On the damping of unsteady flow by compliant boundaries

This paper concerns unsteady motion of an incompressible inviscid fluid near a flexible surface which, in responding to the surface pressure field, absorbs energy. The modification of the flow consequent on energy removal at the boundaries is examined. Energy absorption always occurs when the mechanical surface properties include an element of dissipation. But surface dissipation is not essential; surface waves have a similar property. Unsteady fluid induced forces excite surface waves which carry with them energy that must have originated in the flow. The question of how flow characteristics change as energy is gradually given up to the boundary is examined through a particular model problem from which it becomes evident that surface motion draws vorticity towards the surface. The model chosen is that of a rectilinear vortex adjacent to a weakly responding boundary. Surface motion induces a velocity perturbation which is shown to move the vortex towards the surface whenever the fluid gives energy to that surface.