Finite-amplitude acoustic traveling waves in a fluid that saturates a porous medium: Acceleration wave formation

An analytical study of finite-amplitude acoustic waves in a homentropic fluid that saturates a rigid porous medium is presented. The exact traveling wave solution (TWS) is obtained in terms of the Lambert W-function. It is shown that the acceleration profile assumes the form of an asymmetric diffusive soliton and that a jump discontinuity in the acceleration forms as the TWSs propagation speed approaches the sound speed of the fluid. Additionally, a connection between this TWS and results from singular surface theory is established and the findings of the present study are compared/contrasted with those for the thermoviscous, nonporous case.