Attenuated leaky Rayleigh waves

Abstract

The attenuation of leaky Rayleigh waves due to viscous damping in a boundary layer at the interface of an elastic solid half‐space and a fluid half‐space is studied by matched asymptotic method. Viscosity of the fluid is considered unimportant except in a thin boundary layer at the interface. By keeping the leading order effect, shown by the inverse of square root of a Reynolds number based on the shear velocity of the solid substrate, a new characteristic equation is obtained. One of the numerically obtained solutions gives the leaky Rayleigh wave speed and the attenuation coefficient due to both radiation into fluid and viscous damping of the boundary layer. It is shown that the viscous attenuation in the boundary layer may be as important as that due to radiation into the fluid half‐space for some fluid–substrate combinations. These results may be used to improve our interpretation of experimental results of acoustic signature of materials. Extension of the analysis to a fluid layer instead of a half‐space will be discussed. [Work supported by the Hunt Fellowship.]