The diffraction by a curved impedance wedge with arbitrary angle and its uniform higher order asymptotics

The methods generally considered for the diffraction by a wedge with curved faces are often different as you consider a wedge of narrow or large angle. An original approach, initiated in [1,2] for faces of constant curvatures, and whose results have been used by Borovikov in [3] for his developments on non constant curvature case, permits a new global asymptotic study for an impedance curved wedge of any angle, with arbitrary distinct faces impedances, and for points far or close to the curved surface. Contrary to [4], we can then consider simultaneously diffracted phenomena appearing at different orders. It then becomes possible to study the case where two orders have comparable contributions, for example, the case of a curved plane with a discontinuity of curvature and of materials with low contrasts. In this approach, we reduce the boundary problem on the field to an asymptotic one on the spectral function attached to the representation of the field in the form of a SommerfeldMaliuzhinets integral. The functional equations then obtained are solved, and the asymptotics of the spectral function is developed. Besides, an expression, allowing the transition to an asymptotic expansion with fractional powers, is also given for directions close to the tangents at the edge, where, in particular, creeping waves due to curvature can appear. A new presentation of our method is given here, more developed and detailed than in [1,2]-[5], and a section is specifically devoted to fringe waves. Noting that our expressions apply for arbitrary wedge angle and for arbitrary distinct faces impedances and curvatures at several orders, they allow to recover known results on diffraction coefficients from the case of a discontinuity of curvature to the case of a curved half plane [6]-[12].