  The perturbation equation for aeroacoustics has been derived in a dissipative
medium from the linearized compressible Navier-Stokes equation without any
assumption, by expressing the same in spectral plane as in Continuum
perturbation field in quiescent ambience: Common foundation of flows and
acoustics Sengupta et al., Phys. Fluids,35, 056111 (2023). The governing
partial differential equation (PDE) for the free-field propagation of the
disturbances in the spectral plane provides the dispersion relation between
wavenumber and circular frequency in the dissipative medium, as characterized
by a nondimensional diffusion number. Here, the implications of the dispersion
relation of the perturbation field in the quiescent medium are probed for
different orders of magnitude of the generalized kinematic viscosity, across
large ranges of the wavenumber and the circular frequency. The adopted global
spectral analysis helps not only classify the PDE into parabolic and hyperbolic
types, but also explain the existence of a critical wavenumber depending on
space-time scales.
