A Frequency Selection Criterion in Spatially Developing Flows

摘要

The possible existence of global modes or self‐excited linear resonances in spatially developing systems is explored within the framework of the WKBJ approximation. It is shown that the existence and properties of the dominant global mode may be deduced from the variations of the local absolute frequencyω0with distanceX. The main results are summarized in two theorems: (1) A system with no region of absolute instability does not sustain temporally growing global modes with anO(1) growth rate. (2) If the singularityX, closest to the realX‐axis of the complex functionω0(X) is a saddle point, the most unstable global mode has, to leading order in the WKBJ approximation, a complex frequencyω0(Xs). Thus, it will be temporally growing only ifω0(Xs) is p