LINEAR GLOBAL MODES IN SPATIALLY DEVELOPING MEDIA

Selection criteria for self-excited global modes in doubly infinite on e-dimensional domains are examined in the context of the linearized Gi nzburg-Landau equation with slowly varying coefficients. Following Lyn n & Keller (1970), uniformly valid approximations are sought in the co mplex plane in a region containing all relevant turning points. A mapp ing transformation is introduced to reduce the original Ginzburg-Landa u equation to an exactly solvable comparison equation which qualitativ ely preserves the geometry of the Stokes line network. The specific ca se of two turning points with counted multiplicity is analysed in deta il, particular attention being paid to the allowable configurations of the Stokes line network. It is shown that all global modes are either of type-1, with two simple turning points connected by a common Stoke s line, or of type-2, with a single double-turning point. Explicit app roximations are derived in both instances, for the global frequencies and associated eigenfunctions. It is argued, on geometrical grounds, t hat type-1 global modes may, in principle, be more unstable than type- 2 global modes. This paper is a continuation and extension of the earl ier study of Chomaz, Huerre & Redekopp (1991), where only type-2 globa l modes were investigated via a local WKBJ approximation scheme.