Stability of Acoustic Waves within a Viscous Compressible Heat-Conducting Fluid

Abstract

The question of stability of propagation of acoustic waves within a continuum of compressible viscous heatconducting fluid has been investigated. A bounded solution (i.e., a stable solution) is assured if either of the following two conditions is satified: 411q-(3/4) (v/n) -]P--where P is the Prandtl number, •, the ratio of specific heats, and v and n the bulk and shear viscosities, respectively. According to the theory, the above inequality must be obeyed for all passive fluids with •,> 1. Using experimental values for many different fluids, it appears to be generally obeyed except for the molten metals including mercury and, possibly, the superfluids.