  The cross-magnetic-field (i.e., perpendicular) profile of ion temperature and
the perpendicular profile of the magnetic-field-aligned (parallel) plasma flow
are sometimes inhomogeneous for space and laboratory plasma. Instability caused
by a gradient in either the ion-temperature profile or by shear in the parallel
flow has been discussed extensively in the literature. In this paper,
hydrodynamic plasma stability is investigated, real and imaginary frequency are
quantified over a range of the shear parameter, the normalized wavenumber, and
the ratio of density-gradient and ion-temperature-gradient scale lengths, and
the role of inverse Landau damping is illustrated for the case of combined
ion-temperature gradient and parallel-flow shear. We find that increasing the
ion-temperature gradient reduces the instability threshold for the hydrodynamic
parallel-flow shear instability, also known as the parallel Kelvin-Helmholtz
instability or the D'Angelo instability. We also find that a kinetic
instability arises from the coupled, reinforcing action of both free-energy
sources. For the case of comparable electron and ion temperature, we illustrate
analytically the transition of the D'Angelo instability to the kinetic
instability as the shear parameter, the normalized wavenumber, and the ratio of
density-gradient and ion-temperature-gradient scale lengths are varied and we
attribute the changes in stability to changes in the amount of inverse ion
Landau damping. We show that, near a normalized wavenumber $k_{\perp} \rho_{i}$
of order unity, the real and imaginary values of frequency become comparable
and the growth rate maximizes.
