Using a nonlinear critical layer analysis, we examine the behavior of disturbances to the Holmboe model of a stratified shear layer far Richardson numbers 0 < J less than or equal to 1/4, regarding J as an O(1) quantity rather than a small quantity. By examining the structure of the solution inside the critical layer, we demonstrate that, for this particular flow, disturbances with a phase change of the form predicted by linear stability theory cannot exist on a purely linear basis, and because of this, an instability wave. 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 framework of a nonlinear analysis. We argue further that when nonlinear effects 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, except possibly as a secondary instability. [References: 68]
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