On disturbances to a stratified mixing layer

Using a nonlinear critical layer analysis, we examine the behavior of distu rbances to the Holmboe model of a stratified shear layer far Richardson num bers 0 < J less than or equal to 1/4, regarding J as an O(1) quantity rathe r than a small quantity. By examining the structure of the solution inside the critical layer, we demonstrate that, for this particular flow, disturba nces with a phase change of the form predicted by linear stability theory c annot exist on a purely linear basis, and because of this, an instability w ave. will have no phase change across the critical layer, and that instead we should regard the Richardson number J as a small quantity within the fra mework of a nonlinear analysis. We argue further that when nonlinear effect s are included; disturbances with a phase change can exist, but this leads to such a slow time scale that the flow in question is unlikely to arise, e xcept possibly as a secondary instability.