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 possibl e discontinuities in the eigenfunction as the singular critical point is crossed. Extensions of the linear normal mode approach to include n onlinearity and/or wave packets lead to amplitude evolution equations where, again, critical point singularities are an issue because the co efficients of the amplitude equations generally involve singular integ rals. In the past, viscosity, nonlinearity, or time dependence has bee n introduced in a critical layer centered upon the singular point to r esolve these integrals. The form of the amplitude evolution equation i s greatly influenced by which choice is made. In this paper, a new app roach is proposed in which wave packet effects are dominant in the cri tical layer and it is argued that in many applications this is the app ropriate choice. The theory is applied to two-dimensional wave propaga tion in homogeneous shear flows and also to stratified shear flows. Ot her generalizations are indicated.