We present a back-in-time analysis for the origin of vorticity in viscous separated flows over immersed bodies, using the adjoint-vorticity framework recently introduced by Xiang et al. (2025 J. Fluid Mech. vol. 1011, A33. The solution of the adjoint-vorticity equations yields the volume density of mean deformation, which captures the stretching and tilting of the earlier vorticity that leads to the terminal value. The analysis also takes into account the boundary contributions of vorticity and its flux. Three examples are considered. Steady, axisymmetric separation in the flow over a sphere at Reynolds number $Re=200$ is shown to be established due to wall flux from both upstream and downstream of separation, the latter contribution being absent from the classical description by Lighthill. For unsteady separation at higher $Re=300$, the streamwise vorticity within the wake hairpin vortex is traced back, quantitatively, to the azimuthal vorticity on the sphere. The third configuration is the flow over a prolate spheroid at $Re=3000$. The null vorticity at three-dimensional separation originates from the cancellation of opposite interior contributions adjacent to the separation surface. The contribution from the downstream side migrates across the separation surface into the upstream region due to a tilting effect – a fundamental distinction between two- and three-dimensional separation. We also examine the detached vortical structures. The streamwise vorticity in the primary vortex originates from tilting of near-wall azimuthal vorticity, differing from Lighthill’s conjecture that the origin is streamwise near-wall vorticity that arises due to the reduced Coriolis force. Finally, a necklace vortex in the turbulent wake is traced back in time, and is shown to have contributions from the spheroid trailing-edge shed shear layer and the large-scale counter-rotating primary vortices.

The connection between the drag and vorticity dynamics for viscous flow over a bluff body is explored using the Josephson–Anderson (J–A) relation for classical fluids. The instantaneous rate of work on the fluid, associated with the drag force, is related to the vorticity flux across the streamlines of a background potential flow. The vorticity transport itself is examined by aid of the Huggins vorticity-flux tensor. The analysis is performed for three flows: flow over a sphere at Reynolds numbers $Re=200,3700$, and flow over a prolate spheroid at $Re=3000$ and $20^{\circ }$ incidence. In these flows, the vorticity transport shifts the flow away from and towards the ideal potential flow, with a net balance towards the former effect thus making an appreciable contribution to the drag. The J–A relation is first demonstrated for the flow over a sphere at $Re=200$. The drag power injection is related to the viscous flux of azimuthal vorticity from the wall into the fluid, and the advection of vorticity by the detached shear layer. In the wake, the azimuthal vorticity is advected towards the wake centreline and is annihilated by viscous effects, which contributes a reduction in drag. The analysis of the flow over a sphere at $Re=3700$ is reported for the impulsively started and stationary stages, with emphasis on the effects of unsteady two-dimensional separation and turbulent transport in the transitional wake. The turbulent flux in the wake enhances the transport of mean azimuthal vorticity towards the wake centreline, and is the main driver of the recovery of enthalpy between the rear point of the sphere and far downstream. The rate of work on the fluid by the drag force for a prolate spheroid is mostly due to the transport of vorticity along the separated boundary layers. Primary and secondary separation contribute oppositely to the power injection by the drag force, while the large-scale vortices only re-distribute vorticity without a net contribution. A mechanism for secondary separation is proposed based on the theory of vortex-induced separation.