  We study the effect of corotation resonance on the inertial-acoustic
oscillations (p-modes) of black-hole accretion discs. Previous works have shown
that for barotropic flows (where the pressure depends only on the density),
wave absorption at the corotation resonance can lead to mode growth when the
disc vortensity, $\zeta=\kappa^2/(2\Omega\Sigma)$ (where $\Omega, \kappa,
\Sigma$ are the rotation rate, radial epicyclic frequency and surface density
of the disc, respectively), has a positive gradient at the corotation radius.
Here we generalize the analysis of the corotation resonance effect to
non-barotropic fluids. We show that the mode instability criterion is modified
by the finite radial Brunt-V\"as\"al\"a frequency of the disc. We derive an
analytic expression for the reflectivity when a density wave impinges upon the
corotation barrier, and calculate the frequencies and growth rates of global
p-modes for disc models with various $\alpha$-viscosity parameterizations. We
find that for disc fluids with constant adiabatic index $\Gamma$,
super-reflection and mode growth depend on the gradient of the effective
vortensity, $\zeta_{\rm eff} = \zeta/S^{2/\Gamma}$ (where $S \equiv
P/\Sigma^{\Gamma}$ measures the entropy): when $d\zeta_{\rm eff}/dr > 0$ at the
corotation radius, wave absorption leads to amplification of the p-mode. Our
calculations show that the lowest-order p-modes with azimuthal wave number
$m=2, 3, 4,...$ have the largest growth rates, with the frequencies
approximately in (but distinct from) the $2:3:4...$ commensurate ratios. We
discuss the implications of our results for the high-frequency quasi-periodic
oscillations observed in accreting black-hole systems.
