wave and the total scattering cross section are computed.