Porous Medium Acoustics in the Presence of Viscous Boundary Layers

The importance of the viscous boundary layer flow for porous medium acoustics has been recognized by Biot who analyzed this effect for cylindrical tubes and subsequently extended his low-frequency theory to the full frequency range. In this paper we develop an alternative approach to model attenuation and dispersion associated with the transition from the viscosity- to inertia-dominated regimes. Instead of analyzing the oscillatory Stokes flow in elastically-rigid tubes, we base our analysis on the visocosity-exdended Biot framework. We show that the conversion scattering process from a P-wave into the diffusive slow shear wave is a descriptor of the vorticity diffusion process occurring within the viscous boundary layer. We make use of previous results for conversion scattering from P- to slow S-wave and derive a dynamic-equivalent P-wavenumber from which we deduce attenuation and velocity dispersion. Comparison with the predictions of other models shows that the conversion scattering approach can model attenuation and dispersion associated with the transition from the viscosity- to inertia-dominated regimes.