Vorticity dynamics and Josephson-Anderson relation for flow over spheroid

The connection between drag and vorticity fluxes for flow over spheroid is investigated numerically using the Josephson-Anderson (JA) relation. The JA relation decomposes the instantaneous work done by the drag force into vorticity fluxes across potential streamlines. The decomposition is first verified in canonical conditions including laminar and turbulent flows over a sphere, and subsequently applied to the prolate spheroid. The contributions to the drag force from vorticity fluxes in different flow regions are evaluated and related to local flow structures. These contributions are encapsulated in the instantaneous and mean Huggins vorticity-flux tensors which appear, respectively, in the instantaneous and mean vorticity transport equations. Analysis of the instantaneous tensor underscores the role of vortex-induced separation for the three-dimensional, separated boundary layer around the spheroid. In the downstream wake, the transverse mean-vorticity transport, which is dominated by the turbulent flux, balances the streamwise total pressure gradient. The results provide a novel perspective for drag and three-dimensional separation on bodies of revolution from the viewpoint of vorticity dynamics.