Structure of trailing vortices: Comparison between particle image velocimetry measurements and theoretical models

The velocity field of the trailing vortex behind a wing at different angles of attack has been measured through the stereo particle image velocimetry technique in a water tunnel for Reynolds numbers between 20 000 and 40 000, and for several distances to the wing tip. After filtering out the vortex meandering, the radial profiles of the axial and the azimuthal velocity components and of the radial profiles of the vorticity were compared to the theoretical models for trailing vortices by [ G. K. Batchelor, J. Fluid Mech. 20, 645 (1964) ] and by [ D. W. Moore and P. G. Saffman, Proc. R. Soc. London, Ser. A 333, 491 (1973) ], whose main features are conveniently summarized. We take into account the downstream evolution of these profiles from just a fraction of the wing chord to more than ten chords. The radial profiles of the vorticity and the azimuthal velocity are shown to fit quite well to Moore and Saffman's trailing vortex model, while Batchelor's model does not fit so well, especially in the tails of the profiles. At the downstream distances considered, the radial profiles of the axial velocity do not adjust so well to Moore and Saffman's model as the azimuthal velocity profiles do, but the disagreement with Batchelor's model is quite manifested, especially at the axis. Thus, the details of the flow structure are in better agreement with the predictions of Moore and Saffman's model. The downstream evolution of several key features of the measured velocity profiles is also in agreement with the predictions of Moore and Saffman's model, within the dispersion of the experimental data, but up to the largest axial distance considered in this work we cannot decide if they follow the asymptotic behavior predicted by this model.