Is the transition to unsteadiness in the wake of slender bodies an artefact of boundary conditions ?

Abstract

This work considers the transition to unsteadiness in the wake of 2D slender bodies, and questions the relevance of the generally accepted scenario involving a region of absolute instability within the near wake. The case of a thin plate at zero incidence is first considered. Despite the absence of absolute instability region, global stability analysis reveals the existence of numerous unstable eigenvalues organized along a characteristic "arc-branch" whose properties significantly depends upon the size of the numerical domain. These arc-branch modes are explained as resulting from a non-local pressure perturbation spuriously generated at the outlet of the domain due to the no-stress boundary condition, which then triggers the shedding of vortical structures at the trailing edge of the plate. The case of NACA0012 wing profiles at small incidences is then considered. Global stability analysis reveals that both the non-local spurious feedback mechanism and the classical local feedback mechanism are active. Trying to suppress the spurious feedback by enlarging the size of the numerical domain is shown to be inefficient. On the other hand, filtering methods suppressing the exponential spatial growth of perturbations, with either a sponge or a complex mapping, are found to be efficient. Thanks to these ideas, the critical Reynolds number and Strouhal number at onset can eventually be computed and are mapped for incidences in the range $ \alpha \in [0^o - 5 ^o]$. It is postulated that the non-local feedback mechanism evidenced here could be at play in other strongly convective flows.