Note on the Classic Stability Problem

Abstract

It has come to the writer’s attention (private communication) that a question has arisen concerning his comments (STARR 1950) in regard to the stability of zonal flow. In terms of the problem as outlined previously, and in terms of the same symbolism, the question relates to the statement (I) that a monotone distribution of the vorticity 5 with respect to yo implies stability of zonal motion. The point at issue is whether an incipient small disturbance of otherwise arbitrary nature imposed upon such zonal flow can so alter the circumstances of the problem as to render the previous conclusion unjustified. The purpose of this second note is to show that such small arbitrary perturbations cannot lead to instability and hence need not be considered explicitly in the case of a sensibly montone vorticity distribution.