  The effects of velocity shear on the unstable modes driven by the effective
gravity (Rayleigh-Taylor and interchange) and resistive drift wave
instabilities for inhomogeneous equilibrium fluid/plasma density are analyzed
for the localized eigenmode problems. It is shown that the effect of the
velocity shear drastically depends on the type of instability. Whereas the
velocity shear can significantly suppress both Rayleigh-Taylor and interchange
instabilities, it has only a week impact on the growth rate of the resistive
drift wave. This is directly related to the physical nature of these
instabilities. For the Rayleigh-Taylor and interchange instabilities, the shear
flow tilts the eddies of the stream functions, while for the resistive drift
wave instability the shear flow simply shifts the eddies in the radial
direction with no tilting. However, for large velocity shear, the eigenmode
solutions for resistive drift waves cease to exist.
