Effects of porous boundaries on the dynamics of an inviscid vortex filament

The dynamics of a vortex filament in the proximity of a porous surface are studied theoretically. The porous material is assumed to be characterized by its flow resistance and effective fluid density within its lattice. Results show that the propagation speed of the vortex is reduced upon the introduction of a porous material on to a hard surface. Also, the vortex speed increases with increasing flow resistance at constant effective fluid density. However, this speed increases with the effective fluid density only when the flow resistance is small. At larger flow resistance, a reduction of the speed is observed when the effective fluid density is increased. A similar phenomenon is again observed with the flat surface replaced by a circular cylinder. The study is extended to include the effect of a flow boundary discontinuity where the flat surface is made up of a rigid and a porous surface. Results illustrate that there is a relatively rapid change of vortex acceleration when the vortex moves across the plane of discontinuity, suggesting the possibility of sound generation close to this instant.