Is there any direct significance, physical or otherwise, of the circulation of a vector field (when not connecting it to the curl)?
Every application, problem, example, or physical model of circulation I've seen has to do with curl. But is there ever a case that the circulation itself is of interest?
Interestingly, if the vector field is a fluid velocity field, in units of $m/s$, then the circulation is in units $m^2/s$, suggesting that it is some sort of area per time. But I can find no example or model that explains how circulation should be viewed as an area per time.