  This investigation analyzes the effect of vortex wakes on the Lagrangian
displacement of particles induced by the passage of an obstacle in a
two-dimensional incompressible and inviscid fluid. In addition to the
trajectories of individual particles, we also study their drift and the
corresponding total drift areas in the F\"oppl and Kirchhoff potential flow
models. Our findings, which are obtained numerically and in some regimes are
also supported by asymptotic analysis, are compared to the wakeless potential
flow which serves as a reference. We show that in the presence of the F\"oppl
vortex wake some of the particles follow more complicated trajectories
featuring a second loop. The appearance of an additional stagnation point in
the F\"oppl flow is identified as a source of this effect. It is also
demonstrated that, while the total drift area increases with the size of the
wake for large vortex strengths, it is actually decreased for small circulation
values. On the other hand, the Kirchhoff flow model is shown to have an
unbounded total drift area. By providing a systematic account of the wake
effects on the drift, the results of this study will allow for more accurate
modeling of hydrodynamic stirring.
