  We consider the construction of linear instability of parallel shear flows,
which was developed by Zhiwu Lin (SIAM J. Math. Anal. 35(2), 2003). We give an
alternative simple proof in Sobolev setting of the problem, which exposes the
role of the Plemenj-Sokhotski formula in the emergence of the instability, as
well as does not require the cone condition. Moreover, we localize this
approach to obtain an approximation of the Kelvin-Helmholtz instability of a
flat vortex sheet.
