Phase velocity and attenuation of leaky interface waves at the fluid/porous-medium interface

Karel van Dalen , Guy Drijkoningen , David Smeulders

At the fluid/porous-medium interface the leaky Rayleigh (LR) and leaky Stoneley (LSt) waves can exist. We show that the relation with the corresponding poles in the slowness plane is not unambiguous but depends on the choice of branch cuts. To this end we compute Green’s functions for a point-force excitation using two approaches. When vertical branch cuts are used (approach I), implying that the Riemann sheets of the LR- and LSt-poles obey the radiation condition, a separate leaky interface wave is entirely captured by the corresponding pole residue. In the case of hyperbolic branch cuts (approach II) the poles initially lie on the ''principal'' Riemann sheet. Then, the loop integrals along the branch cuts necessarily contribute to the LR-wave but do not contribute to the LSt-wave because the pole is identical to that in approach I. However, at a certain frequency the LSt-pole migrates to another Riemann sheet and for all higher frequencies the LSt-wave is even fully captured by the loop integrals. Our results show that the phase velocity and attenuation of a separate leaky interface wave can be obtained from the pole location in approach I, but should be extracted from the full Green’s function in approach II.

Keywords: Leaky interface waves; Fluid/porous-medium interface; Poles; Phase velocity and attenuation

Domains: Acoustics [physics.class-ph]

Karel van Dalen, Guy Drijkoningen, David Smeulders. Phase velocity and attenuation of leaky interface waves at the fluid/porous-medium interface. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810811⟩