The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers

TLDR

The study examines the linear stability of bluff‑body wake profiles near the onset of Kármán vortex shedding. The authors analyze a family of mean flow profiles that vary wake depth and width‑to‑mixing‑layer ratio to determine the absolute or convective nature of sinuous instability as a function of profile parameters and Reynolds number. The results reveal that a region of local absolute instability emerges at roughly half the critical Reynolds number for Kármán vortex shedding, so that a substantial absolute region already exists at the onset of global shedding, confirming the qualitative model and showing that frequency predictions based solely on local stability are somewhat arbitrary even at criticality. Published in Physical Review Letters.

Abstract

The linear parallel and incompressible stability of a family of bluff-body wake profiles is studied at Reynolds numbers close to the onset of Kármán vortex shedding. The family of mean flow profiles allows for the variation of the wake depth as well as for a variable ratio of wake width to mixing layer thickness. The absolute or convective nature of the sinuous instability is determined as a function of the profile parameters and Reynolds number. A comparison of this survey with experimental data shows that in bluff-body near wakes a region of local absolute instability begins to form at a Reynolds number of approximately one-half the critical value for Kármán vortex shedding. Hence, at the onset of the global response (Kármán vortex shedding), a substantial region of local absolute instability already exists in the wake. This confirms the qualitative model prediction of Chomaz, Huerre, and Redekopp [submitted to Phys. Rev. Lett. and also shows that the prediction of vortex shedding frequencies, when based on local stability properties alone, is somewhat arbitrary even at the critical Reynolds number.