Scattering of waves from a random cylindrical surface

Abstract

The stochastic theory combined with a group-theoretic consideration developed by the authors for the scattering from a planar and a spherical random surface is applied to the case of a cylindrical random surface, which is assumed to be a homogeneous Gaussian random field, homogeneous with respect to the group of motions on the cylinder, translations along the axis and rotations around the axis. An operator acting on a random field is introduced, which keeps a homogeneous random field invariant, and which gives a representation of the motion-group on the cylinder. As an irreducible representation, i.e., an eigenfunction of the operator, the random wave field is obtained for the mth cylindrical wave injection on the random rough cylinder, and is represented as a stochastic functional of the cylindrical random surface in terms of a Wiener-Ito expansion. The random wave field for a plane-wave injection is decomposed into a sum over m of such random wave fields for the mth cylindrical wave injection. Various statistical characteristics of the scattered wave are calculated from the stochastic wave field so obtained; such as coherent scattering amplitude, coherent power flow, incoherent power flow, angular distributions for the coherent and incoherent scattering, and the power conservation law, especially, a stochastic version of the optical theorem stating that the total scattering cross-section consisting of the coherent and incoherent power flow equals the imaginary part of the coherent forward-scattering amplitude. Approximate solutions are obtained for a slightly rough cylindrical surface with Dirichlet and Neumann boundary conditions. Anomalous scattering does not take place in the case of a cylindrical Neumann surface, contrary to the case of a planar random surface, so that a single scattering approximation could be used for every small roughness. Some numerical calculations are shown of the angular distributions for coherent and incoherent scattering.