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\begin{document}



\title{CURVATURE EFFECTS ON HIGH-FREQUENCY `LEAKY' WAVE
EXCITATION AND PROPAGATION}
\author{B.J. Smith and R.H. Tew}{
Department of Theoretical Mechanics, University of Nottingham\\
University Park, Nottingham NG7 2RD, UK\\
e-mail \hspace{1cm} richard.tew@nottingham.ac.uk}


It is now well established that the coupling between an elastic
structure and a compressible fluid can bring about some very important,
and often quite surprising, phenomena. For example, if an elastic solid
is submerged in a ``light'' fluid, then the Rayleigh wave that could
exist at the surface of the solid {\it en vacuo} is now perturbed
slightly by the addition of a small, pure imaginary component to the
surface wavenumber. This apparently minor perturbation brings about
dramatic changes to the excitation, propagation and acoustic
re-radiation characteristics of this so-called `leaky' wave.

One such change is that this surface wave requires a description in
terms of {\it complex} rays. Another is that it cannot be excited by
plane wave incidence from the fluid if the fluid-solid boundary is flat.
To generate this mode, the incoming field has to have some spatial
distribution in amplitude, as in the case of a Gaussian beam, or else
there must be curvature effects to account for. This curvature might be
in the boundary itself or perhaps in the wavefronts of the insonifying
field. All of these aspects have been investigated and what is presented
here are results appropriate to the case of curvature within the
boundary and plane incoming wavefronts. Specifically, the case of a
convex, wavebearing boundary is examined when it is subject to time-harmonic,
plane wave incidence in the high-frequency limit. Naturally,
most of the incoming rays are specularly reflected and these are
trivially dealt with. However, one {\it critically incident complex ray}
is responsible for launching the leaky surface ray. An inner diffraction
analysis is performed within a complex neighborhood of this excitation
point, taking full account of the curvature, and it is found that the
inner solution (in terms of Fresnel integrals) matches to the outer ray
picture through the intimate dependence of this former solution on the
Stokes phenomenon.

A full description of these phenomena is given and as well as being
informative in its own right, it serves as a good example to illustrate
aspects of the general theory of complex rays which has since been
developed and is to be presented at this meeting by Chapman, Lawry and Saward.


\end{document}
