Continuum perturbation field in quiescent ambience: Common foundation of flows and acoustics

Abstract

Here, the perturbation equation for a dissipative medium is derived from the first principles for the linearized compressible Navier–Stokes equation without Stokes' hypothesis. Dispersion relations of this generic governing equation are obtained, which exhibits both the dispersive and dissipative nature of perturbations traveling in a dissipative medium, depending upon the length scale. We specifically provide a theoretical cutoff wave number above which the perturbation equation represents diffusive and dissipative nature of the quiescent flow. It is shown that perturbation equations for pressure and velocity retain the same form in one-dimension, but it is not the same for multi-dimensional perturbation fields. Such behavior has not been reported before, as per the knowledge of the authors.