A necessary and sufficient instability condition for inviscid shear flow

We derive a condition that is necessary and sufficient for the instability of inviscid, two-dimensional, plane-parallel, shear flow with equilibrium v elocity profiles that are monotonic, real analytic, functions of the cross- stream coordinate. The analysis, which is based upon the Nyquist method, in cludes a means for delineating the possible kinds of bifurcations that invo lve the presence of the continuous spectrum, including those that occur at nonzero wave number. Several examples are given.