Beyond ideal gas: a comprehensive analysis of linear wave dynamics in arbitrary compressible fluids

The propagation of linear waves in non-ideal compressible fluids plays a crucial role in numerous physical and engineering applications, particularly in the study of instabilities, aeroacoustics and turbulence modelling. This work investigates linear waves in viscous and heat-conducting non-ideal compressible fluids, modelled by the Navier–Stokes–Fourier equations and a fully arbitrary equation of state (EOS). The linearised governing equations are derived to analyse the dispersion relations when the EOS differs from that of an ideal gas. Special attention is given to the influence of non-ideal effects and various dimensionless numbers on wave propagation speed and attenuation. By extending classical results from Kovásznay (1953 J. Aeronaut. Sci . vol. 20, no. 10, pp. 657–674) and Chu (1965 Acta Mech . vol. 1, no. 3, pp. 215–234) obtained under the ideal gas assumption, this study highlights the modifications introduced by arbitrary EOSs to the linear wave dynamics in non-ideal compressible flows. This work paves the path for an improved understanding and modelling of wave propagation, turbulence and linear stability in arbitrary viscous and heat-conducting fluids.