Instability mechanisms in meandering streamwise vortex pairs of upswept afterbody wakes

Abstract

Wakes of upswept afterbodies are often characterized by counter-rotating streamwise vortex pairs which meander in space. One application concerns aft regions of cargo aircraft, which are characterized by a relatively flat upswept base. Here we consider a canonical configuration comprised of a cylinder with upswept basal surface. The resulting longitudinal vortices, which are much closer to each other than wing-tip vortices, can adversely influence paratrooper and cargo drop operations as well as trailing aircraft. The unsteady dynamics of these vortices are examined using spatio-temporally resolved Large-Eddy Simulations (LES) and stability considerations. Emphasis is placed on understanding the potential instability dynamics responsible for meandering, which was observed, characterized and quantified at a representative location downstream of the body. The dynamics is then successfully mapped to a matched Batchelor vortex pair, and spatial and temporal stability analyses are performed with both counter-rotating vortices in the computational domain. Both spatial and temporal analyses reveal dipole structures associated with |m| = 1 elliptic modes as dominant modes in afterbody vortices. A short-wave elliptic instability mode is found to dominate the meandering motion in the vortex pair; this mode was stable in the case of an isolated vortex. Further, the strain due to axial velocity plays a key role in the instability and therefore breakdown. The low frequency of the unstable mode (Strouhal number StD ≃ 0.3 based on cylinder diameter) is consistent with the spectral analysis of meandering in the LES. Stability analyses at very low-wavenumber do not exhibit any unstable mode suggesting an absence of the Crow instability.