Abstract

A common problem when considering fluid-solid interaction is to consider the behaviour of small (linearized) perturbations to a steady flow over a deformable boundary. The simplest way to do this is to consider an inviscid incompressible (and isothermal) uniform flow slipping over the boundary. Or, if one is interested in the acoustic response, to consider an inviscid (and homentropic) uniform perfect gas flow slipping over the boundary. And, indeed, this is a very commonly studied problem.

Because of the slipping flow at the boundary, difficulties arise applying a boundary condition there. This boundary condition should link the small motion of the boundary to the small perturbations within the fluid. After some confusion in the 60s see, e.g. Rice 1969), this boundary condition was thought to have been understood in the 70s (Eversman et al 1972, Tester 1973), and is now commonly referred to as the Myers boundary condition. The boundary condition decided on was that the normal displacement of the fluid at the boundary is the same as the normal displacement of the boundary.

Unfortunately, this is not the whole story. In this talk, I aim to show why it is not the whole story, particularly with regard to stability. I will then present an analysis of the effect of a thin viscous boundary layer over the wall, which I hope will take the story a little further.