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

Ion-temperature-gradient sensitivity of the hydrodynamic instability caused by shear in the magnetic-field-aligned plasma flow