The steady incompressible Navier–Stokes equations describing the flow past a fixed rigid body are considered. It is known that the asymptotic behavior of the velocity field is described by the linearization around the velocity at infinity. I will present the asymptotic behavior of the vorticity, which is surprisingly not characterized by the previous linearization but be the linearization around an harmonic flow. I will try to make a link to the Leray problem for large value of the fluxes, where a similar harmonic flow is also the main problem.