Global instabilities in diverging channel flows

Abstract

A global stability study of a divergent channel flow reveals features not obtained hitherto by making either the parallel or the weakly non-parallel (WNP) flow assumption. A divergent channel flow is chosen for this study since it is the simplest spatially developing flow: the Reynolds number is constant downstream, and for a theoretical Jeffery-Hamel flow, the velocity profile obeys similarity. Even in this simple flow, the global modes are shown to be qualitatively different from the parallel or WNP. In particular, the disturbance modes are often not wave-like, and the local scale, estimated from a wavelet analysis, can be a function of both streamwise and normal coordinates. The streamwise variation of the scales is often very different from the expected linear variation. Given recent global stability studies on boundary layers, such spatially extended modes which are not wave-like are unexpected. A scaling argument for why the critical Reynolds number is so sensitive to divergence is offered.