Mt. Vannhieu et F. Ywanne, SOUND-SCATTERING BY SLENDER BODIES OF ARBITRARY SHAPE, The Journal of the Acoustical Society of America, 95(4), 1994, pp. 1726-1733
Scattering of a spherical wave from a perfectly rigid slender body of
arbitrary shape is considered. The point source is assumed to be locat
ed in the far field of each body cross section but may be placed in th
e near field of the target. The problem is investigated theoretically
with the matched asymptotic expansions method and an approximate solut
ion is derived for the scattered pressure, which takes into account th
e curvature of the incident wave front. The presented formalism combin
es the so-called slender-body approximation and the two-dimensional Ki
rchhoff theory. It allows a great simplification in the geometrical de
scription of the body surface and leads to a practical method even for
bodies of complex shape. In the monostatic case, it is theoretically
shown that the obtained solution is asymptotically equivalent to that
provided by geometrical optics for a large class of finite scatterers.
Lastly, monostatic and bistatic angular distributions are computed fo
r a prolate spheroid in the near and far fields to support the present
theory.