Transmission of creeping-wave modes around a periodically modulated impedance cylinder

Motivated by recent advances in radio oceanography, an idealized two-dimensional model of diffraction by a non-uniform cylinder is analyzed. The cylinder is characterized by a surface impedance that varies in a periodic fashion in the azimuthal direction. For excitation by a magnetic line source, a solution for the resulting field is obtained that satisfies the specified periodic boundary condition. This representation for the fields is converted, via a Watson transform procedure, to a form that is more convergent and useful for short wavelengths. It is shown that, for each creeping-wave mode, an infinite number of spatial harmonics is excited. These harmonics are a consequence of the periodic non-uniformity of the surface and they include the backward scattered waves. The latter becomes very strong in the region where the spatial period is half the radio wavelength in accordance with the well-known Bragg phenomenon. In this case, contrary to what is sometimes assumed, the attenuation of the forward creeping waves is much increased. This suggests that perturbation methods, such as used to interpret radio-oceanographic data, may be invalid just in the region when they appear to have the most diagnostic value.