Scattering Amplitudes in a Neighborhood of Limit Rays in Short-Wave Diffraction by Elongated Bodies of Revolution

In the paper, diffraction problems of a plane wave by smooth, convex, and elongated bodies of revolution are considered within the framework of short-wave approximation (axially symmetric cases). The scattering amplitudes are calculated in the direction of limit rays, and the influence of the elonga...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2019-05, Vol.238 (5), p.715-730
Main Authors: Popov, M. M., Semtchenok, N. M.
Format: Article
Language:English
Subjects:
Aircraft
Amplitudes
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
AXIAL SYMMETRY
Bibliographies
Bodies of revolution
BOUNDARY LAYERS
Boundary layers (Fluid dynamics)
CROSS SECTIONS
DIAGRAMS
DIFFRACTION
ELONGATION
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
Plane waves
ROTATION
Scattering
SCATTERING AMPLITUDES
Wave diffraction
WAVE PROPAGATION
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Summary:In the paper, diffraction problems of a plane wave by smooth, convex, and elongated bodies of revolution are considered within the framework of short-wave approximation (axially symmetric cases). The scattering amplitudes are calculated in the direction of limit rays, and the influence of the elongation of the scatterers on the amplitudes behavior is investigated. Mathematical techniques of our approach are based on the Green’s formulas in the exterior of the scatterers and numerical calculations of the wave field current in the boundary layers in the vicinity of the light-shadow zone. It is established that the elongation of axially symmetric bodies relatively weakly affects the scattering amplitudes of the short-wave asymptotics. The main contribution to the amplitudes is made by the solution of the 2D diffraction problem by a convex, smooth curve in the cross section of the scatterers by a plane containing the rotation axis.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04269-y