Stability analysis of the JCAPL equivalent fluid model equations for porous media

The equivalent fluid model (EFM) describes the acoustic properties of rigid porous media by defin- ing it as a fluid with an effective density and an effective compressibility. Their definition are based on the dynamic tortuosity α and the dy- namic compressibility β, known to be complex- valued functions depending on frequency. Among the different models describing α and β, this pa- per focuses on the Johnson-Champoux-Allard- Pride-Lafarge (JCAPL) model [1] where these parameters are defined as irrational functions, behaving like fractional derivatives in the time domain. Here, we present the proof of stabil- ity of the time-domain EFM using the JCAPL model thanks to their oscillatory-diffusive (OD) representations