Surface Waves in an Inhomogeneous Liquid Layer

Abstract

The case of surface-wave propagation in a homogeneous layer embedded in a homogeneous medium has been reported in the literature. On the other hand, if the layer is inhomogeneous, the problem is considerably more complicated. In fact, only for a very few special cases does an exact solution exist. In this study, the inhomogeneity is introduced by allowing the sound velocity to have a layer depth dependence. A method is presented here that demonstrates the manner in which the variation of sound velocity affects the dispersive characteristics of the medium. The structure described is essentially an acoustic waveguide and normal-mode techniques are used to produce a mathematical model. The resulting modified Sturm-Liouville boundary-value problem is converted into a Fredholm integral equation through the use of the Green's-function technique. The kernel of this integral is quantized in such a fashion as to yield the relationship between the phase velocity of the surface wave and the layer depth. Dispersion curves for velocity profiles that could occur in the ocean are presented in the paper.