Rigorous application of the stochastic functional method to plane-wave scattering from a random cylindrical surface

Abstract

The stochastic functional method is applied to plane-wave scattering from a random cylindrical surface, whereupon the Dirichlet boundary condition is rigorously imposed. Analytical results, accurate to second and fourth order in surface roughness, are obtained for the coefficients of the Wiener–Hermite expansion of the secondary scattered wave field. The validity of approximate solutions is numerically investigated by means of the boundary condition criterion and of the energy consistency criterion. The former, which is introduced herein, states that any approximate solution should be in conformity with the boundary condition, whereas the latter pertains to the energy conservation law. The numerical investigation indicates that the rigorous application of the stochastic functional method yields more accurate results in terms of both criteria than did previous treatments of the problem under consideration. Moreover, it is suggested that applicability limits should be set through the mean boundary condition criterion instead of the energy consistency criterion; the latter may lead to underestimating deficiencies of the approximate solution under test.

Scattering of an Acoustic Plane Wave by a Corrugated Cylinder

“…The author is indebted to a referee for many suggestions to improve this letter and for references [1,2].…”

“…In addition, satis"es some boundary condition on S. To investigate the properties of the scattered wave, a versatile technique, with many applications to di!erent con"gurations of cylindrical surfaces [1,2], consists in expanding G and Q in series of Bessel and of Hankel functions and in matching the coe$cients of these expansions to satisfy the boundary condition on S.…”

Enhanced backscattering from a metallic cylinder with a random rough surface

“…Most of the studies, however, have been concentrated on random rough surfaces in a planar geometry. A few works [22][23][24][25][26][27][28] have treated the problems of scattering from cylindrical rough surfaces, but no enhanced backscattering peak has been demonstrated.…”

“…In this paper, the scattering of an electromagnetic wave from a metallic cylinder with a slightly random rough surface is treated by means of the stochastic functional approach, [24][25][26][27] and the effect of surface plasmon waves supported by the cylindrical metal surface on the enhanced backscattering is studied. In the stochastic functional approach, the cylindrical random surface is assumed to be a homogeneous Gaussian random field, homogeneous with respect to the group of motions on the cylinder-i.e., translations along the axis and rotations around the axis.…”

Stochastic Oscillators with Quadratic Nonlinearity Using WHEP and HPM Methods

“…A lot of general applications in fluid mechanics were also studied in [9][10][11]. Scattering problems attracted the WHE applications through many authors [12][13][14][15][16]. The nonlinear oscillators were considered as an opened area for the applications of WHE as can be found in [17][18][19][20][21][22][23].…”