Wave dynamics at an interface between porous media

We investigate the scattered transients within the framework of Biot\'s low-frequency theory. The analysis, for a normally incident fast wave, considers open, mixed and closed boundary conditions. We found that, for non-dissipative media, the reflection coefficient of the slow wave decreases from open to closed boundary conditions as a result of energy transfer to the reflected fast wave. When the fluid viscosity is finite, static slow modes develop at the interface, regardless of its permeability. They are stronger in the open case. The transient analysis confirms that, in the closed case, the relative motion between the solid and the fluid phases vanishes at the interface. Moreover, the power flow balance reveals the existence of interference fluxes between the wave modes. In the transmission medium, the interference fluxes change polarity with frequency, and their main contribution shifts towards lower frequencies for low viscosities. These fluxes behave as a relaxation peak with the coefficient of resistance. In the case of ideal saturating fluids, it is confirmed that these fluxes do not contribute to the power balance.