Growth and decay of acoustic acceleration waves in Darcy-type porous media

The propagation of acoustic waves in a fluid that saturates a Darcy-type porous medium is considered under finite-amplitude theory. The equation of motion is derived, an acceleration wave analysis is carried out, and a travelling wave solution (TWS) is obtained. In addition, analytical findings are supported with numerical work generated by a simple, but effective, finite-difference scheme and results obtained are compared with those of the nonporous and linear cases. Most notably, this analysis reveals the following: (i) that the equation of motion is a new, hyperbolic form of Kuznetsov's equation; (ii) that finite-time blow-up of the wave amplitude is possible even if dissipation is present; (iii) the presence of a porous medium increases, with respect to the nonporous case, the rate at which amplitude growth/decay occurs; (iv) in the case of porous media propagation, not all compressive acceleration waves suffer blow up; and (v) that there exists a connection between acceleration waves and TWSs.