Barotropic instability of zonal flows

The barotropic instability of zonal flows due to infinitesimal normal-mode perturbations is considered, with the zonal flow assumed to be continuous and either monotonic or nonmonotonic and allowed to have one or more inflection points. A sufficient condition for instability is derived for this general flow profile that complements that of Arnol'd (1965), which restricted itself to the prediction of stability only.