The influence of body anisotropy on wake characteristics and enstrophy production for prolate ellipsoids at $ \mathrm{Re}_{D} = 10,000 $

Abstract

The flow around prolate ellipsoids is investigated using Large Eddy Simulation (LES) at a Reynolds number of $ \mathrm{Re}_{D} = 10,000 $. Five different aspect ratios are considered, with $ \mathit{AR} = H/D $ varying from 5:1 to 1:1, where $D$ and $H$ represent the minor- and major- axes, respectively. The major axes of the ellipsoids are set perpendicular to the freestream, and the influence of body anisotropy on boundary layer separation, shear layer behaviour, enstrophy production, and local flow topology is examined. Higher body anisotropy leads to early separation of the boundary layer in the equatorial plane, resulting in a wider wake and a monotonic increase in pressure drag and total drag. Positive enstrophy production reaches a maximum approximately $2.5D$ downstream of the ellipsoids independently of body anisotropy. High body anisotropy leads to sustained negative enstrophy production in the near-wake, specifically near the poles of the 5:1 ellipsoid. Negative production occurs due to the distinct behaviour of streamlines near the high curvature pole, where they undergo strong anisotropic contraction in the cross-stream plane. Interactions between the vorticity vector and the intermediate eigenvector of the strain rate tensor are shown to be the primary source of enstrophy production close to the pole, and the intermediate eigenvalue exhibits negative values in this region. The negative production region is shown to be dominated by the unstable focus / compressing (UF/C) topology, which is consistent with findings from other studies that report negative enstrophy production in turbulent flows.