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 velocity profiles that are monotonic, real analytic, functions of the cross‐stream coordinate. The analysis, which is based upon the Nyquist method, includes a means for delineating the possible kinds of bifurcations that involve the presence of the continuous spectrum, including those that occur at nonzero wave number. Several examples are given.