  Here, variation of the dispersion characteristics of 3D linearised
compressible Navier-Stokes equation with respect to bulk viscosity ratio
$\kappa/\mu$, specific heat ratio $\gamma$ and Prandtl number $Pr$ is
presented. The 3D compressible NSE supports two vortical, one entropic and two
acoustic modes. While the vortical and entropic modes are non-dispersive in
nature, the acoustic modes are dispersive only up to a certain bifurcation
wavenumber. The characteristics and variation of relative diffusion coefficient
for entropic and acoustic modes and a specially designed dispersion function
for acoustic modes with depressed wavenumber $\eta$ is presented which depend
on bulk viscosity ratio, $\gamma$ and $Pr$. At lower wavenumber components, the
deviation of the dispersion function from the inviscid and adiabatic case is
proportional to $\eta^2$ at the leading order and the relative diffusion
coefficients increase linearly with $\kappa/\mu$ and $\gamma$ while varying
inversely with $Pr$. When the bulk viscosity ratio is increased, the shape and
extent of the dispersion function is altered significantly and the change is
more significant for higher wavenumber components. The relative diffusion
coefficient for entropic and acoustic modes show contrasting variation with
wavenumber depending upon $\kappa/\mu$, $\gamma$ and $Pr$. We show by solving
linearised compressible NSE that relatively significant evolution and radiation
of acoustic and/or entropic disturbances are noted when the bulk viscosity
ratio is close to the corresponding critical value for which the bifurcation
wavenumber is maximum. Based on this criterion, we have presented an empirical
relation to obtain $\kappa/\mu$ depending upon $\gamma$ and $Pr$ which would
indicate the range of bulk viscosity ratio for obtaining relatively significant
disturbance evolution.

Fluid Dynamics