TABLE OF CONTENTS In this section, we turn our attention to the boundary-layer problem associated with creeping waves on a general surface. Creeping waves can be launched by a distant incident wave or by a source located on the surface of the object.
To address the boundary-layer problem, we follow exactly the same steps as in Chapter 1 for the case of the cylinder. These are:
choosing an Ansatz
expressing the equations in the surface coordinate system
introducing the Ansatz in the above equations
solving the equations for each order.
Before going into the details of the procedure, we make some preliminary observations pertinent to the method and describe the structure of our presentation.
As shown in Section 1.1.2 of Chapter 1, the surface rays follow the geodesics of the surface. If the creeping waves are generated by a distant incident wave, these geodesics start at the light shadow boundary on the surface and are directed at that boundary along the rays of the incident field. If creeping waves are generated by a point source on the surface, all geodesics start in the point of the source. On a general surface geodesics form a system of curves with one or several caustics that have cusps. Away from caustics the system of geodesics can be chosen as the coordinate system. If s is the curvilinear abscissa along the geodesics, then the main phase factor exp( ikS( r)) is simply exp( iks).
As...
