Can the Study of Hydrodynamic Instabilities Be Useful Beyond Transition ?

Abstract

In the context of transition to turbulence, hydrodynamic stability analyses have been generally successful in describing the early stages of transition, with some notable exceptions such as pipe Poiseuille flow. Over time, the tools of stability analysis have been expanded to deal with spatially inhomogeneous (non parallel) base flows, with secondary instabilities and with finite amplitude perturbations. All these tools have permitted to carry the description of flow perturbations in terms of deterministic instability modes tantalizingly close to transition. However, before a flow becomes really “turbulent”, i.e. more than just unsteady and “complicated”, the stability theoretical approach usually becomes unmanageable. On the other hand, there is ample evidence from laboratory and numerical experiments, that organized structures persist in flows that are considered turbulent by the majority of researchers.