On Howard's technique for perturbing neutral solutions of the Taylor-Goldstein equation

Abstract

Howard's technique for examining the stability characteristics of a two-dimensional, inviscid, heterogeneous shear flow in the vicinity of a neutral curve is considered. Examples are presented for which erroneous conclusions would be obtained by a direct interpretation of the results of this technique. Examples for which instability would be deduced for a stable region; an example for which stability would be deduced for an unstable region; and an example for which the technique breaks down altogether are discussed.The last example is plane Couette flow between two rigid walls, which is shown to be destabilized by the addition of stable stratification. This example thus proves that the existence of a relative extremum in the basic vorticityprofile is not a necessary condition for the instability of an inviscid, heterogeneous shear flow.