2.2.1 Introduction

In the previous sections, we considered creeping waves on perfectly conducting or impedance surfaces in supposition that the impedance Z is either asymptotically large ( Z= O( k ^1/3)), or asymptotically small ( Z= O( k ^?1/3)). The idea of impedance stretching allows the asymptotic expansions for creeping waves on a general surface to be written with some kind of uniformity, so that the case of a perfectly electrically conducting surface (as well as the case of a perfectly magnetic conductor) appears as the limiting case of Z ?0 (or 1/ Z ?0). However, the vicinity of Z=1 is not properly handled by this approach. For example, in the case of the electric creeping wave given by formula (2.47) on an obstacle with non-vanishing torsion ?, we get the next order term of the magnetic field

The second term contains ( Z ?1/ Z) ^?1, and is infinite at Z=1. The same kind of singularity appears in the k ^?1/3 term for the propagation constant (see Section 2.1.8). To address this problem introduced by impedance stretching, we use a twofold approach. First, we present in Section 2.2.2 the analysis for Z= O(1). It is shown that the singularity at Z=1 disappears, but the uniformity when Z ?0 and Z ? ? is lost. For Z= O(1) the creeping waves on the surface...