ASYMPTOTIC OF CREEPING WAVES ON A STRONGLY PROLATE BODY

We study the influence of a small transverse radius of curvature rho(t ) on the acoustic or electromagnetic waves propagating on the surface of a convex body by the boundary-layer method. For rho(t) of order k-1 /3 , the dependency of the field near the surface along the normal is shown to be, as when rho(t) is of order 1, described by the Fock-Airy function w1. However, rho(t) modifies the attenuation and velocity of the waves, by introducing an exponential term. For rho(t) or order k-2 /3, the normal dependency of the field is described by a new special f unction, depending on rho(t). The propagation constant of the wave can be obtained by solving an equation involving this function.