Sound generated by vortices in the presence of a porous half-cylinder mounted on a rigid plane

The sound generated by a single vortex and by two identical vortices in the presence of a half-cylinder made of porous material mounted on a rigid horizontal plane is studied theoretically using the acoustic analogy and the matched asymptotic expansion method. Both longitudinal and transverse dipoles are observed upon the introduction of the porous cylinder, but the former is considerably stronger than the latter in all the cases studied. Results suggest that the amplitudes of the dipoles and the overall acoustical energy radiated can be higher than that in the rigid cylinder case under some suitable combinations of flow parameters, especially when the flow resistance inside the porous material seen by the vortices is very small.