On the propagation of nonlinear acoustic waves in viscous and thermoviscous fluids

Acoustic travelling waves are studied in the context of nonlinear propagation in Newtonian fluids. First, we examine the one-dimensional (1D) versions of four weakly-nonlinear acoustic models, all of which admit known travelling wave solutions (TWS)s in the form of Taylor shocks. Next, we derive the exact, but implicit, kink-type TWS of the compressible 1D Navier–Stokes equations under the homentropic assumption. Then, using three simple metrics, we numerically compare the TWSs of the former with that of the latter. It is shown that, while results for gases are mixed, in the case of liquids, the simple Burgers’ equation yields the TWS that best approximates the profile of the Navier–Stokes equations. Lastly, an energy analysis of the weakly-nonlinear models is carried out, connections between the models are noted, and new critical values of the physical parameters are presented.