The critical Reynolds number of a laminar mixing layer

Abstract

It has hitherto been widely considered that a mixing layer is unstable at all Reynolds numbers. However this is untenable from energy considerations, which demand that there must exist a non-zero Reynolds number below which disturbances cannot extract energy from the mean flow. It is shown here that a linear stability analysis of similarity solutions of the plane mixing layer, including the effects of flow non-parallelism, using the minimal composite theory and the properties of adjoints following Govindarajan & Narasimha (2005), resolves the issue by yielding non-zero critical Reynolds numbers for coflowing streams of any velocity ratio. The critical Reynolds number so found, based on the vorticity thickness and the velocity differential as scales, varies in the narrow range of 59 to 55 as the velocity ratio goes from zero to unity.