This is a complementary data and computer code set to the accepted manuscript "Vortex imprints on a free surface as proxy for surface divergence". It contains the surface layer of the DNS data set used and the code to analyse it in the ways described in the article. The European Union and the Research Council of Norway funded the work. The research by A. Xuan and L. Shen is also supported by the Office of Naval Research and National Science Foundation. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.