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.