Let me preface this by saying that I did my research and have r̶e̶a̶d̶ skimmed a lot of papers on new blade profiles for vertical-axis wind turbines (VAWTs).
What I have yet to read about is a blade profile that is optimized with the recognition that in a VAWT (in contrast to airplanes and HAWTs) the blade is constantly rotating around its vertical axis.
To be fair, my intuition might be wrong here, but a blade that rotates a tiny bit along its circular path is still subject to basically the same conditions it was a mere moment before (ie the air molecules have not had time to move far across the profile). Surely this must have an influence (?), but simulation programs (like xfoil) only simulate independent moments in time and do not capture this continuity.
So ... are there blade profiles that are optimized to constantly travel on a circular path?