Nonlinear evolution of singular disturbances to the Bickley jet

We consider the nonlinear evolution of a disturbance to the Bickley jet, an d the critical layer for the disturbance is located very close to the nose of the jet rather than at the inflection points. Using a nonlinear critical layer analysis, equations governing the evolution of the disturbance are d erived and discussed. When the critical layer is located exactly at the nos e of the jet, we find that the disturbance cannot exist on a linear basis, even with weak viscosity present, but that nonlinear effects inside the cri tical layer do permit the disturbance to exist if both modes are present. H owever, when the phase velocity of the disturbance is perturbed sufficientl y away from unity, so that we have a pair of critical layers slightly above and below the nose rather than a single critical layer, we find that the w aves can exist on a linear basis, and again we derive equations governing t he nonlinear evolution of the disturbance.