Generalised acoustic impedance for viscous fluids

Abstract

A general class of acoustic impedance conditions is considered where a linear dependence is assumed between the fluid velocity and the surface traction. In addition to the classical impedance relating pressure and normal velocity, this generalised definition of the impedance includes effects such as the friction along the surface as well as coupling between the normal velocity and the tangential force on the fluid. After providing a generalised definition based on impedance and admittance matrices, various fundamental principles are considered to ensure the impedance is physically admissible. These principles include the reality, causality, stability and passivity of the surface. To illustrate the influence of the additional parameters introduced by the generalised impedance, a number of results are presented for the reflection of a plane wave on a lined surface, with or without a mean flow.