Updating our perspective on the bi-directional equations of dissipative, finite-amplitude acoustics theory: From Blackstock (1963) to Diaz–Solovchuk–Sheu (2018)

Abstract

The propagation of finite-amplitude acoustic wave-forms in thermoviscous gases, assumed to admit constant transport coefficients, under two newly-introduced third order, bi-directional, equations of motion is investigated. Along with analyzing both under the traveling wave assumption, the present study also compares the wave-profiles exhibited by these new models, the simplest of which follows from Diaz et al. (2018), with those of their established counterparts. Connections between equations that comprise this now expanded collection of six acoustic models are highlighted, and the degree of approximation required to derive each from the acoustic Navier–Stokes–Fourier system is indicated via a hierarchical chart. It is also shown that the long-established model with the fewest approximations and the newer, more heavily approximated, Diaz, et al. model yield the same Taylor shock traveling wave profile.