Viscous boundary layer effects on the Myers impedance boundary condition

This paper considers the effects of a thin laminar compressible viscous boundary layer over acoustic linings. The presence of a vanishingly-thin nonviscous boundary layer at a fluid–solid interface is know to lead to the so-called Myers boundary condition of continuity of normal particle displacement. This boundary condition is now known to lead to instability when applied to an acoustically-lined duct with flow. Despite this, due to a lack of an alternative, the Myers boundary condition is still widely used, with any instability artifacts being removed by artificial smoothing. In the last couple of years, efforts have been made to resolve these issues by modelling a sheared mean flow, using the Pridmore-Brown equation. By satisfying the no-slip boundary condition at the wall, the hydrodynamic instability is removed. However, introducing a smoothly-varying mean flow leads to the presence of so-called critical layers, with their own associated problems. Very little work has included viscosity in such an analysis, which is the underlying reason for the existence of the boundary layer in the first place. This paper builds on the w