Wave Packet Critical Layers in Shear Flows
In the linear inviscid theory of shear flow stability, the eigenvalue problem for a neutral or weakly amplified mode revolves around possible discontinuities in the eigenfunction as the singular critical point is crossed. Extensions of the linear normal mode approach to include nonlinearity and/or wave packets lead to amplitude evolution equations where, again, critical point singularities are an issue because the coefficients of the amplitude equations generally involve singular integrals. In the past, viscosity, nonlinearity, or time dependence has been introduced in a critical layer centered upon the singular point to resolve these integrals. The form of the amplitude evolution equation is greatly influenced by which choice is made. In this paper, a new approach is proposed in which wave packet effects are dominant in the critical layer and it is argued that in many applications this is the appropriate choice. The theory is applied to two‐dimensional wave propagation in homogeneous shear flows and also to stratified shear flows. Other generalizations are indicated.
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Document Type: Research Article
Publication date: January 1, 1994