The classical problem of a viscous flow past a fixed rigid obstacle is modeled by the steady incompressible Navier–Stokes equations. In this problem, it is known that the asymptotic behavior of the velocity field is described by the linearized problem around the velocity at infinity. The aim of this talk is to present the asymptotic behavior of the vorticity, which is surprisingly not characterized by the previous linearization in two dimensions, but by the linearization around a harmonic flow. If time permits, I will make a link to the Leray problem for large values of the fluxes, where a similar harmonic flow is also the main problem. This is joint work with Peter Wittwer.