Comments on the relation between surface wave theory and the theory of reflection

The sextic Stroh formalism, previously extensively used in the analysis of subsonic phenomena, has been used for the analysis of reflection phenomena and leaky surface waves in the first transsonic range of velocities. In particular the behaviour of the reflection problem at the limiting velocity is studied. It is shown that when the condition of free surface can be satisfied without the inhomogeneous partial wave, a situation which would appear to be the natural limiting case of a surface wave of infinite penetration, the body wave alone satisfies the condition of free surface. This result illuminates the Barnett-Lothe existence theorem for subsonic surface waves. The close connection between the reflection problem and the leaky surface wave problem becomes very apparent in the formalism used. It is shown that for a point on a branch of leaky waves where the solution is undamped, the conditions for simple reflection, i.e. reflection only involving the two body waves, are also present. In the vicinity of such a point reflection is accompanied by resonance excitation of leaky waves. The paper concludes with some explicit calculations for transversely isotropic solids.