Comparison of the currents in the Dirichlet and Neumann shortwave diffraction problems of a plane wave from smooth prolate bodies of revolution

Abstract

This paper continues the series of works [1-5] on the shortwave diffraction on the prolate body of revolution. The numerical comparison of the wave currents for Dirichlet and Neumann boundary conditions confirms the continuous transition of the current from the lit area into the shadowed zones through Fock's zone. The formulae for the currents were obtained according to the Leontovich-Fock parabolic equation method [6]. We investigated the influence of the correction term that contains the large parameter, on the Fock's current. This large parameter reflects body's elongation. Diffraction formulae obtained in [1,4], give the integral representation of the field in some neighborhood of the point, which is located on the boundary of geometric shadow. These formulae give a continuous transformation from ray field in the lit area to the field in the shadow using Fock's currents.

Creeping waves in the shadow region with the Dirichlet and Neumann conditions

“…A. S. Kirpichnikova and N. Ya. Kirpichnikova obtained the first three terms of the wave field approximation for the problem with Neumann boundary conditions [7,8]. The novelty of the present paper is in the description of the creeping waves in the shadow region for the Neumann problem.…”

“…This two-scale expansion allows us to obtain formulae for calculating the wave field, in particular, the current on the surface of the scatter at different ratios between M (s) and Λ(s). It can be shown that the recurrent system of equations (8) will retain its asymptotic character at M (s) provided that Λ(s) = M 2−ε for 0 < ε < 2. We use the following scheme to solve system (8).…”

“…It can be shown that the recurrent system of equations (8) will retain its asymptotic character at M (s) provided that Λ(s) = M 2−ε for 0 < ε < 2. We use the following scheme to solve system (8). Operator L 0 is the Airy operator and with homogeneous boundary conditions and it defines the following problem for V 0 :…”